Related papers: Bayesian Posteriors For Arbitrarily Rare Events

Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…

We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…

In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of…

We show that it can be suboptimal for Bayesian decision-making agents employing social learning to use correct prior probabilities as their initial beliefs. We consider sequential Bayesian binary hypothesis testing where each individual…

Rigorously quantifying the information in high contrast imaging data is important for informing follow-up strategies to confirm the substellar nature of a point source, constraining theoretical models of planet-disk interactions, and…

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…

Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…

Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…

With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon…

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

We study how to perform tests on samples of pairs of observations and predictions in order to assess whether or not the predictions are prudent. Prudence requires that that the mean of the difference of the observation-prediction pairs can…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

Economists are often interested in estimating averages with respect to distributions of unobservables, such as moments of individual fixed-effects, or average partial effects in discrete choice models. For such quantities, we propose and…

Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…

Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…

In Bayesian meta-analysis, the specification of prior probabilities for the between-study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the…

In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms…