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Estimating relative abundance is critical for informing conservation and management efforts and for making inferences about the effects of environmental change on populations. Freshwater fisheries span large geographic regions, occupy diverse habitats and consist of varying species assemblages. Monitoring schemes used to sample these diverse populations often result in populations being sampled at different times and under different environmental conditions. Varying sampling conditions can bias estimates of abundance when compared across time, location and species, and properly accounting for these biases is critical for making inferences. We develop a joint species distribution model (JSDM) that accounts for varying sampling conditions due to the environment and time of sampling when estimating relative abundance. The novelty of our JSDM is that we explicitly model sampling effort as the product of known quantities based on time and gear type and an unknown functional relationship to capture seasonal variation in species life history. We use the model to study relative abundance of six freshwater fish species across the state of Minnesota, USA. Our model enables estimates of relative abundance to be compared both within and across species and lakes, and captures the inconsistent sampling present in the data. We discuss how gear type, water temperature and day of the year impact catchability for each species at the lake level and throughout a year. We compare our estimates of relative abundance to those obtained from a model that assumes constant catchability to highlight important differences within and across lakes and species. Synthesis and applications: Our method illustrates that assumptions relating indices of abundance to observed catch data can greatly impact model inferences derived from JSDMs. Specifically, not accounting for varying sampling conditions can bias inference of relative abundance, restricting our ability to detect responses to management inte

© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC., We use a Bayesian spatio-temporal model, first to smooth small-area initial life expectancy estimates inBarcelona for 2020, and second to predict what small-area life expectancy would have been in 2020 inabsence of covid-19 using mortality data from 2007 to 2019. This allows us to estimate and map the small-area life expectancy loss, which can be used to assess how the impact of covid-19 varies spatially, and toexplore whether that loss relates to underlying factors, such as population density, educational level, orproportion of older individuals living alone. We find that the small-area life expectancy loss for men and forwomen have similar distributions, and are spatially uncorrelated but positively correlated with populationdensity and among themselves. On average, we estimate that the life expectancy loss in Barcelona in 2020 was of 2.01 years for men, falling back to 2011 levels, and of 2.11 years for women, falling back to 2006 levels., This work was supported by the grant PID2021-125380OB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe., Peer Reviewed, Postprint (published version)

Road casualties represent an alarming concern for modern societies. During the last years, several authors proposed sophisticated approaches to help authorities implement new policies. These models were usually developed considering a set of socio-economic variables and ignoring the measurement error, which can bias the statistical inference. This paper presents a Bayesian model to analyse car crash occurrences at the network-lattice level, taking into account measurement error in the spatial covariate. The suggested methodology is exemplified by considering the collisions in the road network of Leeds (UK) during 2011–2019. Traffic volumes are approximated using an extensive set of counts obtained from mobile devices and the estimates are adjusted using a spatial measurement error correction.

Aim Globally distributed plant trait data are increasingly used to understand relationships between biodiversity and ecosystem processes. However, global trait databases are sparse because they are compiled from many, mostly small databases. This sparsity in both trait space completeness and geographical distribution limits the potential for both multivariate and global analyses. Thus, ‘gap-filling’ approaches are often used to impute missing trait data. Recent methods, like Bayesian hierarchical probabilistic matrix factorization (BHPMF), can impute large and sparse data sets using side information. We investigate whether BHPMF imputation leads to biases in trait space and identify aspects influencing bias to provide guidance for its usage. Innovation We use a fully observed trait data set from which entries are randomly removed, along with extensive but sparse additional data. We use BHPMF for imputation and evaluate bias by: (1) accuracy (residuals, RMSE, trait means), (2) correlations (bi- and multivariate) and (3) taxonomic and functional clustering (valuewise, uni- and multivariate). BHPMF preserves general patterns of trait distributions but induces taxonomic clustering. Data set–external trait data had little effect on induced taxonomic clustering and stabilized trait–trait correlations. Main Conclusions Our study extends the criteria for the evaluation of gap-filling beyond RMSE, providing insight into statistical data structure and allowing better informed use of imputed trait data, with improved practice for imputation. We expect our findings to be valuable beyond applications in plant ecology, for any study using hierarchical side information for imputation.

The seabird meta-population viability model (mPVA) uses a generalized approach to project abundance and quasi-extinction risk for 102 seabird species under various conservation scenarios. The mPVA is a stage-structured projection matrix that tracks abundance of multiple populations linked by dispersal, accounting for breeding island characteristics and spatial distribution. Data are derived from published studies, grey literature, and expert review (with over 500 contributions). Invasive species impacts were generalized to stage-specific vital rates by fitting a Bayesian state-space model to trend data from Islands where invasive removals had occurred, while accounting for characteristics of seabird biology, breeding islands and invasive species. Survival rates were estimated using a competing hazards formulation to account for impacts of multiple threats, while also allowing for environmental and demographic stochasticity, density dependence and parameter uncertainty.•The mPVA provides resource managers with a tool to quantitatively assess potential benefits of alternative management actions, for multiple species•The mPVA compares projected abundance and quasi-extinction risk under current conditions (no intervention) and various conservation scenarios, including removal of invasive species from specified breeding islands, translocation or reintroduction of individuals to an island of specified location and size, and at-sea mortality amelioration via reduction in annual at-sea deaths.

Road traffic casualties represent a hidden global epidemic, demanding evidence-based interventions. This paper demonstrates a network lattice approach for identifying road segments of particular concern, based on a case study of a major city (Leeds, UK), in which 5862 crashes of different severities were recorded over an 8-year period (2011–2018). We consider a family of Bayesian hierarchical models that include spatially structured and unstructured random effects to capture the dependencies between the severity levels. Results highlight roads that are more prone to collisions, relative to estimated traffic volumes, in the north-west and south of city centre. We analyse the modifiable areal unit problem (MAUP), proposing a novel procedure to investigate the presence of MAUP on a network lattice. We conclude that our methods enable a reliable estimation of road safety levels to help identify ‘hotspots’ on the road network and to inform effective local interventions.

To assess the current dynamics of an epidemic, it is central to collect information on the daily number of newly diseased cases. This is especially important in real-time surveillance, where the aim is to gain situational awareness, for example, if cases are currently increasing or decreasing. Reporting delays between disease onset and case reporting hamper our ability to understand the dynamics of an epidemic close to now when looking at the number of daily reported cases only. Nowcasting can be used to adjust daily case counts for occurred-but-not-yet-reported events. Here, we present a novel application of nowcasting to data on the current COVID-19 pandemic in Bavaria. It is based on a hierarchical Bayesian model that considers changes in the reporting delay distribution over time and associated with the weekday of reporting. Furthermore, we present a way to estimate the effective time-varying case reproduction number Re(t) based on predictions of the nowcast. The approaches are based on previously published work, that we considerably extended and adapted to the current task of nowcasting COVID-19 cases. We provide methodological details of the developed approach, illustrate results based on data of the current pandemic, and evaluate the model based on synthetic and retrospective data on COVID-19 in Bavaria. Results of our nowcasting are reported to the Bavarian health authority and published on a webpage on a daily basis (https://corona.stat.uni-muenchen.de/). Code and synthetic data for the analysis are available from https://github.com/FelixGuenther/nc_covid19_bavaria and can be used for adaption of our approach to different data.

Spatial data is often aggregated into small area. It is challenging to analyse these data. Two new statistical techniques were developed to tackle these challenges. Bayesian meta-analysis models were used to unveil geographic disparities in cancer using the Australian Cancer Atlas. More flexible Bayesian Empirical Likelihood models were used to analyse more complex data including COVID19 deaths. Both methods provided new insights into the analysis of spatial data.

We measure the economic impact of varietal improvement and technological change in flue-cured tobacco across quantity (e.g., yield) and quality dimensions under a voluntary quality constraint. Since 1961, flue-cured tobacco breeders in the United States have been subject to the Minimum Standards Program that sets limits on acceptable quality characteristics for commercial tobacco varieties. We implement a Bayesian hierarchical model to measure the contribution of breeding efforts to changes in tobacco yields and quality between 1954 and 2017. The Bayesian model addresses limited data for varieties in the trials and allows easy generation of the necessary parameters of economic interest.

Environmental temperature is a crucial abiotic factor that influences the success of ectothermic organisms, including hosts and pathogens in disease systems. One example is the amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), which has led to widespread amphibian population declines. Understanding its thermal ecology is essential to effectively predict outbreaks. Studies that examine the impact of temperature on hosts and pathogens often do so in controlled constant temperatures. Although varying temperature experiments are becoming increasingly common, it is unrealistic to test every temperature scenario. Thus, reliable methods that use constant temperature data to predict performance in varying temperatures are needed. In this study, we tested whether we could accurately predict Bd growth in three varying temperature regimes, using a Bayesian hierarchical model fit with constant temperature Bd growth data. We fit the Bayesian hierarchical model five times, each time changing the thermal performance curve (TPC) used to constrain the logistic growth rate to determine how TPCs influence the predictions. We then validated the model predictions using Bd growth data collected from the three tested varying temperature regimes. Although all TPCs overpredicted Bd growth in the varying temperature regimes, some functional forms performed better than others. Varying temperature impacts on disease systems are still not well understood and improving our understanding and methodologies to predict these effects could provide insights into disease systems and help conservation efforts.

American Shad (Alosa sapidissima), Hickory Shad (A. mediocris), and river herrings (Alewife A. pseudoharengus and Blueback Herring A. aestivalis) are anadromous pelagic fishes, which as adults spend most of the annual cycle at sea, but enter the coastal rivers in spring to spawn. Once as one of the most valuable fisheries along the Atlantic coast, Alosa populations have declined in recent decades and current populations are at historic lows. Various management actions have been conducted to restore the populations, and stocks in different river systems display different demographic trends. Demonstration of synthetic diagnostics on the factors impacting these populations is important to better conserve this species group. We developed a Bayesian hierarchical spatiotemporal model to identify the population trends of these species among rivers in the Chesapeake Bay based on results of surveys conducted by the Virginia Department of Game and Inland Fisheries and Maryland Department of Natural Resources and to identify environmental and anthropogenic factors influencing their distribution and abundance. The hierarchical model structure helped to diagnose river-specific population trends and impacts of surrounding factors, and decrease uncertainties in rivers with less samples available. The results demonstrate river-specific heterogeneity of spatiotemporal dynamics of these species and indicate river-specific impacts of multiple factors, including water temperature, river flow, chlorophyll a concentration, and total phosphorus concentration, on their population dynamics. Atlantic Multidecadal Oscillation and Gulf Stream meanders displayed significant influence on the inter-annual trends of Alosa species in rivers with more data available. The results would help to develop river- and species-specific management strategies to recover these species.

American Shad (Alosa sapidissima), Hickory Shad (A. mediocris), and river herrings (Alewife A. pseudoharengus and Blueback Herring A. aestivalis) are anadromous pelagic fishes, which as adults spend most of the annual cycle at sea, but enter the coastal rivers in spring to spawn. Once as one of the most valuable fisheries along the Atlantic coast, Alosa populations have declined in recent decades and current populations are at historic lows. Various management actions have been conducted to restore the populations, and stocks in different river systems display different demographic trends. Demonstration of synthetic diagnostics on the factors impacting these populations is important to better conserve this species group. We developed a Bayesian hierarchical spatiotemporal model to identify the population trends of these species among rivers in the Chesapeake Bay based on results of surveys conducted by the Virginia Department of Game and Inland Fisheries and Maryland Department of Natural Resources and to identify environmental and anthropogenic factors influencing their distribution and abundance. The hierarchical model structure helped to diagnose river-specific population trends and impacts of surrounding factors, and decrease uncertainties in rivers with less samples available. The results demonstrate river-specific heterogeneity of spatiotemporal dynamics of these species and indicate river-specific impacts of multiple factors, including water temperature, river flow, chlorophyll a concentration, and total phosphorus concentration, on their population dynamics. Atlantic Multidecadal Oscillation and Gulf Stream meanders displayed significant influence on the inter-annual trends of Alosa species in rivers with more data available. The results would help to develop river- and species-specific management strategies to recover these species.

Environmental temperature is a crucial abiotic factor that influences the success of ectothermic organisms, including hosts and pathogens in disease systems. One example is the amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), which has led to widespread amphibian population declines. Understanding its thermal ecology is essential to effectively predict outbreaks. Studies that examine the impact of temperature on hosts and pathogens often do so in controlled constant temperatures. Although varying temperature experiments are becoming increasingly common, it is unrealistic to test every temperature scenario. Thus, reliable methods that use constant temperature data to predict performance in varying temperatures are needed. In this study, we tested whether we could accurately predict Bd growth in three varying temperature regimes, using a Bayesian hierarchical model fit with constant temperature Bd growth data. We fit the Bayesian hierarchical model five times, each time changing the thermal performance curve (TPC) used to constrain the logistic growth rate to determine how TPCs influence the predictions. We then validated the model predictions using Bd growth data collected from the three tested varying temperature regimes. Although all TPCs overpredicted Bd growth in the varying temperature regimes, some functional forms performed better than others. Varying temperature impacts on disease systems are still not well understood and improving our understanding and methodologies to predict these effects could provide insights into disease systems and help conservation efforts.

American Shad (Alosa sapidissima), Hickory Shad (A. mediocris), and river herrings (Alewife A. pseudoharengus and Blueback Herring A. aestivalis) are anadromous pelagic fishes, which as adults spend most of the annual cycle at sea, but enter the coastal rivers in spring to spawn. Once as one of the most valuable fisheries along the Atlantic coast, Alosa populations have declined in recent decades and current populations are at historic lows. Various management actions have been conducted to restore the populations, and stocks in different river systems display different demographic trends. Demonstration of synthetic diagnostics on the factors impacting these populations is important to better conserve this species group. We developed a Bayesian hierarchical spatiotemporal model to identify the population trends of these species among rivers in the Chesapeake Bay based on results of surveys conducted by the Virginia Department of Game and Inland Fisheries and Maryland Department of Natural Resources and to identify environmental and anthropogenic factors influencing their distribution and abundance. The hierarchical model structure helped to diagnose river-specific population trends and impacts of surrounding factors, and decrease uncertainties in rivers with less samples available. The results demonstrate river-specific heterogeneity of spatiotemporal dynamics of these species and indicate river-specific impacts of multiple factors, including water temperature, river flow, chlorophyll a concentration, and total phosphorus concentration, on their population dynamics. Atlantic Multidecadal Oscillation and Gulf Stream meanders displayed significant influence on the inter-annual trends of Alosa species in rivers with more data available. The results would help to develop river- and species-specific management strategies to recover these species.

Marine conservation areas are an important tool for the sustainable management of multispecies, small-scale fisheries. Effective spatial management requires a proper understanding of the spatial distribution of target species and the identification of its environmental drivers. Small-scale fisheries, however, often face scarcity and low-quality of data. In these situations, approaches for the prioritization of conservation areas need to deal with scattered, biased, and short-term information and ideally should quantify data- and model-specific uncertainties for a better understanding of the risks related to management interventions. We used a Bayesian hierarchical species distribution modeling approach on annual landing data of the heavily exploited, small-scale, and data-poor fishery of Chwaka Bay (Zanzibar) in the Western Indian Ocean to understand the distribution of the key target species and identify potential areas for conservation. Few commonalities were found in the set of important habitat and environmental drivers among species, but temperature, depth, and seagrass cover affected the spatial distribution of three of the six analyzed species. A comparison of our results with information from ecological studies suggests that our approach predicts the distribution of the analyzed species reasonably well. Furthermore, the two main common areas of high relative abundance identified in our study have been previously suggested by the local fisher as important areas for spatial conservation. By using short-term, catch per unit of effort data in a Bayesian hierarchical framework, we quantify the associated uncertainties while accounting for spatial dependencies. More importantly, the use of accessible and interpretable tools, such as the here created spatial maps, can frame a better understanding of spatio-temporal management for local fishers. Our approach, thus, supports the operability of spatial management in small-scale fisheries suffering from a general lack

In a century where toxicology and chemical risk assessment are embracing alternative methods to animal testing, there is an opportunity to understand the causal factors of neurodevelopmental disorders such as learning and memory disabilities in children, as a foundation to predict adverse effects. New testing paradigms, along with the advances in probabilistic modelling, can help with the formulation of mechanistically-driven hypotheses on how exposure to environmental chemicals could potentially lead to developmental neurotoxicity (DNT). This investigation aimed to develop a Bayesian hierarchical model of a simplified AOP network for DNT. The model predicted the probability that a compound induces each of three selected common key events (CKEs) of the simplified AOP network and the adverse outcome (AO) of DNT, taking into account correlations and causal relations informed by the key event relationships (KERs). A dataset of 88 compounds representing pharmaceuticals, industrial chemicals and pesticides was compiled including physicochemical properties as well as in silico and in vitro information. The Bayesian model was able to predict DNT potential with an accuracy of 76%, classifying the compounds into low, medium or high probability classes. The modelling workflow achieved three further goals: it dealt with missing values; accommodated unbalanced and correlated data; and followed the structure of a directed acyclic graph (DAG) to simulate the simplified AOP network. Overall, the model demonstrated the utility of Bayesian hierarchical modelling for the development of quantitative AOP (qAOP) models and for informing the use of new approach methodologies (NAMs) in chemical risk assessment.

We measure the economic impact of varietal improvement and technological change in flue-cured tobacco across quantity (e.g., yield) and quality dimensions under a voluntary quality constraint. Since 1961, flue-cured tobacco breeders in the United States have been subject to the Minimum Standards Program that sets limits on acceptable quality characteristics for commercial tobacco varieties. We implement a Bayesian hierarchical model to measure the contribution of breeding efforts to changes in tobacco yields and quality between 1954 and 2017. The Bayesian model addresses limited data for varieties in the trials and allows easy generation of the necessary parameters of economic interest.

Probabilistic approaches to hazard assessment use species sensitivity distributions (SSDs) to characterize hazard for toxicants exposure for different species within a community. Many of the assumptions at the core of SSDs are unrealistic, among them the assumption that the tolerance levels of all species in a specific ecological community are a priori exchangeable for each new toxic substance. Here we propose the use of a particular test to detect situations where such an assumption is violated. Then, a new method based on non-nested random effects model is required to identify novel SSDs capable of taking into account species non-exchangeability. Credible intervals, representing SSD uncertainty, could be determined based on our procedure. This leads to new and reliable estimates of the environmental hazard. We present a Bayesian modeling approach to address model inference issues, using Markov chain Monte Carlo sampling.

Marine conservation areas are an important tool for the sustainable management of multispecies, small-scale fisheries. Effective spatial management requires a proper understanding of the spatial distribution of target species and the identification of its environmental drivers. Small-scale fisheries, however, often face scarcity and low-quality of data. In these situations, approaches for the prioritization of conservation areas need to deal with scattered, biased, and short-term information and ideally should quantify data- and model-specific uncertainties for a better understanding of the risks related to management interventions. We used a Bayesian hierarchical species distribution modeling approach on annual landing data of the heavily exploited, small-scale, and data-poor fishery of Chwaka Bay (Zanzibar) in the Western Indian Ocean to understand the distribution of the key target species and identify potential areas for conservation. Few commonalities were found in the set of important habitat and environmental drivers among species, but temperature, depth, and seagrass cover affected the spatial distribution of three of the six analyzed species. A comparison of our results with information from ecological studies suggests that our approach predicts the distribution of the analyzed species reasonably well. Furthermore, the two main common areas of high relative abundance identified in our study have been previously suggested by the local fisher as important areas for spatial conservation. By using short-term, catch per unit of effort data in a Bayesian hierarchical framework, we quantify the associated uncertainties while accounting for spatial dependencies. More importantly, the use of accessible and interpretable tools, such as the here created spatial maps, can frame a better understanding of spatio-temporal management for local fishers. Our approach, thus, supports the operability of spatial management in small-scale fisheries suffering from a general lack

Ce mémoire porte sur l'inférence bayésienne pour des modèles avec des restrictions paramétriques incertaines. On étudie en premier lieu les propriétés des densités a priori et a posteriori pour des cas o\`u l'espace paramétrique est soit borné inférieurement ou doublement borné par une contrainte incertaine.\\ On fournit une analyse bayésienne a posteriori et on se concentre d'abord sur la construction d'un intervalle de crédibilité ad-hoc pour la moyenne normale $\theta$ avec l'a priori $\theta|m \sim \mathbb{I}_{[0 , \infty)} (\theta - m)$ et $m \sim \mathcal{N}(0,\sigma_m^2)$. On démontre que cet intervalle a une crédibilité exacte près du niveau nominal ainsi qu'une probabilité de recouvrement fréquentiste satisfaisante lorsque $\theta \geq 0$ et pour tout $\sigma^2_m \geq 0$.\\ On considère ensuite la prédiction d'une observation future normale de même moyenne et on étudie l'estimation bayésienne par densités prédictives sous la divergence Kullback-Leibler associée à la même loi a priori. On démontre que l'estimateur par densités prédictives de Bayes est minimax et domine la meilleure densité équivariante pour $\theta \geq 0$ et pour tout $\sigma^2_m > 0$, ce qui ajoute au résultat connu pour $\sigma^2_m=0$., We consider Bayesian inference for models with uncertain parametric constraints. We study the cases where the parameter space is lower-bounded and doubly-bounded by an uncertain constraint.\\ We provide Bayesian posterior analysis and then focus on constructing an ad-hoc Bayes credible set for the normal mean $\theta$ with $\theta|m \sim \mathbb{I}_{[0 , \infty)} (\theta - m)$, and $m \sim \mathcal{N}(0,\sigma_m^2)$. We provide evidence of exact credibility being quite close to nominal credibility and of quite satisfactory frequentist coverage probability relative to the nominal credibility when evaluated for $\theta \geq 0$ and for all $\sigma^2_m \geq 0$.\\ We then consider the problem of prediction of a future normal observable with the same mean and derive the Bayesian predictive density estimator under Kullback-Leibler divergence loss associated with the same prior. We demonstrate that the Bayes predictive density estimator is minimax and dominates the best unrestricted invariant predictive density for $\theta \geq 0$ and for all $\sigma^2_m > 0$, thus extending the previously established $\sigma^2_m=0$ case.

Human learning has been characterized by three robust effects (i.e.power law of learning, power law of decay, and spacing), whichhave been validated across multiple domains and time intervals. Toaccount for these different effects mathematical model of learningand retention have been developed. These models hold a great dealof potential for application a wide range of educational and trainingscenarios. However, many models are not validated according fortheir ability to make accurate predictions of human performance.The predictive demand of these models is made increasinglycomplex by the needs of training domain, needing both to predictboth skill decay and reacquisition from little historical data. In thispaper, we examine the predictive capability of the PredictivePerformance Equation (PPE) implemented in a Bayesianhierarchical model. Through a comparison of two Bayesianhierarchical models we show how hierarchical model fit to aparticipant’s performance across a set of items compared to only asingle item improves PPE’s predictive accuracy of both skill decayand reacquisition over multiple learning schedules

Directed acyclic graph (DAG) are widely used for modeling all kinds of relations and processes. Learning DAG structure from observational data is a challenging problem. In this dissertation, we develop novel methods for learning causal DAGs. First we work on learning the DAG structure with predefined outcomes by a Bayesian hierarchical model, where the outcomes are ``mixed'' in the sense that some may be continuous, some binary and others may be counts. We concern with multivariate point-referenced data, where each location yields measurements on multiple variables and build a joint model by hierarchically building conditional distributions with different spatial processes embedded in each conditional distribution. Comparisons in simulation study and data analysis across different spatial models show that the performance is greatly improved by incorporating spatial processes. The second problem we try to solve is the causal relation determination in the bivariate case, i.e. to determine the direction between X and Y. We restrict our attention to non-invertible causal relations between variables and develop a novel testing method for deciding the causal direction. We propose a bivariate nonlinear SEM, where the function f is non-invertible and identify the causal direction by testing for the non-invertibility of the function f. Piecewise linear function with two pieces can capture the change in functional relationships and is used for approximating the non-invertible function f. Causal DAGs are usually not identifiable from observational data and most existing methods only estimate a DAG up to its equivalence class. For the situation with more than two variables, instead of applying the bivariate non-invertible causal model to all of the given variables directly, we avoid the exhaustive search over all possible causal structures by combining current linear structure learning algorithms with our non-invertible causal learning algorithm. In our implementation, an initi

The study of spatiotemporal dynamics of fish populations is important for both stock assessment and fishery management. I explored the impacts of environmental and anthropogenic factors on spatiotemporal patterns of fish populations, and contributed to stock assessment and management by incorporating the inherent spatial structure. Hierarchical models were developed to specify spatial and temporal variations, and Bayesian methods were adopted to fit the models. Yellow perch (Perca flavescens) is one of the most important commercial and recreational fisheries in Lake Erie, which is currently managed using four management units (MUs), with each assessed by a spatially-independent stock-specific assessment model. The current spatially-independent stock-specific assessment assumes that movement of yellow perch among MUs in Lake Erie is statistically negligible and biologically insignificant. I investigated whether the assumption is violated and the effect this assumption has on assessment. I first explored the spatiotemporal patterns of yellow perch abundance in Lake Erie based on data from a 27-year gillnet survey, and analyzed the impacts of environmental factors on spatiotemporal dynamics of the population. I found that yellow perch relative biomass index displayed clear temporal variation and spatial heterogeneity, however the two middle MUs displayed spatial similarities. I then developed a state-space model based on a 7-year tag-recovery data to explore movements of yellow perch among MUs, and performed a simulation analysis to evaluate the impacts of sample size on movement estimates. The results suggested substantial movement between the two stocks in the central basin, and the accuracy and precision of movement estimates increased with increasing sample size. These results demonstrate that the assumption on movements among MUs is violated, and it is necessary to incorporate regional connectivity into stock assessment. I thus developed a tag-integrated multi-reg

Spatio-temporal data in sport is increasing rapidly, however suitable statistical methods for analysing this data are underdeveloped. The current study establishes the need for spatial statistical methods, propose a Bayesian hierarchical model as an appropriate method for comparing spatial variables, and test this model across three spatial scales. The need for spatial statistical methods was established through the identification of spatial autocorrelation. This necessitated the use of a Bayesian hierarchical model to test for an association between spatial ball movement entropy and spatial effectiveness. Posterior distribution results showed a generally positive association such that increases in entropy were associated with increases in effectiveness. The strength and confidence of the associations were impacted by the spatial scale, with the 6 × 6 grid showing the most conclusive evidence of a positive relationship; the 4 × 4 grid was mostly positive, however with a large variation; and finally, the basket-centric scale results were less conclusive. The results of the current study demonstrate the suitability of a Bayesian hierarchical model for testing for associations or differences between spatial variables. With the increase in spatial analyses in sport, this study presents an appropriate statistical method for dealing with complex problems associated with spatial analyses.

The degeneration of the human brain is a complex process, which often affects certain brain regions due to healthy aging or disease. This degeneration can be evaluated on regions of interest (ROI) in the brain through probabilistic networks and morphological estimates. Current approaches for finding such networks are limited to analyses at discrete neuropsychological stages, which cannot appropriately account for connectivity dynamics over the onset of cognitive deterioration, and morphological changes are seldom unified with connectivity networks, despite known dependencies. To overcome these limitations, a probabilistic wombling model is proposed to simultaneously estimate ROI cortical thickness and covariance networks contingent on rates of change in cognitive decline. This proposed model was applied to analyze longitudinal data from healthy control (HC) and Alzheimer's disease (AD) groups and found connection differences pertaining to regions, which play a crucial role in lasting cognitive impairment, such as the entorhinal area and temporal regions. Moreover, HC cortical thickness estimates were significantly higher than those in the AD group across all ROIs. The analyses presented in this work will help practitioners jointly analyze brain tissue atrophy at the ROI-level conditional on neuropsychological networks, which could potentially allow for more targeted therapeutic interventions.

Growth of fish is an important contributor to individual fitness as well as fish production. Explaining and predicting growth variation across populations is thus important from fundamental and applied perspectives, which requires knowledge about the ecological factors involved in shaping growth. To that end, we estimated environment-dependent von Bertalanffy growth models for 13 gravel pit lake populations of Eurasian perch (Perca fluviatilis) from north-western Germany. To identify the main drivers of perch growth, we evaluated the performance of 16 different biotic or abiotic lake variables in explaining growth variation among lakes. In addition, we compared growth predictions from the best-performing model incorporating “complex” variables that require intensive sampling effort, with a model using only “simple”, easily measurable lake variables (e.g. shoreline development factor). The derivation of a simple model aimed at future applications in typically data-poor inland fisheries, predicting expected growth potential from easily measurable lake variables. A model combining metabolic biomass of predators, maximum depth and shoreline development factor performed best in predicting perch growth variation across gravel pits. All three parameters in this model were positively related to perch growth. The best-performing simple model consisted only of the shoreline development factor. Length-at-age predictions from both models were largely identical, highlighting the utility of shoreline development factor in approximating growth potential of perch in gravel pits similar to our study lakes. Our results can be used to inform fisheries management and restoration efforts at existing or newly excavated gravel pit lakes., Bundesamt für Naturschutz http://dx.doi.org/10.13039/501100010415, Bundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347, Spanish Ministry of Economy, Industry and Competitiveness http://dx.doi.org/10.13039/501100010198, Peer Reviewed

Directed acyclic graph (DAG) are widely used for modeling all kinds of relations and processes. Learning DAG structure from observational data is a challenging problem. In this dissertation, we develop novel methods for learning causal DAGs. First we work on learning the DAG structure with predefined outcomes by a Bayesian hierarchical model, where the outcomes are ``mixed'' in the sense that some may be continuous, some binary and others may be counts. We concern with multivariate point-referenced data, where each location yields measurements on multiple variables and build a joint model by hierarchically building conditional distributions with different spatial processes embedded in each conditional distribution. Comparisons in simulation study and data analysis across different spatial models show that the performance is greatly improved by incorporating spatial processes. The second problem we try to solve is the causal relation determination in the bivariate case, i.e. to determine the direction between X and Y. We restrict our attention to non-invertible causal relations between variables and develop a novel testing method for deciding the causal direction. We propose a bivariate nonlinear SEM, where the function f is non-invertible and identify the causal direction by testing for the non-invertibility of the function f. Piecewise linear function with two pieces can capture the change in functional relationships and is used for approximating the non-invertible function f. Causal DAGs are usually not identifiable from observational data and most existing methods only estimate a DAG up to its equivalence class. For the situation with more than two variables, instead of applying the bivariate non-invertible causal model to all of the given variables directly, we avoid the exhaustive search over all possible causal structures by combining current linear structure learning algorithms with our non-invertible causal learning algorithm. In our implementation, an initi

The study of spatiotemporal dynamics of fish populations is important for both stock assessment and fishery management. I explored the impacts of environmental and anthropogenic factors on spatiotemporal patterns of fish populations, and contributed to stock assessment and management by incorporating the inherent spatial structure. Hierarchical models were developed to specify spatial and temporal variations, and Bayesian methods were adopted to fit the models. Yellow perch (Perca flavescens) is one of the most important commercial and recreational fisheries in Lake Erie, which is currently managed using four management units (MUs), with each assessed by a spatially-independent stock-specific assessment model. The current spatially-independent stock-specific assessment assumes that movement of yellow perch among MUs in Lake Erie is statistically negligible and biologically insignificant. I investigated whether the assumption is violated and the effect this assumption has on assessment. I first explored the spatiotemporal patterns of yellow perch abundance in Lake Erie based on data from a 27-year gillnet survey, and analyzed the impacts of environmental factors on spatiotemporal dynamics of the population. I found that yellow perch relative biomass index displayed clear temporal variation and spatial heterogeneity, however the two middle MUs displayed spatial similarities. I then developed a state-space model based on a 7-year tag-recovery data to explore movements of yellow perch among MUs, and performed a simulation analysis to evaluate the impacts of sample size on movement estimates. The results suggested substantial movement between the two stocks in the central basin, and the accuracy and precision of movement estimates increased with increasing sample size. These results demonstrate that the assumption on movements among MUs is violated, and it is necessary to incorporate regional connectivity into stock assessment. I thus developed a tag-integrated multi-reg

A variety of complex data has broadened in many research fields such as epidemiology, genomics, and analytical chemistry with the development of science, technologies, and design scheme over the past few decades. For example, in epidemiology, the matched case-crossover study design is used to investigate the association between the clustered binary outcomes of disease and a measurement error in covariate within a certain period by stratifying subjects' conditions. In genomics, high-correlated and high-dimensional(HCHD) data are required to identify important genes and their interaction effect over diseases. In analytical chemistry, multiple time series data are generated to recognize the complex patterns among multiple classes. Due to the great diversity, we encounter three problems in analyzing those complex data in this dissertation. We have then provided several contributions to semiparametric and nonparametric methods for dealing with the following problems: the first is to propose a method for testing the significance of a functional association under the matched study; the second is to develop a method to simultaneously identify important variables and build a network in HDHC data; the third is to propose a multi-class dynamic model for recognizing a pattern in the time-trend analysis. For the first topic, we propose a semiparametric omnibus test for testing the significance of a functional association between the clustered binary outcomes and covariates with measurement error by taking into account the effect modification of matching covariates. We develop a flexible omnibus test for testing purposes without a specific alternative form of a hypothesis. The advantages of our omnibus test are demonstrated through simulation studies and 1-4 bidirectional matched data analyses from an epidemiology study. For the second topic, we propose a joint semiparametric kernel machine network approach to provide a connection between variable selection and network estimation

Growth of fish is an important contributor to individual fitness as well as fish production. Explaining and predicting growth variation across populations is thus important from fundamental and applied perspectives, which requires knowledge about the ecological factors involved in shaping growth. To that end, we estimated environment-dependent von Bertalanffy growth models for 13 gravel pit lake populations of Eurasian perch (Perca fluviatilis) from north-western Germany. To identify the main drivers of perch growth, we evaluated the performance of 16 different biotic or abiotic lake variables in explaining growth variation among lakes. In addition, we compared growth predictions from the best-performing model incorporating “complex” variables that require intensive sampling effort, with a model using only “simple”, easily measurable lake variables (e.g. shoreline development factor). The derivation of a simple model aimed at future applications in typically data-poor inland fisheries, predicting expected growth potential from easily measurable lake variables. A model combining metabolic biomass of predators, maximum depth and shoreline development factor performed best in predicting perch growth variation across gravel pits. All three parameters in this model were positively related to perch growth. The best-performing simple model consisted only of the shoreline development factor. Length-at-age predictions from both models were largely identical, highlighting the utility of shoreline development factor in approximating growth potential of perch in gravel pits similar to our study lakes. Our results can be used to inform fisheries management and restoration efforts at existing or newly excavated gravel pit lakes., Bundesamt für Naturschutz http://dx.doi.org/10.13039/501100010415, Bundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347, Spanish Ministry of Economy, Industry and Competitiveness http://dx.doi.org/10.13039/501100010198, Peer Reviewed

Growth of fish is an important contributor to individual fitness as well as fish production. Explaining and predicting growth variation across populations is thus important from fundamental and applied perspectives, which requires knowledge about the ecological factors involved in shaping growth. To that end, we estimated environment-dependent von Bertalanffy growth models for 13 gravel pit lake populations of Eurasian perch (Perca fluviatilis) from north-western Germany. To identify the main drivers of perch growth, we evaluated the performance of 16 different biotic or abiotic lake variables in explaining growth variation among lakes. In addition, we compared growth predictions from the best-performing model incorporating “complex” variables that require intensive sampling effort, with a model using only “simple”, easily measurable lake variables (e.g. shoreline development factor). The derivation of a simple model aimed at future applications in typically data-poor inland fisheries, predicting expected growth potential from easily measurable lake variables. A model combining metabolic biomass of predators, maximum depth and shoreline development factor performed best in predicting perch growth variation across gravel pits. All three parameters in this model were positively related to perch growth. The best-performing simple model consisted only of the shoreline development factor. Length-at-age predictions from both models were largely identical, highlighting the utility of shoreline development factor in approximating growth potential of perch in gravel pits similar to our study lakes. Our results can be used to inform fisheries management and restoration efforts at existing or newly excavated gravel pit lakes., Bundesamt für Naturschutz http://dx.doi.org/10.13039/501100010415, Bundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347, Spanish Ministry of Economy, Industry and Competitiveness http://dx.doi.org/10.13039/501100010198, Peer Reviewed

Extreme sea levels are a significant threat to life, property, and the environment. These threats are managed by coastal planers through the implementation of risk mitigation strategies. Central to such strategies is knowledge of extreme event probabilities. Typically, these probabilities are estimated by fitting a suitable distribution to the observed extreme data. Estimates, however, are often uncertain due to the small number of extreme events in the tide gauge record and are only available at gauged locations. This restricts our ability to implement cost-effective mitigation. A remarkable fact about sea-level extremes is the existence of spatial dependences, yet the vast majority of studies to date have analyzed extremes on a site-by-site basis. Here we demonstrate that spatial dependences can be exploited to address the limitations posed by the spatiotemporal sparseness of the observational record. We achieve this by pooling all of the tide gauge data together through a Bayesian hierarchical model that describes how the distribution of surge extremes varies in time and space. Our approach has two highly desirable advantages: 1) it enables sharing of information across data sites, with a consequent drastic reduction in estimation uncertainty; 2) it permits interpolation of both the extreme values and the extreme distribution parameters at any arbitrary ungauged location. Using our model, we produce an observation-based probabilistic reanalysis of surge extremes covering the entire Atlantic and North Sea coasts of Europe for the period 1960–2013.

Growth of fish is an important contributor to individual fitness as well as fish production. Explaining and predicting growth variation across populations is thus important from fundamental and applied perspectives, which requires knowledge about the ecological factors involved in shaping growth. To that end, we estimated environment‐dependent von Bertalanffy growth models for 13 gravel pit lake populations of Eurasian perch (Perca fluviatilis) from north‐western Germany. To identify the main drivers of perch growth, we evaluated the performance of 16 different biotic or abiotic lake variables in explaining growth variation among lakes. In addition, we compared growth predictions from the best‐performing model incorporating “complex” variables that require intensive sampling effort, with a model using only “simple”, easily measurable lake variables (e.g. shoreline development factor). The derivation of a simple model aimed at future applications in typically data‐poor inland fisheries, predicting expected growth potential from easily measurable lake variables. A model combining metabolic biomass of predators, maximum depth and shoreline development factor performed best in predicting perch growth variation across gravel pits. All three parameters in this model were positively related to perch growth. The best‐performing simple model consisted only of the shoreline development factor. Length‐at‐age predictions from both models were largely identical, highlighting the utility of shoreline development factor in approximating growth potential of perch in gravel pits similar to our study lakes. Our results can be used to inform fisheries management and restoration efforts at existing or newly excavated gravel pit lakes.

