Bayesian hierarchical models for the prediction of volleyball results

Statistical modelling of sports data has become more and more popular in the recent years and different types of models have been proposed to achieve a variety of objectives: from identifying the key characteristics which lead a team to win or lose to predicting the outcome of a game or the team rankings in national leagues. Although not as popular as football or basketball, volleyball is a team sport with both national and international level competitions in almost every country. However, there is almost no study investigating the prediction of volleyball game outcomes and team rankings in national leagues. We propose a Bayesian hierarchical model for the prediction of the rankings of volleyball national teams, which also allows to estimate the results of each match in the league. We consider two alternative model specifications of different complexity which are validated using data from the women''s volleyball Italian Serie A1 2017–2018 season.     

Bayesian quantile regression for hierarchical linear models

The paper proposes a Bayesian quantile regression method for hierarchical linear models. Existing approaches of hierarchical linear quantile regression models are scarce and most of them were not from the perspective of Bayesian thoughts, which is important for hierarchical models. In this paper, based on Bayesian theories and Markov Chain Monte Carlo methods, we introduce Asymmetric Laplace distributed errors to simulate joint posterior distributions of population parameters and across-unit parameters and then derive their posterior quantile inferences. We run a simulation as the proposed method to examine the effects on parameters induced by units and quantile levels; the method is also applied to study the relationship between Chinese rural residents' family annual income and their cultivated areas. Both the simulation and real data analysis indicate that the method is effective and accurate.     

Embedding black-box regression techniques into hierarchical Bayesian models

Hierarchical models enable the encoding of a variety of parametric structures. However, when presented with a large number of covariates upon which some component of a model hierarchy depends, the modeller may be unwilling or unable to specify a form for that dependence. Data-mining methods are designed to automatically discover relationships between many covariates and a response surface, easily accommodating non-linearities and higher-order interactions. We present a method of wrapping hierarchical models around data-mining methods, preserving the best qualities of the two paradigms. We fit the resulting semi-parametric models using an approximate Gibbs sampler called HEBBRU. Using a simulated dataset, we show that HEBBRU is useful for exploratory analysis and displays excellent predictive accuracy. Finally, we apply HEBBRU to an ornithological dataset drawn from the eBird database.     

Bayesian hierarchical models for adaptive basket trial designs

Basket trials evaluate a single drug targeting a single genetic variant in multiple cancer cohorts. Empirical findings suggest that treatment efficacy across baskets may be heterogeneous. Most modern basket trial designs use Bayesian methods. These methods require the prior specification of at least one parameter that permits information sharing across baskets. In this study, we provide recommendations for selecting a prior for scale parameters for adaptive basket trials by using Bayesian hierarchical modeling. Heterogeneity among baskets attracts much attention in basket trial research, and substantial heterogeneity challenges the basic assumption of exchangeability of Bayesian hierarchical approach. Thus, we also allowed each stratum-specific parameter to be exchangeable or nonexchangeable with similar strata by using data observed in an interim analysis. Through a simulation study, we evaluated the overall performance of our design based on statistical power and type I error rates. Our research contributes to the understanding of the properties of Bayesian basket trial designs.     

A Bayesian hierarchical model for inference across related reverse phase protein arrays experiments

We consider inference for functional proteomics experiments that record protein activation over time following perturbation under different dose levels of several drugs. The main inference goal is the dependence structure of the selected proteins. A critical challenge is the lack of sufficient data under any one drug and dose level to allow meaningful inference on dependence structure. We propose a hierarchical model to implement the desired inference. The key element of the model is a shared dependence structure on (latent) binary indicators of protein activation.     

Bayesian hierarchical models for linear networks

The purpose of this study is to highlight dangerous motorways via estimating the intensity of accidents and study its pattern across the UK motorway network. Two methods have been developed to achieve this aim. First, the motorway-specific intensity is estimated by using a homogeneous Poisson process. The heterogeneity across motorways is incorporated using two-level hierarchical models. The data structure is multilevel since each motorway consists of junctions that are joined by grouped segments. In the second method, the segment-specific intensity is estimated. The homogeneous Poisson process is used to model accident data within grouped segments but heterogeneity across grouped segments is incorporated using three-level hierarchical models. A Bayesian method via Markov Chain Monte Carlo is used to estimate the unknown parameters in the models and the sensitivity to the choice of priors is assessed. The performance of the proposed models is evaluated by a simulation study and an application to traffic accidents in 2016 on the UK motorway network. The deviance information criterion (DIC) and the widely applicable information criterion (WAIC) are employed to choose between models.     

