Related papers: Testing Order Constraints: Qualitative Differences…
In social and biomedical sciences testing in contingency tables often involves order restrictions on cell-probabilities parameters. We develop objective Bayes methods for order-constrained testing and model comparison when observations…
In statistics, there are a variety of methods for performing model selection that all stem from slightly different paradigms of statistical inference. The reasons for choosing one particular method over another seem to be based entirely on…
In the context of testing general relativity with gravitational waves, constraints obtained with multiple events are typically combined either through a hierarchical formalism or though a combined multiplicative Bayes factor. We show that…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
The comparison of proportions is considered in the asymptotic generalized linear model with the odds ratio as effect size. When several doses are compared with a control assuming an order restriction, a Williams-type trend test can be used.…
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…
Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses…
We provide a brief overview of both Bayes and classical model selection. We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may…
The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data…
Conjoint analysis is a popular experimental design used to measure multidimensional preferences. Researchers examine how varying a factor of interest, while controlling for other relevant factors, influences decision-making. Currently,…
The quality of a Bayes factor crucially depends on the number of regressors, the sample size and the prior on the regression parameters, and hence it has to be established in a case-by-case basis. In this paper we analyze the consistency of…
We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over…
My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to…
The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
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…