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I've recently spent a bit of time getting to grips with Markov Chains. I've created a jupyter notebook which attempts to give an "intuition" into the basic concepts; an overview of some of the maths involved and a idea to use "social mobility" probability density functions with Markov Chains to estimate long term "social class" proportions.

This paper has three sections. The first section uses simulation to develop an intuitive understanding of the ideas behind Markov Chains; the second section looks at some of the mathematics used to represent the problem, leading to the standard eigenvector representation and the final section describes an idea to use Markov Chains together with a probability distribution model of social mobility to predict long term "social class" proportions.

Intuition
Single State Markov Chain - The Law of Large Numbers

The relative frequency/experimental probability gets closer the theoretical probability as the number of trials increases. So, if event A has a given probability, then as the number of trials increases the proportion of times event A occurs gets closer to the probability of A. So a single state Markov Chain has "long term behaviour".
Content of the notebook:
  • Source code
  • Multi State Markov Chains
  • Simulation
  • Markov Model Based on a Social Mobility Probability Distributions
  • Collecting Data
  • Example Output Based on Dummy Data
  • Plot Predictions Against Data in the BBC Report

Extract from the article:

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Comment by Joel Mamedov on June 1, 2018 at 8:10am

Thanks for the article. It would be helpful to give us some context and definitions.

For example what problem you are trying to solve? (give us some practical example) 

What is "social mobility"? and how it is related to the problem you are trying to solve?

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