What do you mean by posterior predictive distribution?

What do you mean by posterior predictive distribution?

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.

How does posterior prediction depend on the simulated data?

Posterior prediction relies on comparing the observed data to data simulated from the model. If the simulated data are similar to the observed, the model could reasonably have produced our observations. However, if the simulated data consistently differ from the observed, the model is not capturing some feature of the data-generating process.

Where can I find code for posterior prediction?

Simulation of posterior predictive datasets (shown in light gray) by drawing samples of means and standard deviations from the posterior distribution. The code for this simulation with the single-normal model can be found in pps_SingleNormal.rev.

Which is the posterior distribution of the mean and standard deviation?

Figure 2 shows some of the parameter values sampled for the mean and standard deviation during the MCMC analysis. MCMC samples from the posterior distribution of the mean and standard deviation for a single Normal distribution.

What is the posterior predictive expected loss in Stan?

The posterior predictive expected loss is 416.67 and can be derived analytical, as shown in my earlier post. Now let me reproduce the answer with Stan as well. Implementing the model in Stan is straightforward and I follow the same steps as in my simple example of last week.

Which is the prior parameter distribution on θ?

The prior parameter distribution on Θ is assumed to be a gamma distribution with parameters α = 4, β = 1000 : Θ ∼ Gamma ( α, β) ℓ i ∼ Exp ( Θ), ∀ i ∈ N In this case the predictive distribution is a Pareto II distribution with density f ( x) = α β α ( x + β) α + 1 and a mean of β α − 1 = 333.33.

Why are the mean and median of the original data not in the centre?

Because while the mean and median of the original data y are almost in centre of these statistics calculated on replicated data sets sampled from the posterior predictive distributions, this was not the case for the minimum, the maximum or the inter-quartile range.

How are parameter values used in posterior prediction?

To perform posterior prediction, we simulate datasets using parameter values drawn from a posterior distribution.

How are posterior predictions generated in parametric bootstrapping?

Vertical arrows show empirical values, and distributions show simulated values. The lighter distributions were generated by posterior predictive simulation and the darker distributions were generated by parametric bootstrapping (similar to posterior prediction, but using only maximum likelihood parameter estimates for simulation).

Which is an example of posterior predictive checking?

Examples of posterior predictive checking can also be found in the rstanarm vignettes and demos. predictive_error and predictive_interval. # Using newdata with a binomial model. # example_model is binomial so we need to set # the number of trials to use for prediction.

What is the posterior predictive output of Stan?

# # Inference for Stan model: stanmodelcode. # # post-warmup draws per chain=9800, total post-warmup draws=39200. # # Samples were drawn using NUTS (diag_e) at Tue May 19 06:06:08 2015. # # convergence, Rhat=1). The output shows a simulated predictive mean of 416.86, close to the analytical answer.