Related papers: Empirical Bayes factors for common hypothesis test…
In this work, we undertake a comprehensive reformulation, modification, and extension of Smith and Spiegelhalter's (1980) and (1982) Bayes Factor work within the evolving subject of Objective Bayes Factors. Our primary focus centers on…
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:…
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
We describe Bayes factors functions based on the sampling distributions of \emph{z}, \emph{t}, $\chi^2$, and \emph{F} statistics, using a class of inverse-moment prior distributions to define alternative hypotheses. These non-local…
We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…
Bayesian model selection provides a natural alternative to classical hypothesis testing based on p-values. While many papers mention that Bayesian model selection is frequently sensitive to prior specification on the parameters, there are…
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard…
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…
Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the…
Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…
Consider a Bayesian situation in which we observe $Y \sim p_{\theta}$, where $\theta \in \Theta$, and we have a family $\{ \nu_h, \, h \in \mathcal{H} \}$ of potential prior distributions on $\Theta$. Let $g$ be a real-valued function of…
A Bayes factor is proposed for testing whether the effect of a key predictor variable on the dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) when one is interested in…
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…
Bayesian design of experiments and sample size calculations usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power therefore often lack closed-form or…
Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…
Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…
The American Statistical Association (ASA) statement on statistical significance and P-values \cite{wasserstein2016asa} cautioned statisticians against making scientific decisions solely on the basis of traditional P-values. The statement…
The Bayes factor is the gold-standard figure of merit for comparing fits of models to data, for hypothesis selection and parameter estimation. However it is little used because it is computationally very intensive. Here it is shown how…