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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.

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