I understand that Markov Chains are very important in modeling phenomena such as intergenerational socio-economic status, weather, random walks, memory-less board games, etc… But I'm struggling to find real, empirical data that satisfies a Markov Chain.
For example, I see a lot of…"imagine that if it rained yesterday, then it will rain today with probability 0.8". Where is this 0.8 from? I can't find anything that references a study, or some dataset upon which these figures are based. Not just weather, but any Markov Chain based model. Anyone have resources or suggestions on where to locate these? I searched the footnotes of a lot of these examples but they haven't revealed anything.
Edit Just because some people have provided answers to this, let me clarify and ask it in a different way: Are there processes in nature, and accompanying datasets, that satisfy the Markov Property to a "high" degree, rather than just toy examples that illustrate it?
Best Answer
Usually these kinds of models are trained using some empirical data. In your example, if you have data about the weather for several years, you can estimate the probability of a rainy day given that previous day was rainy, or given that the previous day was sunny, etc.