Related papers: Bayesian inference: More than Bayes's theorem

The Bayesian Classification represents a supervised learning method as well as a statistical method for classification. Assumes an underlying probabilistic model and it allows us to capture uncertainty about the model in a principled way by…

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…

Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

A product of two Gaussians (or normal distributions) is another Gaussian. That's a valuable and useful fact! Here we use it to derive a refactoring of a common product of multivariate Gaussians: The product of a Gaussian likelihood times a…

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…

In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes…

The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…