Model comparison via Bayes Factor analysis

Results of Bayesian analyses can be utilised for future research in the sense of Dennis Lindley’s motto: “Today’s posterior is tomorrow’s prior” (Lindley, 1972), or as Richard Feynman put it “Yesterday’s sensation is today’s calibration” to which Valentine Telegdi added“…and tomorrow’s background”.

Bayes Factor analysis for model comparison

Robustness test for various priors.

Accumulation of evidence for H1 as a time-series.

Bayesian ANOVA in JASP.

Reliability analysis in JASP.

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At the conceptual meta level, the primary difference between the frequentists and the Bayesian account is that the former treats data as random and parameters as fixed and the latter regards data as fixed and unknown parameters as random.

A Bayes Factor can range from 0 to ∞ and a value of 1 denotes equivalent support for both competing hypotheses. Moreover, LogBF10 can be expressed as a logarithm ranging from -∞ to ∞. A BF of 0 denotes equal support for H0 and H1.

“The prior distribution is a key part of Bayesian inference and represents the information about an uncertain parameter that is combined with the probability distribution of new data to yield the posterior distribution, which in turn is used for future inferences and decisions.” (Gelman, 2006, p. 1634)

In a seminal paper entitled “Inference, method, and decision: towards a Bayesian philosophy of science” Rosenkrantz (Rosenkrantz, 1980, p. 485) discusses the Popperian concept of verisimilitude (truthlikeness) w.r.t. Bayesian decision making and develops a persuasive cogent argument in favour of diffuse priors (i.e., C-systems with a low λ). In a related publication he states: “If your prior is heavily concentrated about the true value (which amounts to a ‘lucky guess’ in the absence of pertinent data), you stand to be slightly closer to the truth after sampling than someone who adopts a diffuse prior, your advantage dissipating rapidly with sample size. If, however, your initial estimate is in error, you will be farther from the truth after sampling, and if the error is substantial, you will be much farther from the truth. I can express this by saying that a diffuse prior is a better choice at ‘almost all’ values of [q1] or, better, that it semi~dominates any highly peaked (or ‘opinionated’) prior. In practice, a diffuse prior never does much worse than a peaked one and ‘generally’ does much better…” (1946)

Frequentist inference
Fixed-effects ANOVAGeneral linear models: mixing continuous and categorical covariatesOutput plot as PDFSimple linear regressionSkewness & Kurtosis
file.choose() is a very handy command which saves the work associated with defining absolute and relative paths which can be quite cumbersome.
list.files for non-interactive selection.
choose.files for selecting multiple files interactively.
Bayes Factor analysis
ttestBF function (one sample) BFmcmc functionttestBF function (two sample)Bayesian meta analysisBayes factor robustness analysis, one-sidedAnimating Robustness-Check of Bayes Factor PriorsSkewness & KurtosisanovaBF function

ttestBF function, which performs the “JZS” t test described by Rouder, Speckman, Sun, Morey, and Iverson (2009).

The posterior function returns a object of type BFmcmc, which inherits the methods of the mcmc class from the coda package.

ttestBF function, which performs the “JZS” t test described by Rouder, Speckman, Sun, Morey, and Iverson (2009).

Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t-tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin and Review, 16, 225-237

Reduce number of comparisons by specifyig the xact model of interest a priori.

Markov chain Monte Carlo methods
MCMC 1GBEST RBEST - Bayesian MCMC power analysis
Various plots
BeanplotsDensity and Rug plotDirac function - Interdisciplinarity versus OverspecialisationGoogle TrendsJASP prior & posterior plot