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Post-disaster recovery modelling of engineering systems has become an important facet of catastrophe risk modelling and management for natural hazards. The post-disaster recovery trajectory of a civil infrastructure system can be quantified using (a) the initial post-disaster functionality level, Qo; (b) rapidity, h (i.e., the rate of functionality restoration); and (c) recovery time, Rt. This study uses a Bayesian estimation approach to derive a set of probabilistic models to estimate Qo, Rt, and h of electric power networks (EPNs) using post-earthquake recovery data from 16 large earthquakes in Japan between 2003 and 2022. The considered predictor (explanatory) variables include earthquake magnitude, year of occurrence, seismic intensity, and exposed population (PEX). Apart from being a simple and efficient stand-alone tool, the proposed data-driven models can be a useful benchmarking tool for simulation-based approaches for EPN recovery modelling. [ABSTRACT FROM AUTHOR]

Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast–slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes. [ABSTRACT FROM AUTHOR]

Integration of Bayesian parameter estimation (BPE) with model‐based design of experiments (MBDoE) aims to estimate process parameters efficiently and systematically. To achieve more efficient use of resources by iteratively selecting informative experiments based on current knowledge about the parameters, an integrated method with BPE and MBDoE is proposed in this article. A built‐in Markov Chain Monte Carlo is also developed to yield not only the distribution profile of the estimated parameters but also aid in the determination of stopping criteria and the estimation of noise. Two applications of dynamic batch reactor systems are presented. Comparative analysis substantiates the superior performance of this approach in terms of parameter accuracy and the efficiency of experimentation. [ABSTRACT FROM AUTHOR]

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power of α , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance I 2 . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale. [ABSTRACT FROM AUTHOR]

In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and the principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be more sensitive to potential departures from general relativity (GR). We extend previous works by employing Bayesian parameter estimation and performing both tests with injections of GR and injections of subtle GR-violated signals. We also apply multi-parameter tests with PCA in the phenomenological test of GW propagation. This work complements previous works and further demonstrates the enhancement provided by the PCA method. Considering a supermassive black hole binary system as the GW source, we show that subtle departures will be more obvious in posteriors of PCA parameters. The departures less than 1σ in original parameters can yield significant departures in first 5 dominant PCA parameters.

Based on VaR and VaB research methods, this paper constructs a regression model based on industry risk-return value metrics using a Bayesian-expected quantile regression algorithm in the context of big data. The parameters of the Bayesian model are estimated using the decision function, and then the metric effects of the model are evaluated using AIC and BIC. Finally, the relationship between industry risk and return is evaluated using the Bayesian-Expectation Quartile regression model. Under the Bayesian-Expectile model, the difference between the correlation coefficients of AIC (−0.7431, −0.9563, −0.7872, −0.9137) and BIC (−0.0547, −0.0768, −0.0559) is relatively small, reflecting the fact that the Internet financial innovations have not significantly pushed up the risk-free rate of return of the society while pushing up the society’s financing cost. In addition, the three models used in this paper have close EvaR prediction results for information technology, daily consumption and telecommunication services, indicating that the credibility of the industry risk prediction results proposed in this paper is high. The relationship between idiosyncratic volatility and the adjusted return for the next period is related to the time-varying nature of the characteristics of individual stocks, as well as the individual stocks of industry-risk firms. Incorporating factors that affect conditional equity premiums into the time-varying conditions of individual stocks can more accurately reflect the risk-taking of individual stocks of risky firms.

BACKGROUND:Insecticides used against Aedes aegypti and other disease vectors can elicit a multitude of dose-dependent effects on behavioral and bionomic traits. Estimating the potential epidemiological impact of a product requires thorough understanding of these effects and their interplay at different dosages. Volatile spatial repellent (SR) products come with an additional layer of complexity due to the potential for altered movement of affected mosquitoes and diffusion of volatile particles of the product beyond the treated house. Here, we propose a paired experimental design and statistical inference framework for estimating these nuanced effects of volatile SRs. METHOD:We fitted a continuous-time Markov chain model in a Bayesian framework to data on marked mosquitoes released in interconnected experimental huts conducted in Iquitos, Peru. We estimated the effects of two dosages of transfluthrin on Ae. aegypti behaviors associated with human-vector contact: repellency, exiting and knockdown in the treated space and in connected, adjacent huts. We validated the framework using simulated data. RESULTS:The odds of a female Ae. aegypti being repelled, and thus prevented from entering a treated hut (HT), increased at both dosages (low dosage: odds = 1.64, 95% highest density interval (HDI) = 1.30-2.09; high dosage: odds = 1.35, HDI = 1.04-1.67). The relative risk of exiting from the treated hut was reduced (low: RR = 0.70, HDI = 0.62-1.09; high: RR = 0.70, HDI = 0.40-1.06), with this effect carrying over to untreated spaces two huts away from the treated hut (H2) (low: RR = 0.79, HDI = 0.59-1.01; high: RR = 0.66, HDI = 0.50-0.87). Knockdown rates were increased in both treated and downstream huts, particularly under high dosage (HT: RR = 8.37, HDI = 2.11-17.35; H1: RR = 1.39, HDI = 0.52-2.69; H2: RR = 2.22, HDI = 0.96-3.86). CONCLUSIONS:Our framework is effective at elucidating multiple effects of volatile chemicals used in SR products, as well as their downstream effects. For the examined formulations of transfluthrin, we found notable dose-dependent effects on repellency, movement and knockdown that carry over to adjacent, untreated spaces.

The last glacial interval experienced abrupt climatic changes called Dansgaard-Oeschger (DO) events. These events manifest themselves as rapid increases followed by slow decreases of oxygen isotope ratios in Greenland ice core records. Despite promising advances, a comprehensive theory of the DO cycles, with their repeated ups and downs of isotope ratios, is still lacking. Here, based on earlier hypotheses, we introduce a dynamical model that explains the DO variability by rapid retreat and slow regrowth of thick ice shelves and thin sea ice in conjunction with changing subsurface water temperatures due to insulation by the ice cover. Our model successfully reproduces observed features of the records, such as the sawtooth shape of the DO cycles, waiting times between DO events across the last glacial, and the shifted antiphase relationship between Greenland and Antarctic ice cores. Our results show that these features can be obtained via internal feedbacks alone. Warming subsurface waters could have also contributed to the triggering of Heinrich events. Our model thus offers a unified framework for explaining major features of multimillennial climate variability during glacial intervals.

Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast-slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes., Competing Interests: Declarations: The authors have no relevant financial or non-financial interests to disclose. The authors declare that the data supporting the findings of this study are available within the paper or its supplementary information files. This work was supported by Grants NIH RO1 DK104998 (EBT), NIH RO1 DK138664 (EBT), University of Iowa Distinguished Scholar Award (EBT)., (© 2024. The Author(s).)

In this study, the interest of ground penetrating radar (GPR) time-lapse measurements for the estimation of hydrodynamic unsaturated soil parameters is investigated using synthetic infiltration experiments. Water movement and electromagnetic wave propagation in the unsaturated zone are modeled using a one-dimensional hydrogeophysical model. The GPR travel time data are analyzed for different reflectors: a moving reflector (the infiltration wetting front) and three fixed reflectors located at different depths in the soil. Global sensitivity analysis (GSA) is employed to assess the influence of the saturated hydraulic conductivity, the saturated and residual water contents, and the Mualem–van Genuchten shape parameters α and n of the soil on the GPR travel time data of the reflectors. Statistical calibration of the soil parameters is then performed using the Markov chain Monte Carlo (MCMC) method. The impact of the type of reflector (moving or fixed) is then evaluated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. GSA results show that the sensitivities of the moving and fixed reflectors data to the hydrodynamic soil parameters are different whereas the fixed reflectors have similar sensitivities. Results of parameter estimation show that the use of only data from the moving or fixed reflectors does not allow a good identification of all soil parameters. When both data are combined, all soil parameters can be well estimated with narrow confidence intervals. [ABSTRACT FROM AUTHOR]

The Cramér-Rao bound (CRB) has been extensively used as a benchmark for estimation performance in both Bayesian and non-Bayesian frameworks. In many practical periodic parameter estimation problems, such as phase, frequency, and direction-of-arrival estimation, the observation model is periodic with respect to the unknown parameters and thus, the appropriate criterion is periodic in the parameter space. Consequently, Bayesian lower bounds on the mean-squared-error (MSE) are not valid bounds for periodic estimation problems. In addition, many Bayesian MSE lower bounds cannot be derived in the periodic case due to their restrictive regularity conditions. For example, the regularity conditions of the Bayesian CRB (BCRB) are not satisfied for parameters with uniform prior distribution. In this letter, we derive a Bayesian Cramér-Rao-type lower bound on the mean-squared-periodic-error (MSPE). The proposed periodic BCRB (PBCRB) is a lower bound on the MSPE of any estimator and has less restrictive regularity conditions than the BCRB. The PBCRB is compared with the MSPE of the minimum MSPE estimator for phase estimation in Gaussian noise and it is shown that the PBCRB is a valid and tight lower bound for this problem. [ABSTRACT FROM AUTHOR]

This study evaluated the effects of prior knowledge obtained from multi‐objective optimization on the uncertainty quantification of simulated ecologically relevant hydrologic indices (ERHIs) using a hydrological model. Two experiments were formulated considering contrasting conditions in prior knowledge when implementing Bayesian parameter estimation. In the first experiment, we reproduced a common modeling practice in the absence of previous information where uniform priors are considered when calibrating hydrological and error model parameters. In the second experiment, near‐optimal Pareto solutions from multi‐objective calibration were used to build a multivariate prior distribution for estimating hydrological and error model parameters using Bayesian calibration. In both experiments, a likelihood function considering heteroscedasticity and autocorrelation effects was employed. The Unified Non‐dominated Sorting Algorithm III was used for multi‐objective calibration, whereas the multiple‐try differential evolution adaptive metropolis algorithm was used for Markov Chain Monte Carlo sampling. The experiments were tested using a hydrologic model. We selected a subset of ERHIs comprised of 32 central tendency Indicators of Hydrologic Alteration and seven additional indices describing basic streamflow statistical properties. In general, using near‐optimal Pareto parameter distributions as prior knowledge in Bayesian calibration reduced both the bias and variability ranges in ERHIs prediction. Furthermore, there was no significant loss in the reliability of streamflow predictions (from 2% to 6%, p = 0.07) when targeting the selected ERHIs, while improving precision (from 66% to 58%, p < 0.05) and reducing the bias (from 6% to 4%, p < 0.05). Moreover, parametric uncertainty substantially shrank by 72% when linking multi‐objective calibration and Bayesian parameter estimation. Key Points: A calibration approach linked multi‐objective optimization and Bayesian inference to improve the prediction of hydrologic indicesThe new approach was compared against Bayesian calibration using uniform priors for model parametersA higher precision in simulated hydrologic indices and large reductions of parametric uncertainty in streamflow predictions were observed [ABSTRACT FROM AUTHOR]

