Related papers: Bayesian Inference from Composite Likelihoods, wit…
In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…
In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution,…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
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…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess…
We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field…
Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…
In this study, we examine a Bayesian approach to analyze extreme daily rainfall amounts and forecast return-levels. Estimating the probability of occurrence and quantiles of future extreme events is important in many applications, including…
A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…