The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be accurately recovered from m measurements with m « N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||0 as an input. However, generally s is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

Estimates of the uncertainty of model output fields (e.g. 2-meter temperature, surface radiation fluxes or wind speed) are of great value to the weather and climate communities. The traditional approach for the uncertainty estimation is to conduct an ensemble of simulations where the model configuration is perturbed, and/or different models are considered. This procedure is very computationally expensive and may not be feasible in particular for higher resolution experiments. In this paper a new method based on Bayesian Hierarchical Models (BHM) that requires just one model run is proposed. It is applied to the Weather Research and Forecasting (WRF) model’s 2-meter temperature in the Botnia-Atlantica region in Scandinavia for a 10-day period in the winter and summer seasons. For both seasons, the estimated uncertainty using the BHM is found to be comparable to that obtained from an ensemble of experiments in which different Planetary Boundary Layer (PBL) schemes are employed. While WRF-BHM is not capable of generating the full set of products obtained from an ensemble of simulations, it can be used to extract commonly used diagnostics including the uncertainty estimation which is the focus of this work. The methodology proposed here is fully general and can easily be extended to any other output variable and numerical model., WindCoE

The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be accurately recovered from m measurements with m « N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||0 as an input. However, generally s is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be accurately recovered from m measurements with m « N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||0 as an input. However, generally s is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

A Bayesian hierarchical model that integrated information about state and observation processes was used to estimate the number of adult Delta Smelt entrained into the southern Sacramento−San Joaquin Delta during water export operations by the California State Water Project and the Central Valley Project. The model hierarchy accounted for dynamic processes of transport, survival, sampling efficiency, and observation. Water export, mark−recapture, and fish facility count data informed each process. Model diagnostics and simulation testing indicated a good fit of the model, and that parameters were jointly estimable in the Bayesian hierarchical model framework. The model was limited, however, by sparse data to estimate survival and State Water Project sampling efficiency. Total December to March entrainment of adult Delta Smelt ranged from an estimated 142,488 fish in 2000 to 53 fish in 2014, and the efficiency of louvers used to divert entrained fish to fish facilities appeared to decline at high and low primary intake channel velocities. Though applied to Delta Smelt, the hierarchical modeling framework was sufficiently flexible to estimate the entrainment of other pelagic species.

Certain general facets of biotic response to climate change, such as shifts in phenology and geographic distribution, are well characterized; however, it is not clear whether the observed similarity of responses across taxa will extend to variation in other population-level processes. We examined population response to climatic variation using long-term incidence data (collected over 42 years) encompassing 149 butterfly species and considerable habitat diversity (10 sites along an elevational gradient from sea level to over 2,700 m in California). Population responses were characterized by extreme heterogeneity that was not attributable to differences in species composition among sites. These results indicate that habitat heterogeneity might be a buffer against climate change and highlight important questions about mechanisms maintaining interpopulation differences in responses to weather. Despite overall heterogeneity of response, population dynamics were accurately predicted by our model for many species at each site. However, the overall correlation between observed and predicted incidence in a cross validation analysis was moderate (Pearson's r = 0.23, SE 0.01), and 97% of observed data fell within the predicted 95% credible intervals. Prediction was most successful for more abundant species as well as for sites with lower annual turnover. Population-level heterogeneity in response to climate variation and the limits of our predictive power highlight the challenges for a future of increasing climatic variability.

The best-worst method (BWM) is a multi-criteria decision-making method which finds the optimal weights of a set of criteria based on the preferences of only one decision-maker (DM) (or evaluator). However, it cannot amalgamate the preferences of multiple decision-makers/evaluators in the so-called group decision-making problem. A typical way of aggregating the preferences of multiple DMs is to use the average operator, e.g., arithmetic or geometric mean. However, averages are sensitive to outliers and provide restricted information regarding the overall preferences of all DMs. In this paper, a Bayesian BWM is introduced to find the aggregated final weights of criteria for a group of DMs at once. To this end, the BWM framework is meaningfully viewed from a probabilistic angle, and a Bayesian hierarchical model is tailored to compute the weights in the presence of a group of DMs. We further introduce a new ranking scheme for decision criteria, called credal ranking, where a confidence level is assigned to measure the extent to which a group of DMs prefers one criterion over one another. A weighted directed graph visualizes the credal ranking based on which the interrelation of criteria and confidences are merely understood. The numerical example validates the results obtained by the Bayesian BWM while it yields much more information in comparison to that of the original BWM., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Information and Communication Technology, Transport and Logistics

A Bayesian hierarchical model that integrated information about state and observation processes was used to estimate the number of adult Delta Smelt entrained into the southern Sacramento−San Joaquin Delta during water export operations by the California State Water Project and the Central Valley Project. The model hierarchy accounted for dynamic processes of transport, survival, sampling efficiency, and observation. Water export, mark−recapture, and fish facility count data informed each process. Model diagnostics and simulation testing indicated a good fit of the model, and that parameters were jointly estimable in the Bayesian hierarchical model framework. The model was limited, however, by sparse data to estimate survival and State Water Project sampling efficiency. Total December to March entrainment of adult Delta Smelt ranged from an estimated 142,488 fish in 2000 to 53 fish in 2014, and the efficiency of louvers used to divert entrained fish to fish facilities appeared to decline at high and low primary intake channel velocities. Though applied to Delta Smelt, the hierarchical modeling framework was sufficiently flexible to estimate the entrainment of other pelagic species.

Certain general facets of biotic response to climate change, such as shifts in phenology and geographic distribution, are well characterized; however, it is not clear whether the observed similarity of responses across taxa will extend to variation in other population-level processes. We examined population response to climatic variation using long-term incidence data (collected over 42 years) encompassing 149 butterfly species and considerable habitat diversity (10 sites along an elevational gradient from sea level to over 2,700 m in California). Population responses were characterized by extreme heterogeneity that was not attributable to differences in species composition among sites. These results indicate that habitat heterogeneity might be a buffer against climate change and highlight important questions about mechanisms maintaining interpopulation differences in responses to weather. Despite overall heterogeneity of response, population dynamics were accurately predicted by our model for many species at each site. However, the overall correlation between observed and predicted incidence in a cross validation analysis was moderate (Pearson's r = 0.23, SE 0.01), and 97% of observed data fell within the predicted 95% credible intervals. Prediction was most successful for more abundant species as well as for sites with lower annual turnover. Population-level heterogeneity in response to climate variation and the limits of our predictive power highlight the challenges for a future of increasing climatic variability.

