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What is posterior predictive checking?
Posterior predictive checks (PPCs) are a great way to validate a model. The idea is to generate data from the model using parameters from draws from the posterior. So, often you will want to know if, for example, your posterior distribution is approximating your underlying distribution.
Is P value Bayesian statistics?
The p-value quantifies the discrepancy between the data and a null hypothesis of interest, usually the assumption of no difference or no effect. A Bayesian approach allows the calibration of p-values by transforming them to direct measures of the evidence against the null hypothesis, so-called Bayes factors.
How do you read posterior?
You can think of posterior probability as an adjustment on prior probability: Posterior probability = prior probability + new evidence (called likelihood). For example, historical data suggests that around 60% of students who start college will graduate within 6 years. This is the prior probability.
What is the idea of posterior predictive checking?
The idea behind posterior predictive checking is simple: if a model is a good fit then we should be able to use it to generate data that looks a lot like the data we observed. To generate the data used for posterior predictive checks we simulate from the posterior predictive distribution.
Which is an example of a posterior predictive distribution?
The posterior predictive distribution is the distribution of the outcome variable implied by a model after using the observed data y (a vector of outcome values), and typically predictors X, to update our beliefs about the unknown parameters θ in the model.
How are PPC functions used in predictive checking?
LOO predictive checks: PPC functions for predictive checks based on (approximate) leave-one-out (LOO) cross-validation. Censored data: PPC functions comparing the empirical distribution of censored data y to the distributions of individual simulated datasets (rows) in yrep.
How to use bayesplot for prior predictive checking?
To use bayesplot for prior predictive checks you can simply use draws from the prior predictive distribution instead of the posterior predictive distribution. See Gabry et al. (2019) for more on prior predictive checking and when it is reasonable to compare the prior predictive distribution to the observed data.