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The study of animal diets and the proportional contribution that different foods make to their diets is an important task in ecology. Stable Isotope Mixing Models (SIMMs) are an important tool for studying an animal's diet and understanding how the animal interacts with its environment. We present cosimmr, a new R package designed to include covariates when estimating diet proportions in SIMMs, with simple functions to produce plots and summary statistics. The inclusion of covariates allows for users to perform a more in-depth analysis of their system and to gain new insights into the diets of the organisms being studied. A common problem with the previous generation of SIMMs is that they are very slow to produce a posterior distribution of dietary estimates, especially for more complex model structures, such as when covariates are included. The widely-used Markov chain Monte Carlo (MCMC) algorithm used by many traditional SIMMs often requires a very large number of iterations to reach convergence. In contrast, cosimmr uses Fixed Form Variational Bayes (FFVB), which we demonstrate gives up to an order of magnitude speed improvement with no discernible loss of accuracy. We provide a full mathematical description of the model, which includes corrections for trophic discrimination and concentration dependence, and evaluate its performance against the state of the art MixSIAR model. Whilst MCMC is guaranteed to converge to the posterior distribution in the long term, FFVB converges to an approximation of the posterior distribution, which may lead to sub-optimal performance. However we show that the package produces equivalent results in a fraction of the time for all the examples on which we test. The package is designed to be user-friendly and is based on the existing simmr framework.

Modelling growth in student achievement is a significant challenge in the field of education. Understanding how interventions or experiences such as part-time work can influence this growth is also important. Traditional methods like difference-in-differences are effective for estimating causal effects from longitudinal data. Meanwhile, Bayesian non-parametric methods have recently become popular for estimating causal effects from single time point observational studies. However, there remains a scarcity of methods capable of combining the strengths of these two approaches to flexibly estimate heterogeneous causal effects from longitudinal data. Motivated by two waves of data from the High School Longitudinal Study, the NCES' most recent longitudinal study which tracks a representative sample of over 20,000 students in the US, our study introduces a longitudinal extension of Bayesian Causal Forests. This model allows for the flexible identification of both individual growth in mathematical ability and the effects of participation in part-time work. Simulation studies demonstrate the predictive performance and reliable uncertainty quantification of the proposed model. Results reveal the negative impact of part time work for most students, but hint at potential benefits for those students with an initially low sense of school belonging. Clear signs of a widening achievement gap between students with high and low academic achievement are also identified. Potential policy implications are discussed, along with promising areas for future research., Comment: 25 pages, 7 figures, 3 tables

Mycotoxins, toxic secondary metabolites produced by certain fungi, pose significant threats to global food safety and public health. These compounds can contaminate a variety of crops, leading to economic losses and health risks to both humans and animals. Traditional lab analysis methods for mycotoxin detection can be time-consuming and may not always be suitable for large-scale screenings. However, in recent years, machine learning (ML) methods have gained popularity for use in the detection of mycotoxins and in the food safety industry in general, due to their accurate and timely predictions. We provide a systematic review on some of the recent ML applications for detecting/predicting the presence of mycotoxin on a variety of food ingredients, highlighting their advantages, challenges, and potential for future advancements. We address the need for reproducibility and transparency in ML research through open access to data and code. An observation from our findings is the frequent lack of detailed reporting on hyperparameters in many studies as well as a lack of open source code, which raises concerns about the reproducibility and optimisation of the ML models used. The findings reveal that while the majority of studies predominantly utilised neural networks for mycotoxin detection, there was a notable diversity in the types of neural network architectures employed, with convolutional neural networks being the most popular., Comment: 39 pages, 8 figures, review paper

In recent years, theoretical results and simulation evidence have shown Bayesian additive regression trees to be a highly-effective method for nonparametric regression. Motivated by cost-effectiveness analyses in health economics, where interest lies in jointly modelling the costs of healthcare treatments and the associated health-related quality of life experienced by a patient, we propose a multivariate extension of BART applicable in regression and classification analyses with several correlated outcome variables. Our framework overcomes some key limitations of existing multivariate BART models by allowing each individual response to be associated with different ensembles of trees, while still handling dependencies between the outcomes. In the case of continuous outcomes, our model is essentially a nonparametric version of seemingly unrelated regression. Likewise, our proposal for binary outcomes is a nonparametric generalisation of the multivariate probit model. We give suggestions for easily interpretable prior distributions, which allow specification of both informative and uninformative priors. We provide detailed discussions of MCMC sampling methods to conduct posterior inference. Our methods are implemented in the R package `suBART'. We showcase their performance through extensive simulations and an application to an empirical case study from health economics. By also accommodating propensity scores in a manner befitting a causal analysis, we find substantial evidence for a novel trauma care intervention's cost-effectiveness.