Bayesian D-optimal designs for exponential regression models

We consider the Bayesian D-optimal design problem for exponential growth models with one, two or three parameters. For the one-parameter model conditions on the shape of the density of the prior distribution and on the range of its support are given guaranteeing that a one-point design is also Bayesian D-optimal within the class of all designs. In the case of two parameters the best two-point designs are determined and for special prior distributions it is proved that these designs are Bayesian D-optimal. Finally, the exponential growth model with three parameters is investigated. The best three-point designs are characterized by a nonlinear equation. The global optimality of these designs cannot be proved analytically and it is demonstrated that these designs are also Bayesian D-optimal within the class of all designs if gamma-distributions are used as prior distributions.     

Evidence of bias in the Eurovision song contest: modelling the votes using Bayesian hierarchical models

The Eurovision Song Contest is an annual musical competition held among active members of the European Broadcasting Union since 1956. The event is televised live across Europe. Each participating country presents a song and receive a vote based on a combination of tele-voting and jury. Over the years, this has led to speculations of tactical voting, discriminating against some participants and thus inducing bias in the final results. In this paper we investigate the presence of positive or negative bias (which may roughly indicate favouritisms or discrimination) in the votes based on geographical proximity, migration and cultural characteristics of the participating countries through a Bayesian hierarchical model. Our analysis found no evidence of negative bias, although mild positive bias does seem to emerge systematically, linking voters to performers.     

Bayesian hierarchical model for the prediction of football results

The problem of modelling football data has become increasingly popular in the last few years and many different models have been proposed with the aim of estimating the characteristics that bring a team to lose or win a game, or to predict the score of a particular match. We propose a Bayesian hierarchical model to fulfil both these aims and test its predictive strength based on data about the Italian Serie A 1991–1992 championship. To overcome the issue of overshrinkage produced by the Bayesian hierarchical model, we specify a more complex mixture model that results in a better fit to the observed data. We test its performance using an example of the Italian Serie A 2007–2008 championship.     

Semiparametric Bayesian hierarchical models for heterogeneous population in nonlinear mixed effect model: application to gastric emptying studies

Gastric emptying studies are frequently used in medical research, both human and animal, when evaluating the effectiveness and determining the unintended side-effects of new and existing medications, diets, and procedures or interventions. It is essential that gastric emptying data be appropriately summarized before making comparisons between study groups of interest and to allow study the comparisons. Since gastric emptying data have a nonlinear emptying curve and are longitudinal data, nonlinear mixed effect (NLME) models can accommodate both the variation among measurements within individuals and the individual-to-individual variation. However, the NLME model requires strong assumptions that are often not satisfied in real applications that involve a relatively small number of subjects, have heterogeneous measurement errors, or have large variation among subjects. Therefore, we propose three semiparametric Bayesian NLMEs constructed with Dirichlet process priors, which automatically cluster sub-populations and estimate heterogeneous measurement errors. To compare three semiparametric models with the parametric model we propose a penalized posterior Bayes factor. We compare the performance of our semiparametric hierarchical Bayesian approaches with that of the parametric Bayesian hierarchical approach. Simulation results suggest that our semiparametric approaches are more robust and flexible. Our gastric emptying studies from equine medicine are used to demonstrate the advantage of our approaches.     

Bayesian neural tree models for nonparametric regression

Frequentist and Bayesian methods differ in many aspects but share some basic optimal properties. In real-life prediction problems, situations exist in which a model based on one of the above paradigms is preferable depending on some subjective criteria. Nonparametric classification and regression techniques, such as decision trees and neural networks, have both frequentist (classification and regression trees (CARTs) and artificial neural networks) as well as Bayesian counterparts (Bayesian CART and Bayesian neural networks) to learning from data. In this paper, we present two hybrid models combining the Bayesian and frequentist versions of CART and neural networks, which we call the Bayesian neural tree (BNT) models. BNT models can simultaneously perform feature selection and prediction, are highly flexible, and generalise well in settings with limited training observations. We study the statistical consistency of the proposed approaches and derive the optimal value of a vital model parameter. The excellent performance of the newly proposed BNT models is shown using simulation studies. We also provide some illustrative examples using a wide variety of standard regression datasets from a public available machine learning repository to show the superiority of the proposed models in comparison to popularly used Bayesian CART and Bayesian neural network models.     

Bayesian model averaging in longitudinal regression models with AR(1) errors with application to a myopia data set

We propose a new iterative algorithm, called model walking algorithm, to the Bayesian model averaging method on the longitudinal regression models with AR(1) random errors within subjects. The Markov chain Monte Carlo method together with the model walking algorithm are employed. The proposed method is successfully applied to predict the progression rates on a myopia intervention trial in children.     

A frequentist assessment of Bayesian inclusion probabilities for screening predictors

Bayesian inclusion probabilities have become a popular tool for variable assessment. From a frequentist perspective, it is often difficult to evaluate these probabilities as typically no Type I error rates are considered, neither are any explorations of power of the methods given. This paper considers how a frequentist may evaluate Bayesian inclusion probabilities for screening predictors. This evaluation looks at both unrestricted and restricted model spaces and develops a framework which a frequentist can utilize inclusion probabilities that preserve Type I error rates. Furthermore, this framework is applied to an analysis of the Arabidopsis thaliana with respect to determining quantitative trait loci associated with cotelydon opening angle.     

Bayesian regression with multivariate linear splines

We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both predictions and local linear parameters. The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data.     

Bayesian factor models in characterizing molecular adaptation

Assessing the selective influence of amino acid properties is important in understanding evolution at the molecular level. A collection of methods and models has been developed in recent years to determine if amino acid sites in a given DNA sequence alignment display substitutions that are altering or conserving a prespecified set of amino acid properties. Residues showing an elevated number of substitutions that favorably alter a physicochemical property are considered targets of positive natural selection. Such approaches usually perform independent analyses for each amino acid property under consideration, without taking into account the fact that some of the properties may be highly correlated. We propose a Bayesian hierarchical regression model with latent factor structure that allows us to determine which sites display substitutions that conserve or radically change a set of amino acid properties, while accounting for the correlation structure that may be present across such properties. We illustrate our approach by analyzing simulated data sets and an alignment of lysin sperm DNA.     

Stochastic models for greenhouse gas emission rate estimation from hydroelectric reservoirs: a Bayesian hierarchical approach

Herein, we propose a fully Bayesian approach to the greenhouse gas emission problem. The goal of this work is to estimate the emission rate of polluting gases from the area flooded by hydroelectric reservoirs. We present models for gas concentration evolution in two ways: first, by proposing them from ordinary differential equation solutions and, second, by using stochastic differential equations with a discretization scheme. Finally, we present techniques to estimate the emission rate for the entire reservoir. In order to carry out the inference, we use the Bayesian framework with Monte Carlo via Markov Chain methods. Discretization schemes over continuous differential equations are used when necessary. These models applied to greenhouse gas emission and Bayesian inference for this purpose are completely new in statistical literature, as far as we know, and contribute to estimate the amount of polluting gases released from hydroelectric reservoirs in Brazil. The proposed models are applied in a real data set and results are presented.     

Bayesian quantile regression for skew-normal linear mixed models

Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples.     

Estimating catch at age from market sampling data by using a Bayesian hierarchical model

Summary.  The paper develops a Bayesian hierarchical model for estimating the catch at age of cod landed in Norway. The model includes covariate effects such as season and gear, and can also account for the within-boat correlation. The hierarchical structure allows us to account properly for the uncertainty in the estimates.     

Conservative prior distributions for variance parameters in hierarchical models

Bayesian hierarchical models typically involve specifying prior distributions for one or more variance components. This is rather removed from the observed data, so specification based on expert knowledge can be difficult. While there are suggestions for “default” priors in the literature, often a conditionally conjugate inverse‐gamma specification is used, despite documented drawbacks of this choice. The authors suggest “conservative” prior distributions for variance components, which deliberately give more weight to smaller values. These are appropriate for investigators who are skeptical about the presence of variability in the second‐stage parameters (random effects) and want to particularly guard against inferring more structure than is really present. The suggested priors readily adapt to various hierarchical modelling settings, such as fitting smooth curves, modelling spatial variation and combining data from multiple sites.     

Parallel Markov chain Monte Carlo for Bayesian hierarchical models with big data,in two stages

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common for the full data set, with most parameters being group specific. Thus, parallel Bayesian MCMC methods that take into account the structure of the model and split the full data set by groups rather than by observations are a more natural approach for analysis. Here, we adapt and extend a recently introduced two-stage Bayesian hierarchical modeling approach, and we partition complete data sets by groups. In stage 1, the group-specific parameters are estimated independently in parallel. The stage 1 posteriors are used as proposal distributions in stage 2, where the target distribution is the full model. Using three-level and four-level models, we show in both simulation and real data studies that results of our method agree closely with the full data analysis, with greatly increased MCMC efficiency and greatly reduced computation times. The advantages of our method versus existing parallel MCMC computing methods are also described.