The use of nanobiomaterials (NBMs) is becoming increasingly popular in the field of medicine. To improve the understanding on the biodistribution of NBMs, the present study aimed to implement and parametrize a physiologically based pharmacokinetic (PBPK) model. This model was used to describe the biodistribution of two NBMs after intravenous administration in rats, namely, poly(alkyl cyanoacrylate) (PACA) loaded with cabazitaxel (PACA-Cbz), and LipImage™ 815. A Bayesian parameter estimation approach was applied to parametrize the PBPK model using the biodistribution data. Parametrization was performed for two distinct dose groups of PACA-Cbz. Furthermore, parametrizations were performed three distinct dose groups of LipImage™ 815, resulting in a total of five different parametrizations. The results of this study indicate that the PBPK model can be adequately parametrized using biodistribution data. The PBPK parameters estimated for PACA-Cbz, specifically the vascular permeability, the partition coefficient, and the renal clearance rate, substantially differed from those of LipImage™ 815. This emphasizes the presence of kinetic differences between the different formulations and substances and the need of tailoring the parametrization of PBPK models to the NBMs of interest. The kinetic parameters estimated in this study may help to establish a foundation for a more comprehensive database on NBM-specific kinetic information, which is a first, necessary step towards predictive biodistribution modeling. This effort should be supported by the development of robust in vitro methods to quantify kinetic parameters. [ABSTRACT FROM AUTHOR]

Many highly reliable products (systems) usually have multiple dependent degradation processes because of their complex structure. Therefore, it is important to investigate the multivariate degradation models along with the reliability assessment in the stochastic modeling. This article proposes a framework for bivariate degradation modeling based on hybrid stochastic processes for products with two performance characteristics (PCs), the dependence of which is captured by copula functions. Considering heterogeneities among product units, different random effects are introduced in marginal stochastic processes. Then two classes of reliability functions based on joint posterior distributions are derived. In addition, a simulation study indicates that the holistic Bayesian parameter estimation method is better than the two-step Bayesian parameter estimation method. Finally, this article concludes with a case application to demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Monitoring airborne nanoparticles has a vital role in indoor air quality control due to their hazardous effects on human health. Detecting particles becomes more challenging as their sizes decrease. While research-grade instruments like the scanning mobility particle sizer (SMPS) can provide detailed and useful information, they are not practical for personal use due to their size and cost. This study aims to provide a comparable prediction of the temporal size distribution of ultrafine particles (UFPs, < 100 nm) using mid-cost measurements from a handheld particle sizer, which is more economical but has a narrower detectable size range. To achieve this, the study builds upon a computational modeling approach based on a mass-balance equation to estimate the time-varying particle size distribution, while accounting for particle evolution processes such as coagulation, deposition, and ventilation. The analytical model for indoor UFPs requires prior information regarding particle dynamic behavior, such as the size-resolved deposition rate and source emission rate. This study estimates, rather than pre-determines, the model parameters required for the temporal prediction of indoor UFP size distribution by applying Bayesian parameter inference with the analytical model of indoor aerosol. The results indicate that the present model reasonably predicts the temporal evolution of particle distributions, comparable to that of the SMPS. Furthermore, this study demonstrates the identifiability of model parameters, considering both the entire and detectable size ranges, through variance-based global sensitivity analysis. [Display omitted] • This study proposes a model for particle size distribution using mid-cost sensors. • The model applies Bayesian inference to estimate key aerosol dynamics parameters. • Despite sensor limitations, the model achieves accuracy close to high-end sizers. • Sensitivity analysis confirms the parameter identifiability in the present model. [ABSTRACT FROM AUTHOR]

The attraction effect in decision-making is a famous exampleof how preferences are influenced by the availability of otheroptions. One emerging hypothesis for the effect is that biasesin attention influence preferences. In the past, these ideashave been explored indirectly through computationalmodeling and eye tracking. In the present paper, we directlymanipulate attention through presentation order, presentingchoice options sequentially. Our results show thatpresentation order has a large impact on the effect – somepresentation orders enhance the effect and other ordersreverse the effect. To understand these results, we fit adynamic model, called the Multiattribute Linear BallisticAccumulator model, to the choice and response time data.Modeling results reveal that presentation order influences theallocation of attention on the positive and negative differencesbetween options. In sum, our results show that attention has adirect impact on the attraction effect.

As a formal theory, Bundesen’s theory of visual attention (TVA) enables the estimation of several theoretically meaningful parameters involved in attentional selection and visual encoding. As of yet, TVA has almost exclusively been used in restricted empirical scenarios such as whole and partial report and with strictly controlled stimulus material. We present a series of experiments in which we test whether the advantages of TVA can be exploited in more realistic scenarios with varying degree of stimulus control. This includes brief experimental sessions conducted on different mobile devices, computer games, and a driving simulator. Overall, six experiments demonstrate that the TVA parameters for processing capacity and attentional weight can be measured with sufficient precision in less controlled scenarios and that the results do not deviate strongly from typical laboratory results, although some systematic differences were found.

Throughout our lives, we are faced with a variety of causalreasoning problems. Arguably, the most successful models ofcausal reasoning, Causal Graphical Models (CGMs), performwell in some situations, but there is considerable variation inhow well they are able to account for data, both across scenar-ios and between individuals. We propose a model of causalreasoning based on quantum probability (QP) theory that ac-counts for behavior in situations where CGMs fail. WhetherQP or classical models are appropriate depends on the repre-sentation of events constructed by the reasoner. We describean experiment that suggests the representation of events canchange with experience to become more classical, and that therepresentation constructed can vary between individuals, in away that correlates with a simple measure of cognitive ability,The Cognitive Reflection Task.

To estimate the compressive capacity of concrete filled circular steel tubular column, a compressive model for concrete filled circular steel tubular columns based on influence parameters is developed by using Bayesian multivariate statistical theory and the collected 170 test results. The model is simplified through the Bayesian parameters removal process. And the performance of the developed probabilistic model is confirmed by comparing with the calculation results of existing codes such as Technical Specification for Concrete Tubular Structures(GB 50396-2014), AISC360-2010 of American Society for Steel Structures and AIJ-SRC01 of Japanese Building Society. Good agreement between the compressive strengths obtained by the simplified model based on Bayesian and test results is achieved. And the results updating Bayesian dynamic are closer to the tests than the code. The simplified model can be used in calculating compressive strength for concrete filled circular steel tubular columns.

Compared with other fermentation processes in food industry, cocoa bean fermentation is uncontrolled and not standardized. A detailed mechanistic understanding can therefore be relevant for cocoa bean quality control. Starting from an existing mathematical model of cocoa bean fermentation we analyse five additional biochemical mechanisms derived from the literature. These mechanisms, when added to the baseline model either in isolation or in combination, were evaluated in terms of their capacity to describe experimental data. In total, we evaluated 32 model variants on 23 fermentation datasets. We interpret the results from two perspectives: (1) success of the potential mechanism, (2) discrimination of fermentation protocols based on estimated parameters. The former provides insight in the fermentation process itself. The latter opens an avenue towards reverse-engineering empirical conditions from model parameters. We find support for two mechanisms debated in the literature: consumption of fructose by lactic acid bacteria and production of acetic acid by yeast. Furthermore, we provide evidence that model parameters are sensitive to differences in the cultivar, temperature control and usage of steel tanks compared with wooden boxes. Our results show that mathematical modelling can provide an alternative to standard chemical fingerprinting in the interpretation of fermentation data.

To overcome the challenges associated with poor temporal stability of perovskite solar cells, methods are required that allow for fast iteration of fabrication and characterisation, such that optimal device performance and stability may be actively pursued. Currently, establishing the causes of underperformance is both complex and time-consuming, and optimisation of device fabrication is thus inherently slow. Here, we present a means of computational device characterisation of mobile halide ion parameters from room temperature current–voltage ( $J-V$ ) measurements only , requiring ∼2 h of computation on basic computing resources. With our approach, the physical parameters of the device may be reverse-modelled from experimental $J-V$ measurements. In a drift-diffusion (DD) model, the set of coupled DD partial differential equations cannot be inverted explicitly, so a method for inverting the DD simulation is required. We show how Bayesian Parameter Estimation coupled with a DD perovskite solar cell model can determine the extent to which device parameters affect performance measured by $J-V$ characteristics. Our method is demonstrated by investigating the extent to which device performance is influenced by mobile halide ions for a specific fabricated device. The ion vacancy density N _0 and diffusion coefficient D _I were found to be precisely characterised for both simulated and fabricated devices. This result opens up the possibility of pinpointing origins of degradation by finding which parameters most influence device $J-V$ curves as the cell degrades.

In this review, we outline the expected tests of gravity that will be achieved at cosmological scales in the upcoming decades. We focus mainly on constraints on phenomenologically parameterized deviations from general relativity, which allow to test gravity in a model-independent way, but also review some of the expected constraints obtained with more physically motivated approaches. After reviewing the state-of-the-art for such constraints, we outline the expected improvement that future cosmological surveys will achieve, focusing mainly on future large-scale structures and cosmic microwave background surveys but also looking into novel probes on the nature of gravity. We will also highlight the necessity of overcoming accuracy issues in our theoretical predictions, issues that become relevant due to the expected sensitivity of future experiments. [ABSTRACT FROM AUTHOR]

Advancements in microbially explicit ecosystem models incorporate increasingly accurate representations of microbial physiology and enzyme‐mediated depolymerization of soil organic matter in predicting biogeochemical responses to global change. However, a major challenge with model structural improvements is the requirement for additional parameters, which are often poorly constrained sources of uncertainty. Furthermore, it is often unclear how to best focus data collection efforts toward reducing model uncertainty. Here, we use Dual Arrhenius Michaelis‐Menten Microbial Carbon and Nitrogen Physiology, a microbially mediated, coupled soil C and N cycling model, as a tool to explore the influence of microbial physiological and enzyme kinetic parameters on model estimates. We first quantify the potential for constraining model parameters using empirical measurements of soil respiration. We then use simulated data to identify which additional sources of data collection from the field would provide the greatest impact for constraining model estimates. We find that modeled soil C and N pools and fluxes are disproportionately sensitive to only a few parameters (e.g., activation energies and microbial CUE), while others exert less influence (e.g., Michaelis‐Menten half‐saturation constants). While some parameters can be constrained by the available data on heterotrophic respiration, the collection of additional data on dissolved organic C and N pools in the soil is identified as a high‐priority data need. Improving our ability to model the interactions of soil microbial physiology, soil chemistry, enzyme activities, and environmental factors on C and N cycling will require closely considering model uncertainties and prioritizing future data collection opportunities based on their impact on model performance. Plain Language Summary: Soil biogeochemical models have increasingly realistic representations of microbial processes; however, model outputs are associated with multiple types of uncertainty. We quantify the uncertainty associated with specific parameters in Dual Arrhenius Michaelis‐Menten Microbial Carbon and Nitrogen Physiology, a microbial coupled carbon and nitrogen cycle model. Reducing uncertainty in model outputs can be achieved through collecting additional data. We use existing and simulated data to identify which types of data would be most useful in reducing parameter uncertainty for this model, which may serve as an example for other microbial soil biogeochemical models. Key Points: Model outputs are highly sensitive to certain enzyme rate parameters (e.g., activation energies), and less sensitive to other parametersRespiration data helped constrain enzyme activation energies and carbon use efficiency; dissolved organic CN data would be a high priorityThis approach can reduce parameter uncertainty in biogeochemical models by tailoring data collection to reduce model uncertainty [ABSTRACT FROM AUTHOR]

Geographic profiling, a mathematical model originally developed in criminology, is increasingly being used in ecology and epidemiology. Geographic profiling boasts a wide range of applications, such as finding source populations of invasive species or breeding sites of vectors of infectious disease. The model provides a cost‐effective approach for prioritizing search strategies for source locations and does so via simple data in the form of the positions of each observation, such as individual sightings of invasive species or cases of a disease. In doing so, however, classic geographic profiling approaches fail to make the distinction between those areas containing observed absences and those areas where no data were recorded. Absence data are generated via spatial sampling protocols but are often discarded during the inference process. Here we construct a geographic profiling model that resolves these issues by making inferences via count data, analyzing a set of discrete sentinel locations at which the number of encounters has been recorded. Crucially, in our model this number can be zero. We verify the ability of this new model to estimate source locations and other parameters of practical interest via a Bayesian power analysis. We also measure model performance via real‐world data in which the model infers breeding locations of mosquitoes in bromeliads in Miami‐Dade County, Florida, USA. In both cases, our novel model produces more efficient search strategies by shifting focus from those areas containing observed absences to those with no data, an improvement over existing models that treat these areas equally. Our model makes important improvements upon classic geographic profiling methods, which will significantly enhance real‐world efforts to develop conservation management plans and targeted interventions. [ABSTRACT FROM AUTHOR]

Uncertainties in L-band (1.4. GHz) microwave radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation optical depth and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an estimate of uncertainty. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at multiple incidence angles, at horizontal and vertical polarizations, and for morning and evening overpasses. Tb simulations are generated with the land model component of the Goddard Earth Observing System (version 5) and confronted with Tb observations from the Soil Moisture Ocean Salinity satellite mission. The maximum a posteriori density (MAP) parameter values reduce the root-mean-square differences between observed and simulated long-term Tb averages and standard deviations to 3.4. K and 2.3. K, respectively. The relative uncertainty of the posterior RTM parameter estimates is typically less than 25% of the MAP parameter value, whereas it exceeds 100% for literature-based prior parameter estimates. It is also shown that the parameter values estimated through Particle Swarm Optimization are in close agreement with those obtained from MCMC simulation. The MCMC results for the RTM parameter values and the uncertainties presented herein are directly relevant to the need for accurate Tb modeling in global land data assimilation systems. © 2014 Elsevier Inc.

Uncertainties in L-band (1.4. GHz) microwave radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation optical depth and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an estimate of uncertainty. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at multiple incidence angles, at horizontal and vertical polarizations, and for morning and evening overpasses. Tb simulations are generated with the land model component of the Goddard Earth Observing System (version 5) and confronted with Tb observations from the Soil Moisture Ocean Salinity satellite mission. The maximum a posteriori density (MAP) parameter values reduce the root-mean-square differences between observed and simulated long-term Tb averages and standard deviations to 3.4. K and 2.3. K, respectively. The relative uncertainty of the posterior RTM parameter estimates is typically less than 25% of the MAP parameter value, whereas it exceeds 100% for literature-based prior parameter estimates. It is also shown that the parameter values estimated through Particle Swarm Optimization are in close agreement with those obtained from MCMC simulation. The MCMC results for the RTM parameter values and the uncertainties presented herein are directly relevant to the need for accurate Tb modeling in global land data assimilation systems. © 2014 Elsevier Inc.

Some of the most influential theories in organizational sciences explicitly describe a dynamic, multilevel process. Yet the inherent complexity of such theories makes them difficult to test. These theories often describe multiple subprocesses that interact reciprocally over time at different levels of analysis and over different time scales. Computational (i.e., mathematical) modeling is increasingly advocated as a method for developing and testing theories of this type. In organizational sciences, however, efforts that have been made to test models empirically are often indirect. We argue that the full potential of computational modeling as a tool for testing dynamic, multilevel theory is yet to be realized. In this article, we demonstrate an approach to testing dynamic, multilevel theory using computational modeling. The approach uses simulations to generate model predictions and Bayesian parameter estimation to fit models to empirical data and facilitate model comparisons. This approach enables a direct integration between theory, model, and data that we believe enables a more rigorous test of theory. [ABSTRACT FROM AUTHOR]

Estimation after model selection refers to the problem where the exact observation model is unknown and is assumed to belong to a set of candidate models. Thus, a data-based model-selection stage is performed prior to the parameter estimation stage, which affects the performance of the subsequent estimation. In this letter, we investigate post-model-selection Bayesian parameter estimation of a random vector with an unknown deterministic support set, where this support set represents the model. First, we present different estimators, including the oracle minimum mean-squared-error (MMSE), the coherent MMSE, the selected MMSE, and the full model MMSE. Then, we develop the selective Bayesian Cramér-Rao bound (BCRB) and selective tighter BCRB, which are lower bounds on the mean-squared-error (MSE) for any coherent estimator. [ABSTRACT FROM AUTHOR]

Mathematical epidemiological models have a broad use, including both qualitative and quantitative applications. With the increasing availability of data, large-scale quantitative disease spread models can nowadays be formulated. Such models have a great potential, e.g., in risk assessments in public health. Their main challenge is model parameterization given surveillance data, a problem which often limits their practical usage. We offer a solution to this problem by developing a Bayesian methodology suitable to epidemiological models driven by network data. The greatest difficulty in obtaining a concentrated parameter posterior is the quality of surveillance data; disease measurements are often scarce and carry little information about the parameters. The often overlooked problem of the model's identifiability therefore needs to be addressed, and we do so using a hierarchy of increasingly realistic known truth experiments. Our proposed Bayesian approach performs convincingly across all our synthetic tests. From pathogen measurements of shiga toxin-producing Escherichia coli O157 in Swedish cattle, we are able to produce an accurate statistical model of first-principles confronted with data. Within this model we explore the potential of a Bayesian public health framework by assessing the efficiency of disease detection and -intervention scenarios.

Mathematical models of SARS-CoV-2 (the virus which causes COVID-19) spread are used for guiding the design of mitigation steps and helping identify impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections and mortality counts are compounded by geographic heterogeneity of the population. This complicates prediction, particularly when using models assuming well-mixed populations. To address this problem, we account for the differences between rural and urban settings using network-based, distributed models where the spread of the pandemic is described in distinct local cohorts with nested SE(A)IR models, i.e., modified SEIR models that include infectious asymptomatic individuals. The model parameters account for the SARS-CoV-2 transmission mostly via human-to-human contact, and the fact that contact frequency among individuals differs between urban and rural areas, and may change over time. The probability that the virus spreads into an uninfected community is associated with influx of individuals from communities where the infection is already present, thus each node is characterized by its internal contact and by its connectivity with other nodes. Census data are used to set up the adjacency matrix of the network, which can be modified to simulate changes in mitigation measures. Our network SE(A)IR model depends on easily interpretable parameters estimated from available community level data. The parameters estimated with Bayesian techniques include transmission rate and the ratio asymptomatic to symptomatic infectious individuals. The methodology predicts that the latter quantity approaches 0.5 as the epidemic reaches an equilibrium, in full agreement with the May 22, 2020 CDC modeling. The network model gives rise to a spatially distributed computational model that explains the geographic dynamics of the contagion, e.g., in larger cities surrounded by suburban and rural areas. The time courses of the infected cohorts in the different counties predicted by the network model are remarkably similar to the reported observations. Moreover, the model shows that monitoring the infection prevalence in each county, and adopting local mitigation measures as infections climb beyond a certain threshold, is almost as effective as blanket measures, and more effective than reducing inter-county mobility.

This review presents some of the challenges in constructing models of atomic nuclei starting from theoretical descriptions of the strong interaction between nucleons. The focus is on statistical computing and methods for analyzing the link between bulk properties of atomic nuclei, such as radii and binding energies, and the underlying microscopic description of the nuclear interaction. The importance of careful model calibration and uncertainty quantification of theoretical predictions is highlighted.

A commonly used approach to parameter estimation in computational models is the so-called grid search procedure: the entire parameter space is searched in small steps to determine the parameter value that provides the best fit to the observed data. This approach has several disadvantages: first, it can be computationally very expensive; second, one optimal point value of the parameter is reported as the best fit value; we cannot quantify our uncertainty about the parameter estimate. In the main journal article that this methods article accompanies (Jäger et al., 2020, Interference patterns in subject-verb agreement and reflexives revisited: A large-sample study, Journal of Memory and Language), we carried out parameter estimation using Approximate Bayesian Computation (ABC), which is a Bayesian approach that allows us to quantify our uncertainty about the parameter's values given data. This customization has the further advantage that it allows us to generate both prior and posterior predictive distributions of reading times from the cue-based retrieval model of Lewis and Vasishth, 2005. • Instead of the conventional method of using grid search, we use Approximate Bayesian Computation (ABC) for parameter estimation in the [4] model. • The ABC method of parameter estimation has the advantage that the uncertainty of the parameter can be quantified.

