A note on using simulated implicit likelihood estimation to analyze summaries from a designed experiment

Abstract

In this article, we use Simulated Implicit Likelihood Estimation (SimILE) to analyze summary statistics, the sample mean and variance of lognormally distributed replicates, when only these summaries are available at each run of a designed experiment. Because the likelihood for the summary statistics is unknown, by simulating lognormal random variables, SimILE estimates the likelihood and uses it in a Bayesian analysis. We first consider normally distributed replicates where the exact likelihood is known and then lognormally distributed replicates. We illustrate these cases with simulated data where we know the answers and compare the SimILE results in the cases where the exact likelihood is known.

Keywords:

• Bayesian inference
• factorial design
• lognormal
• simulation

Acknowledgement

We thank Cee Cee Essix for her encouragement and support. We thank two anonymous reviewers whose insightful comments on an earlier version helped improve the exposition of this article.

About the author

Michael S. Hamada is a Scientist and holds a PhD in Statistics from the University of Wisconsin–Madison. He is a Fellow of the American Statistical Association, American Society for Quality, and Los Alamos National Laboratory. His research interests include design and analysis of experiments, measurement system assessment, quality control, and reliability.