Bayes factor: A better solution for hypothesis testing

2011 ◽  
Author(s):  
Jeffrey N. Rouder
Keyword(s):  
Hypothesis Testing ◽  
Bayes Factor

scholarly journals Bayesian Inference and Testing Any Hypothesis You Can Specify

2018 ◽  
Vol 1 (2) ◽  
pp. 281-295 ◽  
Author(s):  
Alexander Etz ◽  
Julia M. Haaf ◽  
Jeffrey N. Rouder ◽  
Joachim Vandekerckhove
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Special Form ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Alternative Hypotheses ◽  
Competing Models

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model-selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that the researcher specify exactly what is meant by a “null” hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, but in all cases the inferential procedure is based on the same underlying method of likelihood comparison. An associated app can be found at https://osf.io/mvp53/ . This article is the work of the authors and is reformatted from the original, which was published under a CC-By Attribution 4.0 International license and is available at https://psyarxiv.com/wmf3r/ .

scholarly journals Author Correction: Using Bayes factor hypothesis testing in neuroscience to establish evidence of absence

2020 ◽  
Vol 23 (11) ◽  
pp. 1453-1453
Author(s):  
Christian Keysers ◽  
Valeria Gazzola ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Hypothesis Testing ◽  
Bayes Factor ◽  
Evidence Of Absence

Decision qualities of Bayes factor and p value-based hypothesis testing.

2017 ◽  
Vol 22 (2) ◽  
pp. 340-360 ◽  
Author(s):  
Minjeong Jeon ◽  
Paul De Boeck
Keyword(s):  
Hypothesis Testing ◽  
Bayes Factor ◽  
P Value

scholarly journals A New Bayesian Two-Sample t Test and Solution to the Behrens–Fisher Problem Based on Gaussian Mixture Modelling with Known Allocations

2021 ◽  
Author(s):  
Riko Kelter
Keyword(s):  
Hypothesis Testing ◽  
Effect Size ◽  
Bayes Factor ◽  
R Package ◽  
Gaussian Mixture ◽  
Control Group ◽  
Mixture Modelling ◽  
Region Of Practical Equivalence ◽  
And Control ◽  
Theoretical Results

AbstractTesting differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t test relies on null hypothesis significance testing (NHST) via p values, which has several drawbacks. Bayesian alternatives were recently introduced using the Bayes factor, which has its own limitations. This paper introduces an alternative to current Bayesian two-sample t tests by interpreting the underlying model as a two-component Gaussian mixture in which the effect size is the quantity of interest, which is most relevant in clinical research. Unlike p values or the Bayes factor, the proposed method focusses on estimation under uncertainty instead of explicit hypothesis testing. Therefore, via a Gibbs sampler, the posterior of the effect size is produced, which is used subsequently for either estimation under uncertainty or explicit hypothesis testing based on the region of practical equivalence (ROPE). An illustrative example, theoretical results and a simulation study show the usefulness of the proposed method, and the test is made available in the R package . In sum, the new Bayesian two-sample t test provides a solution to the Behrens–Fisher problem based on Gaussian mixture modelling.

scholarly journals Conflicts in Bayesian Statistics Between Inference Based on Credible Intervals and Bayes Factors

2020 ◽  
Vol 18 (1) ◽  
pp. 2-27
Author(s):  
Miodrag M. Lovric
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Credible Interval ◽  
Test Point ◽  
Type I ◽  
Null Hypothesis Testing ◽  
Frequentist Statistics ◽  
Credible Intervals ◽  
Point Null Hypothesis

In frequentist statistics, point-null hypothesis testing based on significance tests and confidence intervals are harmonious procedures and lead to the same conclusion. This is not the case in the domain of the Bayesian framework. An inference made about the point-null hypothesis using Bayes factor may lead to an opposite conclusion if it is based on the Bayesian credible interval. Bayesian suggestions to test point-nulls using credible intervals are misleading and should be dismissed. A null hypothesized value may be outside a credible interval but supported by Bayes factor (a Type I conflict), or contrariwise, the null value may be inside a credible interval but not supported by the Bayes factor (Type II conflict). Two computer programs in R have been developed that confirm the existence of a countable infinite number of cases, for which Bayes credible intervals are not compatible with Bayesian hypothesis testing.

scholarly journals Efficiency in Sequential Testing: Comparing the Sequential Probability Ratio Test and the Sequential Bayes Factor Test

2020 ◽  
Author(s):  
Angelika Stefan ◽  
Felix D. Schönbrodt ◽  
Nathan J. Evans ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Hypothesis Testing ◽  
Bayes Factor ◽  
Sequential Probability Ratio Test ◽  
Sequential Testing ◽  
Sufficient Evidence ◽  
Ratio Test ◽  
Testing Procedures ◽  
Probability Ratio ◽  
Sequential Hypothesis ◽  
Sequential Probability