The best-worst method (BWM) is a multi-criteria decision-making method which finds the optimal weights of a set of criteria based on the preferences of only one decision-maker (DM) (or evaluator). However, it cannot amalgamate the preferences of multiple decision-makers/evaluators in the so-called group decision-making problem. A typical way of aggregating the preferences of multiple DMs is to use the average operator, e.g., arithmetic or geometric mean. However, averages are sensitive to outliers and provide restricted information regarding the overall preferences of all DMs. In this paper, a Bayesian BWM is introduced to find the aggregated final weights of criteria for a group of DMs at once. To this end, the BWM framework is meaningfully viewed from a probabilistic angle, and a Bayesian hierarchical model is tailored to compute the weights in the presence of a group of DMs. We further introduce a new ranking scheme for decision criteria, called credal ranking, where a confidence level is assigned to measure the extent to which a group of DMs prefers one criterion over one another. A weighted directed graph visualizes the credal ranking based on which the interrelation of criteria and confidences are merely understood. The numerical example validates the results obtained by the Bayesian BWM while it yields much more information in comparison to that of the original BWM., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Information and Communication Technology, Transport and Logistics

The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be accurately recovered from m measurements with m « N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||0 as an input. However, generally s is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be accurately recovered from m measurements with m « N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||0 as an input. However, generally s is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

BACKGROUND:It is widely recognized that there are multiple risk factors for early-life mortality. In practice most interventions to curb early-life mortality target births based on a single risk factor, such as poverty. However, most premature deaths are not from the targeted group. Thus interventions target many births that are at not at high risk and miss many births at high risk. METHODS:Using data from the second wave of Demographic and Health Surveys from India and a hierarchical Bayesian model, we estimate infant mortality risk for 73.320 infants in India as a function of 4 risk factors. We show how this information can be used to improve program targeting. We compare our novel approach against common programs that target groups based on a single risk factor. RESULTS:A conventional approach that targets mothers in the lowest quintile of income correctly identifies only 30% of infant deaths. By contrast, using four risk factors simultaneously we identify a group of births of the same size that includes 57% of all deaths. Using the 2012 census to translate these percentages into numbers, there were 25.642.200 births in 2012 and 4.4% died before the age of one. Our approach correctly identifies 643.106 of 1.128.257 infant deaths while poverty only identifies 338.477 infant deaths. CONCLUSION:Our approach considerably improves program targeting by identifying more infant deaths than the usual approach that targets births based on a single risk factor. This leads to more efficient program targeting. This is particularly useful in developing countries, where resources are lacking and needs are high.

I propose a distributed Markov chain Monte Carlo (MCMC) algorithm for estimating Bayesian hierarchical models when the number of cross-sectional units is very large and the objects of interest are the unit-level parameters. The two-stage algorithm is asymptotically exact, retains the flexibility of a standard MCMC algorithm, and is easy to implement. The algorithm constructs an estimator of the posterior predictive distribution of the unit-level parameters in the first stage, and uses the estimator as the prior distribution in the second stage for the unit-level draws. Both stages are embarrassingly parallel. I demonstrate the algorithm with simulated data from a hierarchical logit model and show that it is faster and more efficient than a single machine algorithm by at least an order of magnitude. For a relatively small number of observations per cross-sectional unit, the algorithm is both faster and has better mixing properties than the standard hybrid Gibbs sampler. I illustrate my approach with data on 1,100,000 donors to a charitable organization, and simulations with up to 100 million units.

The development of mortality models is important in order to reconstruct historical processes, understand current patterns and predict future trends. Mortality models are particularly useful when the available data are sparse, unreliable or incomplete. Traditionally, mortality patterns in data-rich populations were used to observe mathematical or empirical regularities, which could be applied to data-sparse populations. However, as a wider variety of data have become available, the focus of model building has shifted to developing flexible models that perform well in a variety of contexts. This dissertation introduces Bayesian methods of mortality estimation in three contexts where the available data are imperfect. The first paper develops a method to estimate subnational mortality in situations with small populations and highly-variable data. The second paper develops a unified modeling framework to estimate and project neonatal mortality in all countries worldwide, including those with limited and poor-quality data. The third paper introduces a new dataset to study mortality inequalities in the United States, and develops methods to deal with the truncated and censored mortality information that is available. In all three contexts, the modeling approaches combine strengths from traditional demographic models, which capture mortality regularities across age, with the flexibility of Bayesian frameworks, which allow for multiple data sources to be incorporated, information to be shared across time and space, and uncertainty to be assessed.

Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Journal of Animal Ecology 87 (2018): 682-690, doi:10.1111/1365-2656.12790., Phenological changes have been observed in a variety of systems over the past century. There is concern that, as a consequence, ecological interactions are becoming increasingly mismatched in time, with negative consequences for ecological function. Significant spatial heterogeneity (inter-site) and temporal variability (inter-annual) can make it difficult to separate intrinsic, extrinsic, and stochastic drivers of phenological variability. The goal of this study was to understand the timing and variability of breeding phenology of Adélie penguins under fixed environmental conditions, and to use those data to identify a ‘null model’ appropriate for disentangling the sources of variation in wild populations. Data on clutch initiation were collected from both wild and captive populations of Adélie penguins. Clutch initiation in the captive population was modeled as a function of year, individual, and age to better understand phenological patterns observed in the wild population. Captive populations displayed as much inter-annual variability in breeding phenology as wild populations, suggesting that variability in breeding phenology is the norm and thus may be an unreliable indicator of environmental forcing. The distribution of clutch initiation dates was found to be moderately asymmetric (right skewed) both in the wild and in captivity, consistent with the pattern expected under social facilitation. The role of stochasticity in phenological processes has heretofore been largely ignored. However, these results suggest that inter-annual variability in breeding phenology can arise independent of any environmental or demographic drivers and that synchronous breeding can enhance inherent stochasticity. This complicates efforts to relate phenological variation to environmental variability in the 53 wild. Accordingly, we must be careful to consider random forcing in phenological processes, lest we fit models to data dominated by random noise. This is particularly true for c, Funding to HJL and CY was provided by the National Science Foundation Grant OPP/GSS 1255058, and to SJ, HJL, and CY, by the National Science Foundation Grant 1341474.