With the rapid development of Additive Manufacturing (AM) comes an urgent need for advanced monitoring and control of the process. Many aspects of the AM process play a significant role in the efficiency, accuracy and repeatability of the process, with temperature regulation being one of the most important ones. In this work, we solve the problem of optimal tracking control for a state space temperature model of a Big Area Additive Manufacturing (BAAM) system. In particular, we address the problem of designing a Linear Quadratic Tracking (LQT) controller when access to the exact system state is not possible, except in the form of measurements. We initially solve the problem with a model-based approach based on reinforcement learning concepts, with state estimation through an observer. We then design a model-free reinforcement-learning based controller with an internal state estimation step and demonstrate its performance through a simulator of the systems' behaviour. Our results showcase the possibility of achieving comparable results while learning optimal policies directly from process data, without the need for an accurate, intricate model of the process. We consider this outcome to be a significant stride towards autonomous intelligent manufacturing.

Designing efficient closed-loop control algorithms is a key issue in Additive Manufacturing (AM), as various aspects of the AM process require continuous monitoring and regulation, with temperature being a particularly significant factor. Here we study closed-loop control of a state space temperature model with a focus on both model-based and data-driven methods. We demonstrate these approaches using a simulator of the temperature evolution in the extruder of a Big Area Additive Manufacturing system (BAAM). We perform an in-depth comparison of the performance of these methods using the simulator. We find that we can learn an effective controller using solely simulated process data. Our approach achieves parity in performance compared to model-based controllers and so lessens the need for estimating a large number of parameters of the intricate and complicated process model. We believe this result is an important step towards autonomous intelligent manufacturing.

We present reslr, an R package to perform Bayesian modelling of relative sea level data. We include a variety of different statistical models previously proposed in the literature, with a unifying framework for loading data, fitting models, and summarising the results. Relative sea-level data often contain measurement error in multiple dimensions and so our package allows for these to be included in the statistical models. When plotting the output sea level curves, the focus is often on comparing rates of change, and so our package allows for computation of the derivative of sea level curves with appropriate consideration of the uncertainty. We provide a large example dataset from the Atlantic coast of North America and show some of the results that might be obtained from our package.

We introduce an R package for fitting Stable Isotope Mixing Models (SIMMs) via both Markov chain Monte Carlo and Variational Bayes. The package is mainly used for estimating dietary contributions from food sources taken via measurements of stable isotope ratios from animals. It can also be used to estimate proportional contributions of a mixture from known sources, for example apportionment of river sediment, amongst many other use cases. The package contains a simple structure which allows non-expert users to interface with the package, with most of the computational complexity hidden behind the main fitting functions. In this paper we detail the background to these functions and provide case studies on how the package should be used. Further examples are available in the online package vignettes., Comment: 27 pages, 9 figures

Environmental monitoring is crucial to our understanding of climate change, biodiversity loss and pollution. The availability of large-scale spatio-temporal data from sources such as sensors and satellites allows us to develop sophisticated models for forecasting and understanding key drivers. However, the data collected from sensors often contain missing values due to faulty equipment or maintenance issues. The missing values rarely occur simultaneously leading to data that are multivariate misaligned sparse time series. We propose two models that are capable of performing multivariate spatio-temporal forecasting while handling missing data naturally without the need for imputation. The first model is a transformer-based model, which we name SERT (Spatio-temporal Encoder Representations from Transformers). The second is a simpler model named SST-ANN (Sparse Spatio-Temporal Artificial Neural Network) which is capable of providing interpretable results. We conduct extensive experiments on two different datasets for multivariate spatio-temporal forecasting and show that our models have competitive or superior performance to those at the state-of-the-art., Comment: 11 pages, 7 figures

Bayesian Causal Forests (BCF) is a causal inference machine learning model based on a highly flexible non-parametric regression and classification tool called Bayesian Additive Regression Trees (BART). Motivated by data from the Trends in International Mathematics and Science Study (TIMSS), which includes data on student achievement in both mathematics and science, we present a multivariate extension of the BCF algorithm. With the help of simulation studies we show that our approach can accurately estimate causal effects for multiple outcomes subject to the same treatment. We also apply our model to Irish data from TIMSS 2019. Our findings reveal the positive effects of having access to a study desk at home (Mathematics ATE 95% CI: [0.20, 11.67]) while also highlighting the negative consequences of students often feeling hungry at school (Mathematics ATE 95% CI: [-11.15, -2.78] , Science ATE 95% CI: [-10.82,-1.72]) or often being absent (Mathematics ATE 95% CI: [-12.47, -1.55])., Comment: 26 pages, 6 figures

We propose a Bayesian, noisy-input, spatial-temporal generalised additive model to examine regional relative sea-level (RSL) changes over time. The model provides probabilistic estimates of component drivers of regional RSL change via the combination of a univariate spline capturing a common regional signal over time, random slopes and intercepts capturing site-specific (local), long-term linear trends and a spatial-temporal spline capturing residual, non-linear, local variations. Proxy and instrumental records of RSL and corresponding measurement errors inform the model and a noisy-input method accounts for proxy temporal uncertainties. Results focus on the decomposition of RSL over the past 3000 years along the Atlantic coast of North America.

We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the model. Simulation experiments show that our method out-performs previous related models and machine learning algorithms under different sample sizes and degrees of complexity. We further explore the applicability of our model by analysing real-world data related to wheat production across Ireland from 2010 to 2019. Our model performs competitively and overcomes key limitations found in other analogous approaches. Finally, we adapt a set of visualisations for the posterior distribution of the tensor effects that facilitate the identification of optimal interactions between the tensor variables whilst accounting for the uncertainty in the posterior distribution.

Passive acoustic monitoring is used widely in ecology, biodiversity, and conservation studies. Data sets collected via acoustic monitoring are often extremely large and built to be processed automatically using Artificial Intelligence and Machine learning models, which aim to replicate the work of domain experts. These models, being supervised learning algorithms, need to be trained on high quality annotations produced by experts. Since the experts are often resource-limited, a cost-effective process for annotating audio is needed to get maximal use out of the data. We present an open-source interactive audio data annotation tool, NEAL (Nature+Energy Audio Labeller). Built using R and the associated Shiny framework, the tool provides a reactive environment where users can quickly annotate audio files and adjust settings that automatically change the corresponding elements of the user interface. The app has been designed with the goal of having both expert birders and citizen scientists contribute to acoustic annotation projects. The popularity and flexibility of R programming in bioacoustics means that the Shiny app can be modified for other bird labelling data sets, or even to generic audio labelling tasks. We demonstrate the app by labelling data collected from wind farm sites across Ireland.

We present vivid, an R package for visualizing variable importance and variable interactions in machine learning models. The package provides a range of displays including heatmap and graph-based displays for viewing variable importance and interaction jointly and partial dependence plots in both a matrix layout and an alternative layout emphasizing important variable subsets. With the intention of increasing a machine learning models' interpretability and making the work applicable to a wider readership, we discuss the design choices behind our implementation by focusing on the package structure and providing an in-depth look at the package functions and key features. We also provide a practical illustration of the software in use on a data set., Comment: 15 pages, 7 figures

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across various fields of sciences, including but not limited to biology, (bio)chemistry, engineering, environmental science, medical science, psychology, social science, etc. The phenomenal growth of the application of functional data clustering indicates the urgent need for a systematic approach to develop efficient clustering methods and scalable algorithmic implementations. On the other hand, there is abundant literature on the cluster analysis of time series, trajectory data, spatio-temporal data, etc., which are all related to functional data. Therefore, an overarching structure of existing functional data clustering methods will enable the cross-pollination of ideas across various research fields. We here conduct a comprehensive review of original clustering methods for functional data. We propose a systematic taxonomy that explores the connections and differences among the existing functional data clustering methods and relates them to the conventional multivariate clustering methods. The structure of the taxonomy is built on three main attributes of a functional data clustering method and therefore is more reliable than existing categorizations. The review aims to bridge the gap between the functional data analysis community and the clustering community and to generate new principles for functional data clustering.

Turbidity is commonly monitored as an important water quality index. Human activities, such as dredging and dumping operations, can disrupt turbidity levels and should be monitored and analyzed for possible effects. In this paper, we model the variations of turbidity in Dublin Bay over space and time to investigate the effects of dumping and dredging while controlling for the effect of wind speed as a common atmospheric effect. We develop a novel Vector Auto-Regressive Conditional Heteroskedasticity (VARCH) approach to modelling the dynamical behaviour of turbidity over different locations and at different water depths. We use daily values of turbidity during the years 2017-2018 to fit the model. We show that the results of our fitted model are in line with the observed data and that the uncertainties, measured through Bayesian credible intervals, are well calibrated. Furthermore, we show that the daily effects of dredging and dumping on turbidity are negligible in comparison to that of wind speed., Comment: 11 pages, 9 figures

Tree-based regression and classification has become a standard tool in modern data science. Bayesian Additive Regression Trees (BART) has in particular gained wide popularity due its flexibility in dealing with interactions and non-linear effects. BART is a Bayesian tree-based machine learning method that can be applied to both regression and classification problems and yields competitive or superior results when compared to other predictive models. As a Bayesian model, BART allows the practitioner to explore the uncertainty around predictions through the posterior distribution. In this paper, we present new visualization techniques for exploring BART models. We construct conventional plots to analyze a model's performance and stability as well as create new tree-based plots to analyze variable importance, interaction, and tree structure. We employ Value Suppressing Uncertainty Palettes (VSUP) to construct heatmaps that display variable importance and interactions jointly using color scale to represent posterior uncertainty. Our new visualizations are designed to work with the most popular BART R packages available, namely BART, dbarts, and bartMachine. Our approach is implemented in the R package bartMan (BART Model ANalysis)., Comment: 25 pages, 15 figures

In plant breeding the presence of a genotype by environment (GxE) interaction has a strong impact on cultivation decision making and the introduction of new crop cultivars. The combination of linear and bilinear terms has been shown to be very useful in modelling this type of data. A widely-used approach to identify GxE is the Additive Main Effects and Multiplicative Interaction Effects (AMMI) model. However, as data frequently can be high-dimensional, Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible. In this article, we consider a variational inference approach for such a model. We derive variational approximations for estimating the parameters and we compare the approximations to MCMC using both simulated and real data. The new inferential framework we propose is on average two times faster whilst maintaining the same predictive performance as MCMC.

We propose a simple yet powerful extension of Bayesian Additive Regression Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for random effects to be included at the terminal node level of a set of regression trees, making HE-BART a non-parametric alternative to mixed effects models which avoids the need for the user to specify the structure of the random effects in the model, whilst maintaining the prediction and uncertainty calibration properties of standard BART. Using simulated and real-world examples, we demonstrate that this new extension yields superior predictions for many of the standard mixed effects models' example data sets, and yet still provides consistent estimates of the random effect variances. In a future version of this paper, we outline its use in larger, more advanced data sets and structures.

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

We propose a Bayesian hierarchical model which produces probabilistic reconstructions of hydroclimatic variability in Queensland Australia. The model provides a standardised approach to hydroclimate reconstruction using multiple palaeoclimate proxy records derived from natural archives such as speleothems, ice cores and tree rings. The method combines time-series modelling with inverse prediction to quantify the relationships between a given hydroclimate index and relevant proxies over an instrumental period and subsequently reconstruct the hydroclimate back through time. We present case studies for Brisbane and Fitzroy catchments focusing on two hydroclimate indices, the Rainfall Index (RFI) and the Standardised Precipitation-Evapotranspiration Index (SPEI). The probabilistic nature of the reconstructions allows us to estimate the probability that a hydroclimate index in any reconstruction year was lower (higher) than the minimum (maximum) value observed over the instrumental period. In Brisbane, the RFI is unlikely (probabilities < 20%) to have exhibited extremes beyond the minimum/maximum values observed between 1889 and 2017. However, in Fitzroy there are several years during the reconstruction period where the RFI is likely (> 50% probability) to have exhibited behaviour beyond the minimum/maximum of what has been observed. For SPEI, the probability of observing such extremes since the end of the instrumental period in 1889 doesn't exceed 50% in any reconstruction year in Brisbane or Fitzroy., Comment: 20 pages, 10 figures

We investigate the changing nature of the frequency, magnitude and spatial extent of extreme temperatures in Ireland from 1931 to 2022. We develop an extreme value model that captures spatial and temporal non-stationarity in extreme daily maximum temperature data. We model the tails of the marginal variables using the generalised Pareto distribution and the spatial dependence of extreme events by a semi-parametric Brown-Resnick r-generalised Pareto process, with parameters of each model allowed to change over time. We use weather station observations for modelling extreme events since data from climate models (not conditioned on observational data) can over-smooth these events and have trends determined by the specific climate model configuration. However, climate models do provide valuable information about the detailed physiography over Ireland and the associated climate response. We propose novel methods which exploit the climate model data to overcome issues linked to the sparse and biased sampling of the observations. Our analysis identifies a temporal change in the marginal behaviour of extreme temperature events over the study domain, which is much larger than the change in mean temperature levels over this time window. We illustrate how these characteristics result in increased spatial coverage of the events that exceed critical temperatures.

We propose an extension of the N-mixture model which allows for the estimation of both abundances of multiple species simultaneously and their inter-species correlations. We also propose further extensions to this multi-species N-mixture model, one of which permits us to examine data which has an excess of zero counts, and another which allows us to relax the assumption of closure inherent in N-mixture models through the incorporation of an AR term in the abundance. The inclusion of a multivariate normal distribution as prior on the random effect in the abundance facilitates the estimation of a matrix of interspecies correlations. Each model is also fitted to avian point data collected as part of the NABBS 2010-2019. Results of simulation studies reveal that these models produce accurate estimates of abundance, inter-species correlations and detection probabilities at both small and large sample sizes, in scenarios with small, large and no zero inflation. Results of model-fitting to the North American Breeding Bird Survey data reveal an increase in Bald Eagle population size in southeastern Alaska in the decade examined.Our novel multi-species N-mixture model accounts for full communities, allowing us to examine abundances of every species present in a study area and, as these species do not exist in a vacuum, allowing us to estimate correlations between species' abundances.While previous multi-species abundance models have allowed for the estimation of abundance and detection probability, ours is the first to address the estimation of both positive and negative inter-species correlations, which allows us to begin to make inferences as to the effect that these species' abundances have on one another. Our modelling approach provides a method of quantifying the strength of association between species' population sizes, and is of practical use to population and conservation ecologists., Comment: 60 pages, 4 figures

We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear component is responsible for estimating the main effects and BART accounts for non-specified interactions and non-linearities. Previous semi-parametric models based on BART have assumed that the set of covariates in the linear predictor and the BART model are mutually exclusive in an attempt to avoid poor coverage properties and reduce bias in the estimates of the parameters in the linear predictor. The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with this bias and resolve non-identifiability issues between the parametric and non-parametric components, even when they have covariates in common. This allows us to model complex interactions involving the covariates of primary interest, both among themselves and with those in the BART component. Our novel method is developed with a view to analysing data from an international education assessment, where certain predictors of students' achievements in mathematics are of particular interpretational interest. Through additional simulation studies and another application to a well-known benchmark dataset, we also show competitive performance when compared to regression models, alternative formulations of semi-parametric BART, and other tree-based methods. The implementation of the proposed method is available at \url{https://github.com/ebprado/CSP-BART}., Comment: 48 pages, 8 tables, 10 figures

Variable importance, interaction measures, and partial dependence plots are important summaries in the interpretation of statistical and machine learning models. In this paper we describe new visualization techniques for exploring these model summaries. We construct heatmap and graph-based displays showing variable importance and interaction jointly, which are carefully designed to highlight important aspects of the fit. We describe a new matrix-type layout showing all single and bivariate partial dependence plots, and an alternative layout based on graph Eulerians focusing on key subsets. Our new visualizations are model-agnostic and are applicable to regression and classification supervised learning settings. They enhance interpretation even in situations where the number of variables is large. Our R package vivid (variable importance and variable interaction displays) provides an implementation., Comment: 31 pages, 10 figures

Bayesian optimization (BO) is an approach to globally optimizing black-box objective functions that are expensive to evaluate. BO-powered experimental design has found wide application in materials science, chemistry, experimental physics, drug development, etc. This work aims to bring attention to the benefits of applying BO in designing experiments and to provide a BO manual, covering both methodology and software, for the convenience of anyone who wants to apply or learn BO. In particular, we briefly explain the BO technique, review all the applications of BO in additive manufacturing, compare and exemplify the features of different open BO libraries, unlock new potential applications of BO to other types of data (e.g., preferential output). This article is aimed at readers with some understanding of Bayesian methods, but not necessarily with knowledge of additive manufacturing; the software performance overview and implementation instructions are instrumental for any experimental-design practitioner. Moreover, our review in the field of additive manufacturing highlights the current knowledge and technological trends of BO. This article has a supplementary material online.