Abstract Background Insecticides used against Aedes aegypti and other disease vectors can elicit a multitude of dose-dependent effects on behavioral and bionomic traits. Estimating the potential epidemiological impact of a product requires thorough understanding of these effects and their interplay at different dosages. Volatile spatial repellent (SR) products come with an additional layer of complexity due to the potential for altered movement of affected mosquitoes and diffusion of volatile particles of the product beyond the treated house. Here, we propose a paired experimental design and statistical inference framework for estimating these nuanced effects of volatile SRs. Method We fitted a continuous-time Markov chain model in a Bayesian framework to data on marked mosquitoes released in interconnected experimental huts conducted in Iquitos, Peru. We estimated the effects of two dosages of transfluthrin on Ae. aegypti behaviors associated with human-vector contact: repellency, exiting and knockdown in the treated space and in connected, adjacent huts. We validated the framework using simulated data. Results The odds of a female Ae. aegypti being repelled, and thus prevented from entering a treated hut (H T), increased at both dosages (low dosage: odds = 1.64, 95% highest density interval (HDI) = 1.30–2.09; high dosage: odds = 1.35, HDI = 1.04–1.67). The relative risk of exiting from the treated hut was reduced (low: RR = 0.70, HDI = 0.62–1.09; high: RR = 0.70, HDI = 0.40–1.06), with this effect carrying over to untreated spaces two huts away from the treated hut (H 2) (low: RR = 0.79, HDI = 0.59–1.01; high: RR = 0.66, HDI = 0.50–0.87). Knockdown rates were increased in both treated and downstream huts, particularly under high dosage (H T: RR = 8.37, HDI = 2.11–17.35; H 1: RR = 1.39, HDI = 0.52–2.69; H 2: RR = 2.22, HDI = 0.96–3.86). Conclusions Our framework is effective at elucidating multiple effects of volatile chemicals used in SR products, as well as their downstream effects. For the examined formulations of transfluthrin, we found notable dose-dependent effects on repellency, movement and knockdown that carry over to adjacent, untreated spaces.

A common goal is extraction of physico‐chemical parameter values such as pre‐exponentials and activation energies from experiment. Ever increasing knowledge from experiments and computations is enabling semi‐quantitative prior predictions of such values. When prior knowledge of physically realistic ranges is available, a method named Bayesian parameter estimation (BPE) enables more physically realistic parameter estimation relative to unsophisticated fitting by seeking the most probable value when considering together the uncertainties from prior knowledge, experimental data, and approximations in the model. An impediment to widespread use of BPE is a lack of understanding, training, and user‐friendly software. Along with this invited publication, a general software package for BPE is being released that is user‐friendly and that does not require understanding of the math behind the methodology. Two previously unpublished catalysis science examples are provided along with considerations and guidelines for successful application of BPE. Following this work, BPE can become more widespread to enable extraction of physically meaningful parameter values. [ABSTRACT FROM AUTHOR]

Evidence accumulation models have been one of the most dominant modeling frameworks used to study rapid decision-making over the past several decades. These models propose that evidence accumulates from the environment until the evidence for one alternative reaches some threshold, typically associated with caution, triggering a response. However, researchers have recently begun to reconsider the fundamental assumptions of how caution varies with time. In the past, it was typically assumed that levels of caution are independent of time. Recent investigations have however suggested the possibility that levels of caution decrease over time and that this strategy provides more efficient performance under certain conditions. Our study provides the first comprehensive assessment of this newer class of models accounting for time-varying caution to determine how robustly their parameters can be estimated. We assess five overall variants of collapsing threshold/urgency signal models based on the diffusion decision model, linear ballistic accumulator model, and urgency gating model frameworks. We find that estimation of parameters, particularly those associated with caution/urgency modulation are most robust for the linearly collapsing threshold diffusion model followed by an urgency-gating model with a leakage process. All other models considered, particularly those with ballistic accumulation or nonlinear thresholds, are unable to recover their own parameters adequately, making their usage in parameter estimation contexts questionable. [ABSTRACT FROM AUTHOR]

In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and the principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be more sensitive to potential departures from general relativity (GR). We extend previous works by employing Bayesian parameter estimation and performing both tests with injections of GR and injections of subtle GR-violated signals. We also apply multi-parameter tests with PCA in the phenomenological test of GW propagation. This work complements previous works and further demonstrates the enhancement provided by the PCA method. Considering a supermassive black hole binary system as the GW source, we show that subtle departures will be more obvious in posteriors of PCA parameters. The departures less than 1 σ in original parameters can yield significant departures in first 5 dominant PCA parameters. • Multi-parameter tests of GW generation and propagation. • PCA is helpful in capturing potential subtle departures. • Using the Bayesian tool in parameter estimation. [ABSTRACT FROM AUTHOR]

Medicinal herb collection has historical and cultural roots in many rural communities in developing countries. Areas where herb collection occurs may overlap with biodiversity hotspots and crucial habitat of endangered and threatened species. However, impacts of such practices on wildlife are unknown and possibly underestimated, perhaps due to the elusive nature of such activities. We examined this phenomenon in Wolong Nature Reserve, China, a protected area in the South‐Central China biodiversity hotspot that also supports a community of Tibetan, Qiang and Han people who use herb collection as a supplementary source of livelihood. We adopted a participatory approach in which we engaged local people in outlining spatial and temporal dynamics of medicinal herb collection practices. We found that the overall spatial extent of herb collection increased in the past two decades. We then overlaid herb collection maps with localities of giant panda (Ailuropoda melanoleuca) feces collected over two time points in the reserve. Using a Bayesian parameter estimation, we found evidence for declined giant panda occurrence in the areas most recently impacted by emerging medicinal herb collection. Our methodology demonstrates the potential power of integrating participatory approaches with quantitative methods for processes like herb collection that may be difficult to examine empirically. We discuss future directions for improving explanatory power and addressing uncertainty in this type of mixed‐method, interdisciplinary research. This work has implications for future attempts to understand whether and how prevalent but subtle human activities may affect wildlife conservation. [ABSTRACT FROM AUTHOR]

