Related papers: On Bayes factor functions
We describe Bayes factors based on z, t, $\chi^2$, and F statistics when non-local moment prior distributions are used to define alternative hypotheses. The non-local alternative prior distributions are centered on standardized effects. The…
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
Partial correlation coefficients are widely applied in the social sciences to evaluate the relationship between two variables after accounting for the influence of others. In this article, we present Bayes Factor Functions (BFFs) for…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
Bayes factors for composite hypotheses have difficulty in encoding vague prior knowledge, as improper priors cannot be used and objective priors may be subjectively unreasonable. To address these issues I revisit the posterior Bayes factor,…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
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…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
A staple of Bayesian model comparison and hypothesis testing, Bayes factors are often used to quantify the relative predictive performance of two rival hypotheses. The computation of Bayes factors can be challenging, however, and this has…
We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same…
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…
Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…
We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss…
Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…
We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic…
Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…