Statistical estimation by imitation

Parameter estimation in a subcritical percolation model with colouring, or cross-contamination rate estimation for microfluidics

We have just published a research paper1 about a nice combination of statistics and applied probability theory. The story opens with a novel mathematical model to quantify unwanted cross-contamination within lab-on-a-chip microfluidic devices. We apply the method of simulated moments (MSM) to estimate the parameters of the model. This method uses computer simulation with many different parameter proposals until the simulated data is close enough to the observed data. Our main contribution is that we prove the statistical consistency (`correctness’) of this method. Proving that the estimate will converge with probability 1 to the true parameter value as the sample size tends to infinity was a challenge because of the dependence among our random sample’s variables.

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