Related papers: Bayesian Inference for Non-Parametric Extreme Valu…

Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…

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…

The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model.…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…

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…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…

Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the…

Rare events can potentially occur in many applications. When manifested as opportunities to be exploited, risks to be ameliorated, or certain features to be extracted, such events become of paramount significance. Due to their sporadic…

Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

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…

A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…

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…

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the…

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,…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…

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…