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Richard_Zink

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May 27, 2014

MCMC Diagnostics Add-In

The MCMC Diagnostics add-in calculates convergence diagnostics as well as equal-tailed and HPD credible intervals for a data set containing posterior samples from one or more parallel Markov chains. Included are two posterior probability calculators. This add-in does not perform MCMC but allows for straightforward analysis and review of posterior samples.


The dialog below displays an example for 60,000 MCMC samples for 3 independently run Markov chains from a Bayesian hierarchical model of 40 adverse events from Mehrotra & Heyse (2004).  The independent Markov chains are provided so that Gelman-Rubin diagnostics are computed.


6577_MCMC Dialog.png


The figure below shows the Diagnostics panel where each parameter is summarized using several graphs and analyses.  These analyses include


  1. Histogram with non-parametric density curve and summary statistics for chain 1
  2. Trace plot of MCMC samples for chain 1
  3. Plots and tests to assess autocorrelation of samples across time for chain 1
  4. If multiple chains are provided, a trace plot of all chains to assess convergence is provided along with Gelman-Rubin diagnostics

6578_MCMC1.png

Forest plots containing equal-tailed and highest posterior density (HPD) credible intervals are provided for chain 1.

6579_MCMC2.png

A univariate probability calculator is provided to calculate the probability that each parameter is within the supplied range.  Here, I calculate the probability that the parameter is positive, which would indicate that there is excess risk on the novel treatment.

6585_MCMC3.png

The multivariate probability calculator lets you calculate when sets of parameters meet criteria jointly.  Here, I calculate the probability that the first five parameters are simultaneously positive. This can be interpreted as the probability that the first five adverse events show excess risk simultaneously.

6586_MCMC4.png

Go to support.sas.com/resources/papers/proceedings13/179-2013.pdf for more detail.


Mehrotra DV & Heyse JF. (2004). Use of the False Discovery Rate for Evaluating Clinical Safety Data. Statistical Methods in Medical Research 13: 227-238.

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