The outbreak of a novel coronavirus causing severe acute respiratory syndrome in December 2019 has escalated into a worldwide pandemic. In this work, we propose a compartmental model to describe the dynamics of transmission of infection and use it to obtain the optimal vaccination control. The model accounts for the various stages of the vaccination and the optimisation is focused on minimising the infections to protect the population and relieve the healthcare system. As a case study we selected the Republic of Ireland. We use data provided by Ireland's COVID-19 Data-Hub and simulate the evolution of the pandemic with and without the vaccination in place for two different scenarios, one representative of a national lockdown situation and the other indicating looser restrictions in place. One of the main findings of our work is that the optimal approach would involve a vaccination programme where the older population is vaccinated in larger numbers earlier while simultaneously part of the younger population also gets vaccinated to lower the risk of transmission between groups. We compare our simulated results with that of the vaccination policy taken by the Irish government to explore the advantages of our optimisation method. Our comparison suggests that a similar reduction in cases may have been possible even with a reduced set of vaccinations being available for use.

X-ray ptychography has revolutionised nanoscale phase contrast imaging at large-scale synchrotron sources in recent years. We present here the first successful demonstration of the technique in a small-scale laboratory setting. We conducted an experiment with a liquid metal-jet X-ray source and a single photon-counting detector with a high spectral resolution. The experiment used a spot size of 5 microns to produce a ptychographic phase image of a Siemens star test pattern with a sub-micron spatial resolution. The result and methodology presented show how high-resolution phase contrast imaging can now be performed at small-scale laboratory sources worldwide., Comment: 14 pages, 4 figures

We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and Zero-Inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as Implicit and Explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by-product of OD modelling. The central objective in such analyses is often concerned with inference on the effect of covariates on the mean, in light of the apparent excess of zeros in the counts. Typically the modelling of the excess zeros per se is a secondary objective and there are choices to be made between, and within, the OD and ZI approaches. The contribution of this paper is primarily conceptual. We contrast, descriptively, the impact on zeros of the two approaches. We further offer a novel descriptive characterisation of alternative ZI models, including the classic hurdle and mixture models, by providing a unifying theoretical framework for their comparison. This in turn leads to a novel and technically simpler ZI model. We develop the underlying theory for univariate counts and touch on its implication for multivariate count data., Comment: 41 pages, 3 figures, 1 table

We develop a new approach for feature selection via gain penalization in tree-based models. First, we show that previous methods do not perform sufficient regularization and often exhibit sub-optimal out-of-sample performance, especially when correlated features are present. Instead, we develop a new gain penalization idea that exhibits a general local-global regularization for tree-based models. The new method allows for more flexibility in the choice of feature-specific importance weights. We validate our method on both simulated and real data and implement itas an extension of the popular R package ranger., Comment: 13 pages, 2 figures

Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners and is very flexible for predicting in the presence of non-linearity and high-order interactions. In this paper, we introduce an extension of BART, called Model Trees BART (MOTR-BART), that considers piecewise linear functions at node levels instead of piecewise constants. In MOTR-BART, rather than having a unique value at node level for the prediction, a linear predictor is estimated considering the covariates that have been used as the split variables in the corresponding tree. In our approach, local linearities are captured more efficiently and fewer trees are required to achieve equal or better performance than BART. Via simulation studies and real data applications, we compare MOTR-BART to its main competitors. R code for MOTR-BART implementation is available at https://github.com/ebprado/MOTR-BART.

The detection of anomalies in real time is paramount to maintain performance and efficiency across a wide range of applications including web services and smart manufacturing. This paper presents a novel algorithm to detect anomalies in streaming time series data via statistical learning. We adapt the generalised extreme studentised deviate test [1] to streaming data by using a sliding window approach. This is made computationally feasible by recursive updates of the Grubbs test statistic [2]. Moreover, a priority queue [3] is employed to reduce memory requirements, where subsets of the required data streaming window are maintained in the algorithm rather than the full list. Our method is statistically principled. It is suitable for streaming data and it outperforms the AnomalyDetection software package, recently released by Twitter Inc. (Twitter) [4] and used by multiple teams at Twitter as their state of the art on a daily basis [5]. The methodology is demonstrated using an example of unlabelled data from the Twitter AnomalyDetection GitHub repository and using a real manufacturing example with labelled anomalies.

