Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and
p
values. In part I of this series we outline ten ...prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al.
this issue
).
Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the ...results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting:
planning
the analysis,
executing
the analysis,
interpreting
the results, and
reporting
the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared towards analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.
Statistical procedures such as Bayes factor model selection and Bayesian model averaging require the computation of normalizing constants (e.g., marginal likelihoods). These normalizing constants are ...notoriously difficult to obtain, as they usually involve highdimensional integrals that cannot be solved analytically. Here we introduce an R package that uses bridge sampling (Meng and Wong 1996; Meng and Schilling 2002) to estimate normalizing constants in a generic and easy-to-use fashion. For models implemented in Stan, the estimation procedure is automatic. We illustrate the functionality of the package with three examples.
Efficiency in redundancy Gronau, Quentin F; Moran, Rani; Eidels, Ami
Scientific reports,
07/2024, Letnik:
14, Številka:
1
Journal Article
Recenzirano
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In engineering, redundancy is the duplication of vital systems for use in the event of failure. In studies of human cognition, redundancy often refers to the duplication of the signal. Scores of ...studies have shown the salutary effects of a combined auditory and visual signal over single modality, the advantage of processing complete faces over facial features, and more recently the advantage of two observers over one. But what if the signal (or the number of observers) is fixed and cannot be altered or augmented? Can people improve the efficiency of information processing by recruiting an additional, redundant system? Here we demonstrate that recruiting a second redundant system can, under reasonable assumptions about human capacity, result in improved performance. Recruiting a second redundant system may come with a higher energy cost, but may be worthwhile in high-stakes situations where processing information accurately is crucial.
Informed Bayesian t-Tests Gronau, Quentin F.; Ly, Alexander; Wagenmakers, Eric-Jan
The American statistician,
04/2020, Letnik:
74, Številka:
2
Journal Article
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Across the empirical sciences, few statistical procedures rival the popularity of the frequentist
-test. In contrast, the Bayesian versions of the
-test have languished in obscurity. In recent years, ...however, the theoretical and practical advantages of the Bayesian
-test have become increasingly apparent and various Bayesian t-tests have been proposed, both objective ones (based on general desiderata) and subjective ones (based on expert knowledge). Here, we propose a flexible t-prior for standardized effect size that allows computation of the Bayes factor by evaluating a single numerical integral. This specification contains previous objective and subjective t-test Bayes factors as special cases. Furthermore, we propose two measures for informed prior distributions that quantify the departure from the objective Bayes factor desiderata of predictive matching and information consistency. We illustrate the use of informed prior distributions based on an expert prior elicitation effort.
Supplementary materials
for this article are available online.
Bayesian hypothesis testing presents an attractive alternative to
p
value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability ...to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the
t
-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP (
http://www.jasp-stats.org
), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder’s BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.
This paper introduces JASP, a free graphical software package for basic statistical procedures such as t tests, ANOVAs, linear regression models, and analyses of contingency tables. JASP is ...open-source and differentiates itself from existing open-source solutions in two ways. First, JASP provides several innovations in user interface design; specifically, results are provided immediately as the user makes changes to options, output is attractive, minimalist, and designed around the principle of progressive disclosure, and analyses can be peer reviewed without requiring a "syntax". Second, JASP provides some of the recent developments in Bayesian hypothesis testing and Bayesian parameter estimation. The ease with which these relatively complex Bayesian techniques are available in JASP encourages their broader adoption and furthers a more inclusive statistical reporting practice. The JASP analyses are implemented in R and a series of R packages.
In this guide, we present a reading list to serve as a concise introduction to Bayesian data analysis. The introduction is geared toward reviewers, editors, and interested researchers who are new to ...Bayesian statistics. We provide commentary for eight recommended sources, which together cover the theoretical and practical cornerstones of Bayesian statistics in psychology and related sciences. The resources are presented in an incremental order, starting with theoretical foundations and moving on to applied issues. In addition, we outline an additional 32 articles and books that can be consulted to gain background knowledge about various theoretical specifics and Bayesian approaches to frequently used models. Our goal is to offer researchers a starting point for understanding the core tenets of Bayesian analysis, while requiring a low level of time commitment. After consulting our guide, the reader should understand how and why Bayesian methods work, and feel able to evaluate their use in the behavioral and social sciences.
A Conceptual Introduction to Bayesian Model Averaging Hinne, Max; Gronau, Quentin F.; van den Bergh, Don ...
Advances in methods and practices in psychological science,
06/2020, Letnik:
3, Številka:
2
Journal Article
Recenzirano
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Many statistical scenarios initially involve several candidate models that describe the data-generating process. Analysis often proceeds by first selecting the best model according to some criterion ...and then learning about the parameters of this selected model. Crucially, however, in this approach the parameter estimates are conditioned on the selected model, and any uncertainty about the model-selection process is ignored. An alternative is to learn the parameters for all candidate models and then combine the estimates according to the posterior probabilities of the associated models. This approach is known as Bayesian model averaging (BMA). BMA has several important advantages over all-or-none selection methods, but has been used only sparingly in the social sciences. In this conceptual introduction, we explain the principles of BMA, describe its advantages over all-or-none model selection, and showcase its utility in three examples: analysis of covariance, meta-analysis, and network analysis.
Cognitive Bias Modification (CBM) refers to a family of interventions targeting substance-related cognitive biases, which have been found to play a role in the maintenance of addictive behaviors. In ...this study, we conducted a Bayesian meta-analysis of individual patient data from studies investigating the effects of CBM as a behavior change intervention for the treatment of alcohol and tobacco use disorders, in individuals aware of the behavior change goal of the studies. Main outcomes included reduction in the targeted cognitive biases after the intervention and in substance use or relapse rate at the short-to-long term follow-up. Additional moderators, both at the study-level (type of addiction and CBM training) and at the participant-level (amount of completed training trials, severity of substance use), were progressively included in a series of hierarchical mixed-effects models. We included 14 studies involving 2435 participants. CBM appeared to have a small effect on cognitive bias (0.23, 95% credible interval = 0.06–0.41) and relapse rate (−0.27, 95% credible interval = −0.68 – 0.22), but not on reduction of substance use. Increased training practice showed a paradoxical moderation effect on relapse, with a relatively lower chance of relapse in the control condition with increased practice, compared to the training condition. All effects were associated with extremely wide 95% credible intervals, which indicate the absence of enough evidence in favor or against a reliable effect of CBM on cognitive bias and relapse rate in alcohol and tobacco use disorders. Besides the need for a larger body of evidence, research on the topic would benefit from a stronger adherence to the current methodological standards in randomized controlled trial design and the systematic investigation of shared protocols of CBM.
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