Related papers: Test Martingales, Bayes Factors and $p$-Values

Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper,…

Bayesian diversity estimators are martingales converging almost surely and in mean with common limit and local behavior with plug in estimators.

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…

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…

Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…

A common task in high-throughput biology is to screen for associations across thousands of units of interest, e.g., genes or proteins. Often, the data for each unit are modeled as Gaussian measurements with unknown mean and variance and are…

In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…

Inverse classification, the process of making meaningful perturbations to a test point such that it is more likely to have a desired classification, has previously been addressed using data from a single static point in time. Such an…

The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger…

In the context of Bayesian factor analysis, it is possible to compute mean plausible values, which might be used as covariates or predictors or in order to provide individual scores for the Bayesian latent variables. Previous simulation…

In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…

A standard assumption in the Bayesian estimation of linear regression models is that the regressors are exogenous in the sense that they are uncorrelated with the model error term. In practice, however, this assumption can be invalid. In…

Increased availability of data and accessibility of computational tools in recent years have created unprecedented opportunities for scientific research driven by statistical analysis. Inherent limitations of statistics impose constrains on…

The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…

We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the…

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…

The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…

Models are consistently treated as approximations and all procedures are consistent with this. They do not treat the model as being true. In this context $p$-values are one measure of approximation, a small $p$-value indicating a poor…

Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a p-value. Although there is considerable confusion concerning the meaning of p-values, leading to their misuse, they…

We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter…