Related papers: Bayes, E-values and Testing

The rejection threshold used for e-values and e-processes is by default set to $1/\alpha$ for a guaranteed type-I error control at $\alpha$, based on Markov's and Ville's inequalities. This threshold can be wasteful in practical…

Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is…

Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…

We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over…

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…

Empirical Bayes methods can improve inference on unobservable individual effects by borrowing strength across units. This paper proposes nonparametric empirical Bayes confidence intervals (NP-EBCIs) for unobservable individual effects in a…

Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to…

Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that…

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

Recent advances in reasoning techniques have substantially improved the performance of large language models (LLMs), raising expectations for their ability to provide accurate, truthful, and reliable information. However, emerging evidence…

We develop E-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These E-variables lead to exact,…

The Bayesian Mallows model is a flexible tool for analyzing data in the form of complete or partial rankings, and transitive or intransitive pairwise preferences. In many potential applications of preference learning, data arrive…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

Machine learning models in high-stakes applications, such as recidivism prediction and automated personnel selection, often exhibit systematic performance disparities across sensitive subpopulations, raising critical concerns regarding…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

Anytime valid sequential tests permit us to stop testing based on the current data, without invalidating the inference. Given a maximum number of observations $N$, one may believe this must come at the cost of power when compared to a…

Variational Autoencoders (VAEs) have experienced recent success as data-generating models by using simple architectures that do not require significant fine-tuning of hyperparameters. However, VAEs are known to suffer from…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…