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Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this…

This paper investigates two environmental applications related to climate change, where observations consist of bounded counts. The binomial and beta-binomial (BB) models are commonly used for bounded count data, with the BB model offering…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive…

Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…

The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the…

Bayesian models that can handle both over and under dispersed counts are rare in the literature, perhaps because full probability distributions for dispersed counts are rather difficult to construct. This note takes a first look at Bayesian…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Although models for count data with over-dispersion have been widely considered in the literature, models for under-dispersion -- the opposite phenomenon -- have received less attention as it is only relatively common in particular research…

Count data are ubiquitous in ecology and the Poisson generalized linear model (GLM) is commonly used to model the association between counts and explanatory variables of interest. When fitting this model to the data, one typically proceeds…

Generalized linear models (GLMs) using a regression procedure to fit relationships between predictor and target variables are widely used in automobile insurance data. Here, in the process of ratemaking and in order to compute the premiums…

Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of…

Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. As a model-based RL method, it has two key components: (1)…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

This paper proposes new linear regression models to deal with overdispersed binomial datasets. These new models, called tilted beta binomial regression models, are defined from the tilted beta binomial distribution, proposed assuming that…

In pre-clinical and medical quality control, it is of interest to assess the stability of the process under monitoring or to validate a current observation using historical control data. Classically, this is done by the application of…

Beta-binomial/Poisson models have been used by many authors to model multivariate count data. Lora and Singer (Statistics in Medicine, 2008) extended such models to accommodate repeated multivariate count data with overdipersion in the…

This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text,…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…