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In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…
This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…
This analysis derives the maximum likelihood estimator and applies Bayesian inference to model geometric Brownian motion, incorporating jump diffusion to account for sudden market shifts. The Bayesian approach is implemented using Markov…
Generalized linear mixed models (GLMM) encompass large class of statistical models, with a vast range of applications areas. GLMM extends the linear mixed models allowing for different types of response variable. Three most common data…
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…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
Background: Mendelian randomization (MR) is a useful approach to causal inference from observational studies when randomised controlled trials are not feasible. However, study heterogeneity of two association studies required in MR is often…
This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution,…
We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder,…
In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…
RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in the model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the overdispersion parameter…
In this paper, we introduce the increasing belief criterion in association rule mining. The criterion uses a recursive application of Bayes' theorem to compute a rule's belief. Extracted rules are required to have their belief increase with…
Bayesian model-averaged meta-analysis allows quantification of evidence for both treatment effectiveness $\mu$ and across-study heterogeneity $\tau$. We use the Cochrane Database of Systematic Reviews to develop discipline-wide empirical…
Evidence accumulation models (EAMs) are an important class of cognitive models used to analyze both response time and response choice data recorded from decision-making tasks. Developments in estimation procedures have helped EAMs become…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and…