#statstab #229 Prior Modeling
by @betanalpha
Thoughts: Thorough overview of the prior elicitation process and ways to think about priors.
#stats #priors #probability #metascience #bayes #bayesian
https://betanalpha.github.io/assets/case_studies/prior_modeling.html
#statstab #228 Applied Modelling in Drug Development - Setting priors in {brms}
Thoughts: Part of a larger book, useful bit for understanding how to set priors & check them for bayesian models & meta-analyses
#stats #brms #priors #metaanalysis #bayesian #r #bayes #drugs #clinicaltrials
#statstab #227 Parameterization of Response Distributions in {brms}
Thoughts: If you use #brms and can read mathematical notation (who can't, right?), this page will be useful.
#r #bayes #models #distributions #likelihood #stats
https://cran.r-project.org/web/packages/brms/vignettes/brms_families.html
#statstab #217 The distribution of p-values obtained in replications depends only on the original p-value. How can it be true?
Thoughts: A great discussion where the author @thenewstats chimes in to explain the issue.
"A p-value is an #estimate of p(Data | Null Hypothesis). " – not correct. A p-value is an estimate of
p(Data or other imagined data | Null Hypothesis)
so not even just of the actual data you have. Which is why p-values depend on your stopping rule (and do not satisfy the "likelihood principle"). In this regard, see Jeffreys's quote below.
Imagine you design an experiment this way: "I'll test 10 subjects, and in the meantime I apply for a grant. At the time the 10th subject is tested, I'll know my application's outcome. If the outcome is positive, I'll test 10 more subjects; if it isn't, I'll stop". Not an unrealistic situation.
With this stopping rule, your p-value will depend on the probability that you get the grant. This is not a joke.
"*What the use of P implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.* This seems a remarkable procedure. On the face of it the fact that such results have not occurred might more reasonably be taken as evidence for the law, not against it." – H. Jeffreys, "Theory of Probability" § VII.7.2 (emphasis in the original) <https://doi.org/10.1093/oso/9780198503682.001.0001>.
Online free book: Introduction to Bayesian Data Analysis for Cognitive Science
https://bayes.club/@ShravanVasishth/113330289055047281
#bayes #Rstats #STAN #brms #OpenAccess #OA #CognitiveScience #CogSci @cogsci
#statstab #196 JASP Bayesian ANOVA
Thoughts: @JASPStats is used by researchers to "add some bayes factors" to their results. But, do you know what those actually reflect? Here is what their team says: