Related papers: Inferences from prior-based loss functions

Predictive Bayesian inference (PBI) represents a model-and prior-agnostic approach to standard Bayesian inference which allows users to quantify uncertainty for a functional of interest only by specifying a forward predictive model for…

Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…

Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…

Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing…

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 ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…

Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are…

In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation; this leads to a Bayesian recurrent unit…

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…

Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work,…

In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…