This paper addresses the application of a Bayesian parameter estimation method to a regional seismic risk assessment of curved concrete bridges. For this purpose, numerical models of case-study bridges are simulated to generate multiparameter demand models of components, consisting of various uncertainty parameters and an intensity measure (IM). The demand models are constructed using a Bayesian parameter estimation method and combined with limit states to derive the parameterized fragility curves. These fragility curves are used to develop bridge-specific and bridge-class fragility curves. Moreover, a stepwise removal process in the Bayesian parameter estimation is performed to identify significant parameters affecting component demands. [ABSTRACT FROM AUTHOR]

Hightlights • Efficient approach to accurately predict the End of Discharge in Li–Po batteries. • A simplified battery model that allows improving efficiency in prognostics. • A practical aerodynamic-based model for the power consumption in multirotors. • A novel correction loop that diminishes bias in recursive Bayesian estimation. Abstract This article presents a holistic framework for the design, implementation and experimental validation of Battery Management Systems (BMS) in rotatory-wing Unmanned Aerial Vehicles (UAVs) that allows to accurately (i) estimate the State of Charge (SOC), and (ii) predict the End of Discharge (EOD) time of lithium-polymer batteries in small-size multirotors by using a model-based prognosis architecture that is efficient and feasible to implement in low-cost hardware. The proposed framework includes a simplified battery model that incorporates the electric load dependence, temperature dependence and SOC dependence by using the concept of Artificial Evolution to estimate some of its parameters, along with a novel Outer Feedback Correction Loop (OFCL) during the estimation stage which adjusts the variance of the process noise to diminish bias in Bayesian state estimation and helps to compensate problems associated with incorrect initial conditions in a non-observable dynamic system. Also, it provides an aerodynamic-based characterization of future power consumption profiles. A quadrotor has been used as validation platform. The results of this work will allow making decisions about the flight plan and having enough confidence in those decisions so that the mission objectives can be optimally achieved. [ABSTRACT FROM AUTHOR]

Abstract We present a method for localizing an unknown source of radiation in an urban environment using a distributed detector network. This method employs statistical parameter estimation techniques, relying on an approximation for the response of a detector to the source based on a simplified model of the underlying transport phenomena, combined with a Metropolis-type sampler that is modified to propagate the effect of fixed epistemic uncertainties in the material macroscopic cross sections of objects in the scene. We apply this technique to data collected during a measurement campaign conducted in a realistic analog for an urban scene using a network of six mobile detectors. Our initial results are able to localize the source to within approximately 8 m over a scene of size 300 m × 200 m in two independent trials with 30 min count times, including a characterization of the uncertainty associated with the poorly known macroscopic cross sections of objects in the scene. In these measurements, the nearest detectors were between 20 m to 30 m from the source, and recorded count rates between approximately 3 and 13 times background. A few detectors had line-of-sight to the source, while the majority were obscured by objects present in the scene. After extending our model to account for the orientation of the detectors and correcting for anomalies in the measurement data we were able to further improve the localization accuracy to approximately 2 m in both trials. [ABSTRACT FROM AUTHOR]

In a lot of dynamic processes, the fractional differential operators not only appear as discrete fractional, but they also have a continuous nature in some sense. In the article, we consider the space fractional coupled nonlinear Schrödinger equations. A Legendre spectral scheme is proposed for obtaining the numerical solution of the considered equations. The convergence analysis of the numerical method is discussed, and it is shown to be convergent of spectral accuracy in space and second-order accuracy in time. The conservation laws of the fully discrete system are analyzed rigorously. Moreover, the Bayesian method is given to estimate many parameters of this system. Some numerical results are presented to verify the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This study started from the request of providing predictions on hospitalization and Intensive Care Unit (ICU) rates that are caused by COVID-19 for the Umbria region in Italy. To this purpose, we propose the application of a computational framework to a SEIR-type (Susceptible, Exposed, Infected, Removed) epidemiological model describing the different stages of COVID-19 infection. The model discriminates between asymptomatic and symptomatic cases and it takes into account possible intervention measures in order to reduce the probability of transmission. As case studies, we analyze not only the epidemic situation in Umbria but also in Italy, in order to capture the evolution of the pandemic at a national level. First of all, we estimate model parameters through a Bayesian calibration method, called Conditional Robust Calibration (CRC), while using the official COVID-19 data of the Italian Civil Protection. Subsequently, Conditional Robustness Analysis (CRA) on the calibrated model is carried out in order to quantify the influence of epidemiological and intervention parameters on the hospitalization rates. The proposed pipeline properly describes the COVID-19 spread during the lock-down phase. It also reveals the underestimation of new positive cases and the need of promptly isolating asymptomatic and presymptomatic cases. The results emphasize the importance of the lock-down timeliness and provide accurate predictions on the current evolution of the pandemic.