In a sequential hypothesis test, the analyst checks at multiple steps during data collectionwhether sufficient evidence has accrued to make a decision about the tested hypotheses.As soon as sufficient information has been obtained, data collection is terminated. Here,we compare two sequential hypothesis testing procedures that have recently been proposedfor use in psychological research: the Sequential Probability Ratio Test (SPRT; Schnuerch& Erdfelder, 2020) and the Sequential Bayes Factor Test (SBFT; Schönbrodt et al., 2017).We show that although the two methods have been presented as distinct methodologies inthe past, they share many similarities and can even be regarded as two instances of thesame overarching hypothesis testing framework. We demonstrate that the two methods usethe same mechanisms for evidence monitoring and error control, and that differences inefficiency between the methods depend on the exact specification of the statistical modelsinvolved. Given the close relationship between the SPRT and SBFT, we argue that thechoice of the sequential testing method should be regarded as a continuous choice withina unified framework rather than a dichotomous choice between two methods. We presentseveral considerations researchers can make to navigate the design decisions in the SPRTand SBFT.

scholarly journals BGGM: Bayesian Gaussian Graphical Models in R

2020 ◽  
Author(s):  
Donald Ray Williams ◽  
Joris Mulder
Keyword(s):  
Bayesian Inference ◽  
Hypothesis Testing ◽  
Graphical Models ◽  
Model Comparison ◽  
Bayes Factor ◽  
R Package ◽  
Predictive Distribution ◽  
Gaussian Graphical Models ◽  
Posterior Predictive Distribution

The R package BGGM provides tools for making Bayesian inference in Gaussian graphicalmodels (GGM). The methods are organized around two general approaches for Bayesian inference: (1) estimation and (2) hypothesis testing. The key distinction is that the formerfocuses on either the posterior or posterior predictive distribution (Gelman, Meng, & Stern,1996; see section 5 in Rubin, 1984), whereas the latter focuses on model comparison withthe Bayes factor (Jeffreys, 1961; Kass & Raftery, 1995).

scholarly journals BGGM: A R Package for Bayesian Gaussian Graphical Models

2019 ◽  
Author(s):  
Donald Ray Williams ◽  
Joris Mulder
Keyword(s):  
Hypothesis Testing ◽  
Graphical Models ◽  
Bayes Factor ◽  
R Package ◽  
Predictive Distribution ◽  
Gaussian Graphical Models ◽  
Posterior Predictive Distribution ◽  
Bayesian Approaches ◽  
Bayesian Hypothesis Testing ◽  
Partial Correlations

Gaussian graphical models (GGM) allow for learning conditional independence structures that are encoded by partial correlations. Whereas there are several \proglang{R} packages for classical (i.e., frequentist) methods, there are only two that implement a Bayesian approach. These are exclusively focused on identifying the graphical structure; that is, detecting non-zero effects. The \proglang{R} package \pkg{BGGM} not only fills this gap, but it also includes novel Bayesian methodology for extending inference beyond identifying non-zero relations. \pkg{BGGM} is built around two Bayesian approaches for inference--estimation and hypothesis testing. The former focuses on the posterior distribution and includes extensions to assess predictability, as well as methodology to compare partial correlations. The latter includes methods for Bayesian hypothesis testing, in both exploratory and confirmatory contexts, with the novel matrix-$F$ prior distribution. This allows for testing order and equality constrained hypotheses, as well as a combination of both with the Bayes factor. Further, there are two approaches for comparing any number of GGMs with either the posterior predictive distribution or Bayesian hypothesis testing. This work describes the software implementation of these methods. We end by discussing future directions for \pkg{BGGM}.

scholarly journals Advantages Masquerading as ‘Issues’ in Bayesian Hypothesis Testing: A Commentary on Tendeiro and Kiers (2019)

2019 ◽  
Author(s):  
Don van Ravenzwaaij ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Statistical Evidence ◽  
Central Component ◽  
P Values ◽  
Bayesian Hypothesis Testing ◽  
Bayesian Testing

Tendeiro and Kiers (2019) provide a detailed and scholarly critique of Null Hypothesis Bayesian Testing (NHBT) and its central component –the Bayes factor– that allows researchers to update knowledge and quantify statistical evidence. Tendeiro and Kiers conclude that NHBT constitutes an improvement over frequentist p-values, but primarily elaborate on a list of eleven ‘issues’ of NHBT. In this commentary, we provide context to each issue and conclude that many issues may in fact be conceived as pronounced advantages of NHBT.

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