stan posterior predictive distribution

I continue my Stan experiments with another insurance example. The posterior parameter distributions include both \(\mu\) and \(\sigma\) in the 95% credible interval. The distribution of posterior predictive check (y_ppc) is wider, taking into account the uncertainty of the parameters.The interquartile range and mean of my initial fake data and the sample of the posterior predictive distribution look very similar. 4.1.2 Example: grid approximation. The bayesplot PPC module provides various plotting functions for creating graphical displays comparing observed data to simulated data from the posterior (or prior) predictive distribution. See below for a brief discussion of the ideas behind posterior predictive checking, a description of the structure of this package, and tips on providing an interface to bayesplot from another package. Fit the model to the data to get the posterior distribution of the parameters: \(p(\theta | D)\) Simulate data from the fitted model: \(p(\tilde{D} | \theta, D)\) Compare the simulated data (or a statistic thereof) to the observed data and a statistic thereof. Draw from the posterior predictive distribution of the outcome(s) given interesting values of the predictors in order to visualize how a manipulation of a predictor affects (a function of) the outcome(s). Evaluate how well the model fits the data and possibly revise the model. The second way in which the beta model is used here is as a full joint probability model coded in Stan and sampled with NUTS HMC to derive a full posterior density. posterior_predict() methods should return a \(D\) by \(N\) matrix, where \(D\) is the number of draws from the posterior predictive distribution and \(N\) is the number of data ... (CRAN, GitHub). Let’s demonstrate a simulation from the posterior distribution with the Poisson-gamma conjugate model of Example 2.1.1.Of course we know that the true posterior distribution for this model is \[ \text{Gamma}(\alpha + n\overline{y}, \beta + n), \] and thus we wouldn’t have to simulate at all to find out the posterior of this model. Compute posterior samples of the expected value/mean of the posterior predictive distribution. Description Usage Arguments Value Note See Also Examples. The latter allows the model to gorge on data, update its parameters, and then make predictions based on the posterior predictive distribution, while the former forces the model to make predictions using the prior predictive distribution. Description. 3.5.1 Comparing different likelihoods; ... 11.2 A first simple example with Stan: ... Stan uses the shape of the unnormalized posterior to sample from the actual posterior distribution. From this density, prediction are made and compared to the empirical observations (posterior predictive check). Or, to put it differently I have a customer of three years and I’d like to predict the expected claims cost for the next year to set or adjust the premium. 3.5 Posterior predictive distribution. Description. View source: R/posterior_predict.R. In rstanarm: Bayesian Applied Regression Modeling via Stan. Some options are beyond my limited knowledge (ie Log Posterior vs Sample Step Size), so I usually look at the posterior distribution of the regression parameters (Diagnose -> NUTS (plots) -> By model parameter), the histogram should be more or less normal. See Box 11.1 for a more detailed explanation. In brms: Bayesian Regression Models using 'Stan' Description Usage Arguments Details Value Examples. Can be performed for the data used to fit the model (posterior predictive checks) or for new data. View source: R/posterior_epred.R. Draw from posterior distribution using Markov Chain Monte Carlo (MCMC). Posterior predictive checks The pre-compiled models in rstanarm already include a y_rep variable (our model predictions) in the generated quantities block (your posterior distributions). 9.2 Posterior Predictive Checks. One method evaluate the fit of a model is to use posterior predictive checks. Sampling with Stan HMC for Posterior Prediction. The posterior predictive distribution is the distribution of the outcome implied by the model after using the observed data to update our beliefs about the unknown parameters in the model. Here I am particular interested in the posterior predictive distribution from only three data points.