Mean and variance of first passage time in Markov chains with unknown parameters

TL;DR

This paper introduces a Monte Carlo method to estimate the mean and variance of first passage times in Markov chains with unknown parameters, accounting for data sample size effects, demonstrated through a biological example.

Contribution

It presents a novel Monte Carlo approach for estimating passage time moments in Markov chains with empirically derived parameters, emphasizing the role of sample size.

Findings

Monte Carlo method effectively estimates moments with unknown parameters.

Application to biological data demonstrates practical utility.

Highlights importance of sample size in variance estimation.

Abstract

There are known expressions to calculate the moments of the first passage time in Markov chains. Nevertheless, it is commonly forgotten that in most applications the parameters of the Markov chain are constructed using estimates based upon empirical data and in those cases the data sample size should play an important role in estimating the variance. Here we provide a Monte Carlo approach to estimate the first two moments of the passage time in this situation. We illustrate this method with an example using data from the biological field.