Related papers: Bayesian inference for Gibbs random fields using c…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1,…

Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future population. The accuracy of these models is often…

Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…

Fitting mixed models to complex survey data is a challenging problem. Most methods in the literature, including the most widely used one, require a close relationship between the model structure and the survey design. In this paper we…

Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…

Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…

Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates…

Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be…

For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a…

By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…

Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…

Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…