Related papers: Posterior Adaptation With New Priors

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification.…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

Minimum Bayes factors are commonly used to transform two-sided p-values to lower bounds on the posterior probability of the null hypothesis, as in Pericchi et al. (2017). In this article, we show posterior probabilities of hypothesis by…

We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups,…

We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a…

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…

When using mixture models it may be the case that the modeller has a-priori beliefs or desires about what the components of the mixture should represent. For example, if a mixture of normal densities is to be fitted to some data, it may be…

It is a relatively well-known fact that in problems of Bayesian model selection improper priors should, in general, be avoided. In this paper we derive a proper and parsimonious uniform prior for regression coefficients. We then use this…

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

Deep learning is increasingly moving towards a transfer learning paradigm whereby large foundation models are fine-tuned on downstream tasks, starting from an initialization learned on the source task. But an initialization contains…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

We develop a representation of a decision maker's uncertainty based on e-variables. Like the Bayesian posterior, this *e-posterior* allows for making predictions against arbitrary loss functions that may not be specified ex ante. Unlike the…

Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…

Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…