In this study, we begin a comprehensive characterisation of temperature extremes in Ireland for the period 1981-2010. We produce return levels of anomalies of daily maximum temperature extremes for an area over Ireland, for the 30-year period 1981-2010. We employ extreme value theory (EVT) to model the data using the generalised Pareto distribution (GPD) as part of a three-level Bayesian hierarchical model. We use predictive processes in order to solve the computationally difficult problem of modelling data over a very dense spatial field. To our knowledge, this is the first study to combine predictive processes and EVT in this manner. The model is fit using Markov chain Monte Carlo (MCMC) algorithms. Posterior parameter estimates and return level surfaces are produced, in addition to specific site analysis at synoptic stations, including Casement Aerodrome and Dublin Airport. Observational data from the period 2011-2018 is included in this site analysis to determine if there is evidence of a change in the observed extremes. An increase in the frequency of extreme anomalies, but not the severity, is observed for this period. We found that the frequency of observed extreme anomalies from 2011-2018 at the Casement Aerodrome and Phoenix Park synoptic stations exceed the upper bounds of the credible intervals from the model by 20% and 7% respectively.

We examined the use of three conventional anomaly detection methods and assess their potential for on-line tool wear monitoring. Through efficient data processing and transformation of the algorithm proposed here, in a real-time environment, these methods were tested for fast evaluation of cutting tools on CNC machines. The three-dimensional force data streams we used were extracted from a turning experiment of 21 runs for which a tool was run until it generally satisfied an end-of-life criterion. Our real-time anomaly detection algorithm was scored and optimised according to how precisely it can predict the progressive wear of the tool flank. Most of our tool wear predictions were accurate and reliable as illustrated in our off-line simulation results. Particularly when the multivariate analysis was applied, the algorithm we develop was found to be very robust across different scenarios and against parameter changes. It shall be reasonably easy to apply our approach elsewhere for real-time tool wear analytics.

Characterizing the spatio-temporal variability of relative sea level (RSL) and estimating local, regional, and global RSL trends requires statistical analysis of RSL data. Formal statistical treatments, needed to account for the spatially and temporally sparse distribution of data and for geochronological and elevational uncertainties, have advanced considerably over the last decade. Time-series models have adopted more flexible and physically-informed specifications with more rigorous quantification of uncertainties. Spatio-temporal models have evolved from simple regional averaging to frameworks that more richly represent the correlation structure of RSL across space and time. More complex statistical approaches enable rigorous quantification of spatial and temporal variability, the combination of geographically disparate data, and the separation of the RSL field into various components associated with different driving processes. We review the range of statistical modeling and analysis choices used in the literature, reformulating them for ease of comparison in a common hierarchical statistical framework. The hierarchical framework separates each model into different levels, clearly partitioning measurement and inferential uncertainty from process variability. Placing models in a hierarchical framework enables us to highlight both the similarities and differences among modeling and analysis choices. We illustrate the implications of some modeling and analysis choices currently used in the literature by comparing the results of their application to common datasets within a hierarchical framework. In light of the complex patterns of spatial and temporal variability exhibited by RSL, we recommend non-parametric approaches for modeling temporal and spatio-temporal RSL., Comment: 30 pages, 7 figures

We propose a new framework for the modelling of count data exhibiting zero inflation (ZI). The main part of this framework includes a new and more general parameterisation for ZI models which naturally includes both over- and under-inflation. It further sheds new theoretical light on modelling and inference and permits a simpler alternative, which we term as multiplicative, in contrast to the dominant mixture and hurdle models. Our approach gives the statistician access to new types of ZI of which mixture and hurdle are special cases. We outline a simple parameterised modelling approach which can help to infer both ZI type and degree and provide an underlying treatment that shows that current ZI models are themselves typically within the exponential family, thus permitting much simpler theory, computation and classical inference. We outline some possibilities for a natural Bayesian framework for inference; and a rich basis for work on correlated ZI counts. The present paper is an incomplete report on the underlying theory. A later version will include computational issues and provide further examples., Comment: 24 pages, 3 figures