Modeling Dependent Random Variables Using Markov Chains | by Roman Paolucci | Feb, 2024

In my earlier article discussing Maximum Likelihood Estimation of Parameters for Random Variables, we acted as a hospital menace supervisor, senior doctor statistician, data science nurse (I nonetheless have truly no idea who could possibly be in charge of this) and developed a straightforward likelihood model to estimate our menace of not having adequate beds to accommodate new victims. To carry out this we made the subsequent assumptions:

• Assume all victims checked in to the hospital will attempt similar day
• Assume victims checked in on daily basis are unbiased of one another

Though impractical, these assumptions enabled us to model the number of victims in a given day as a Poisson random variable (see Common Random Variables) which has a well-defined distribution function we would use to estimate the possibility of being unable to accommodate a model new affected particular person.

A quick digression — in any case, the Poisson random variable is parameterized by lambda which fashions the expectation and variance of victims on a given day. We spent a majority of the sooner article discussing the most interesting statistical technique to estimate this parameter given a set of seen data using the tactic of most likelihood estimation. When you’re unfamiliar with this technique of choosing an estimator for our parameter estimates I encourage you to try that article as we could even be making use of the thought herein.

Incorrect assumptions overestimate or underestimate menace or potentialities counting on the violation. As an example, assuming everyone checks in and checks out on the similar day underestimates menace because it’s likely some victims will maintain in a single day.

This article will seemingly be broken up into the subsequent sections.

• Introduction to Markov Chains and Transition Matrices
• Computing Arbitrary Step Transition Possibilities
• Redefining and Fixing the Distinctive Draw back as a Markov Chain
• Absorbing States
• Most Chance Estimation of Transition Possibilities
• Calibrating a Transition Matrix to Info and…