Stephen A. Andrews, David Sigeti · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2017
These are a set of slides about Bayesian hypothesis testing, where many hypotheses are tested. The conclusions are the following: The value of the Bayes factor obtained when using the median of the posterior marginal is almost the minimum value of the Bayes factor. The value of τ2 which minimizes the Bayes factor is a reasonable choice for this parameter. This allows a likelihood ratio to be computed with is the least favorable to H0.
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Luz Adriana Pereira Hoyos · 2019
In this thesis, we propose novel Bayesian Nonparametric hypothesis testing procedures for correlated data. First, we develop and study a proposal for comparing the distributions of paired samples. Next, we propose and analyze a hypothesis testing procedure for longitudinal data analysis. Both proposals are based on a flexible model for the joint distribution of the observations. The flexibility is given by a mixture of Dirichlet processes. Besides, for setting up the hypothesis testing procedures, we use a hierarchical representation with a spike-slab prior specification for the base measure of the Dirichlet process and a prior specification on the space of models. For the paired sample test, we use an appropriate parametrization for the kernel of the mixture to facilitate the comparisons and posterior inference. Consequently, the joint model allows us to derive the marginal distributions and test whether they differ or not. The procedure exploits the correlation between samples, relaxes the parametric assumptions, and detects possible differences throughout the entire distributions. For the longitudinal data, we propose to use a mixture of Dependent Dirichlet Processes to capture the correlation between the repeated measurements. The weights of the mixture are built via a stick-breaking prior, that comes from a Markovian process evolving in time. The effect of the predictors is modeled by the underlying atoms. The proposal can provide an estimation of the density through the time for different levels of the predictors, and at the same time can identify the effect of the predictors, without assuming restrictive distributional assumptions. We show the performance throughout the document of our proposals in illustrations with simulated and real data sets. Finally, we provide concluding remarks and discuss open problems.
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Xiao Liu · OSF Preprints (OSF Preprints) · 2022
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Hakan Erdogmus · Figshare · 2021
This package provides the data and calculations for the example used in the article "Bayesian Inference Demystified for Software Engineering Researchers: a Step-by-Step Introduction." It consists of two items:<br>- a spreadsheet file that can be opened with Excel or Google Sheets: compares NHST with Bayesian HT<br>- a JASP meta-analysis that can be opened with the open-source JASP statistical software (downloadable from jasp-stats.org). <br><br>
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Erdogmus, Hakan · Figshare · 2021
This package provides the data and calculations for the example used in the article "Bayesian Inference Demystified for Software Engineering Researchers: a Step-by-Step Introduction." It consists of two items:<br>- a spreadsheet file that can be opened with Excel or Google Sheets: compares NHST with Bayesian HT<br>- a JASP meta-analysis that can be opened with the open-source JASP statistical software (downloadable from jasp-stats.org). <br><br>
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Thomas H. Wonnacott · Journal of Applied Statistics · 1986
(1986). Bayesian and Classical hypothesis testing. Journal of Applied Statistics: Vol. 13, No. 2, pp. 149-157.
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Ma, Wei Ji, van den Berg, Ronald · Purdue e-Pubs (Purdue University System) · 2015
Asking subjects to rate their confidence is one of the oldest procedures in psychophysics. Remarkably, quantitative models of confidence ratings have been scarce. The Bayesian confidence hypothesis (BCH) states that an observer’s confidence rating is monotonically related to the posterior probability of their choice. I will report tests of this hypothesis in two visual categorization tasks: one requiring rapid categorization of a single oriented stimulus, the other a deliberative judgment typically made by scientists, namely interpreting scatterplots. We find evidence against the Bayesian confidence hypothesis in both tasks.
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Mills, Jeffrey A. · 2018
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Isabel Natário · Emerging topics in statistics and biostatistics · 2024
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Baruch Fischhoff, Tal Marom · Defense Technical Information Center (DTIC) · 1982
Bayesian inference provides a general framework for testing hypotheses. It is a normative method, in the sense of prescribing how hypotheses should be tested. However, it may also be used descriptively, by characterizing people's actual hypothesis-testing behavior in terms of its consistency with or departures from the model. Such a characterization may facilitate the development of psychological accounts of how that behavior is produced (i.e., as the result of failed attempts to act in a Bayesian fashion, as the result of attempts of process information in non-Bayesian ways. This essay exploits the descriptive potential of Bayesian inference. First, it identifies a set of logically possible forms of non-Bayesian behavior. Second, it reviews existing research in a variety of areas in order to see whether these possibilities are ever realized. The analysis shows that in some situations, several apparently distinct phenomena are usefully viewed as special cases of the same kind of behavior, whereas in other situations previous investigations have conferred a common label (e.g., confirmation bias) to several distinct phenomena. It also calls into question a number of attributions of judgmental bias, suggesting that in some cases the bias is different than what has previously been claimed, whereas in others, there may be no bias at all. (Author)
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Eric‐Jan Wagenmakers, Peter Grünwald · Psychological Science · 2006
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Chen, Fang · ThinkTech (Texas Tech University) · 2022
This dissertation consists of three distinct but related research projects. The \nfirst two projects focus on the Bayesian hypothesis test for correlations and partial \ncorrelations. The third project deals with the Bayesian test for equality of means in \nhigh dimensions. \nIn the first project, we derive Bayes factor-based testing procedures for the presence of a correlation and a partial correlation. The proposed Bayesian tests are \nobtained by restricting the class of the alternative hypotheses to maximize the probability of rejecting the null hypothesis when the Bayes factor is larger than a specified \nthreshold. It turns out that they depend simply on the frequentist t-statistics with \nthe associated critical values and can thus be easily calculated by using a spreadsheet \nin Excel and, in fact, by just adding one more step after one has performed the frequentist correlation tests. In addition, they can yield an identical decision with the \nfrequentist paradigm, provided that the evidence threshold of the Bayesian tests is \ndetermined by the significance level of the frequentist paradigm. We illustrate the \nperformance of the proposed procedures through simulated and real-data examples. \nIn the second project, we follow the work of Held and Ott [22] and propose a \nsample-size adjusted minimum Bayes factor (minBF) for testing the presence of a \ncorrelation and a partial correlation. The proposed minBF is related to the two-sided \np-value from the frequentist test and can be easily calculated using either a pocket \ncalculator or spreadsheets, so long as the researcher is familiar with the frequentist \nparadigm. It turns out that the minBF increases with an increasing sample size, \nwhich implies that the maximal evidence of the two-sided p-value decreases with \nincreasing sample size. Simulation studies and two real-data applications are provided \nfor illustrative purposes. \nIn the third project, we study the problem of testing the equality of two mean \nvectors in high dimensional settings. We consider a permutation test from a Bayesian \npoint of view by hierarchical clustering, which might make more efficient use of covariance structure at high dimensions. Moreover, our proposed Bayes factor is invariant \nunder linear transformations of the marginal distributions and has a closed-form expression. We showed by simulation that our proposed Bayesian procedure has higher power than competing tests in the literature.
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Sandra Andraszewicz · 2016
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Romy Lorenz, Adam Hampshire, Robert Leech · Trends in Cognitive Sciences · 2017
Cognitive neuroscientists are often interested in broad research questions, yet use overly narrow experimental designs by considering only a small subset of possible experimental conditions. This limits the generalizability and reproducibility of many research findings. Here, we propose an alternative approach that resolves these problems by taking advantage of recent developments in real-time data analysis and machine learning. Neuroadaptive Bayesian optimization is a powerful strategy to efficiently explore more experimental conditions than is currently possible with standard methodology. We argue that such an approach could broaden the hypotheses considered in cognitive science, improving the generalizability of findings. In addition, Bayesian optimization can be combined with preregistration to cover exploration, mitigating researcher bias more broadly and improving reproducibility.
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Stephen A. Andrews, David Sigeti · 2018
A common problem in data analysis is testing a point hypothesis.For example, one might test whether or not the mean of a distribution is zero.We describe the standard Bayesian approach, which requires the choice of a width parameter to define a prior distribution for an alternative hypothesis.Standard practice is to choose this width parameter to be the least favorable choice for the original, point hypothesis.This approach, however, is ad-hoc and not informed by the data.We examine this practice in more detail than in previous work by constructing a hierarchical model, where the width parameter is an unknown value subject to inference.This yields a marginal posterior distribution for the width parameter.We then show that using the median of this marginal posterior distribution as the width parameter in the Bayesian comparison between the hypotheses gives results which are very similar to those obtained from the existing approaches.This gives a more rigorous and data-informed justification for the standard practice of choosing a width parameter which is least favorable to the point hypothesis.
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Anonymous Author(s) · Zenodo (CERN European Organization for Nuclear Research) · 2026
Bayesian hypothesis testing for quantum algorithms. This repository provides reference implementations of sequential Bayesian hypothesis testing (BHT) procedures to certify success probabilities of quantum states/circuits and quantum algorithms under finite-shot sampling. It also includes utilities to log experimental runs and summarize results as CSV for analysis.
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Holmes, Chris C., Caron, François, Griffin, Jim E. et al. · arXiv (Cornell University) · 2009
In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 )}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$, with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to evaluate the evidence for the null hypothesis $H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. Our method is based upon a nonparametric Pólya tree prior centered either subjectively or using an empirical procedure. We show that the Pólya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null $\mathrm{Pr}(H_0|\{\mathbf {y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.
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Thomas Schultze · OSF Preprints (OSF Preprints) · 2022
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Anonymous Author(s) · Zenodo (CERN European Organization for Nuclear Research) · 2026
Bayesian hypothesis testing for quantum algorithms. This repository provides reference implementations of sequential Bayesian hypothesis testing (BHT) procedures to certify success probabilities of quantum states/circuits and quantum algorithms under finite-shot sampling. It also includes utilities to log experimental runs and summarize results as CSV for analysis.
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Chris C. Holmes, François Caron, Jim E. Griffin et al. · Bayesian Analysis · 2015
In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples y(1)~iidF(1) and y(2)~iidF(2), with F(1),F(2) unknown, we wish to evaluate the evidence for the null hypothesis H0:F(1)≡F(2) versus the alternative H1:F(1)≠F(2). Our method is based upon a nonparametric Pólya tree prior centered either subjectively or using an empirical procedure. We show that the Pólya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null Pr(H0|{y(1),y(2)})
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