Related papers: Why bother with Bayesian t-tests?
Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…
This paper studies whether Bayesian simultaneous three-way hypothesis tests can be logically coherent. Two types of results are obtained. First, under the standard error-wise constant loss, only for a limited set of models can a Bayes…
This paper explores an approach to Bayesian sample size determination in clinical trials. The approach falls into the category of what is often called "proper Bayesian", in that it does not mix frequentist concepts with Bayesian ones. A…
Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm,…
This paper deals with a new Bayesian approach to the standard one-sample $z$- and $t$- tests. More specifically, let $x_1,\ldots,x_n$ be an independent random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. The…
We present the fundamental ideas underlying statistical hypothesis testing using the frequentist framework. We begin with a simple example that builds up the one-sample t-test from the beginning, explaining important concepts such as the…
Null hypothesis significance testing remains popular despite decades of concern about misuse and misinterpretation. We believe that much of the problem is due to language: significance testing has little to do with other meanings of the…
We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is…
To perform statistical inference for time series, one should be able to assess if they present deterministic or stochastic trends. For univariate analysis one way to detect stochastic trends is to test if the series has unit roots, and for…
Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…
Although there are many ideas for the formulations of statistical hypothesis testing, we consider that the likelihood ratio test is the most reasonable and orthodox. However, it is not handy, and thus, it is not usual in elementary books.…
Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose…
The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…
Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure…