Markov Models

A Markov model represents next-state probabilities using a current state assumed sufficient for that prediction. Earlier history is conditionally irrelevant given that state within the model; the state may itself contain accumulated consequences of history.

The Markov property says that, conditional on the chosen current state, earlier history adds no information to the model's next-state distribution. The phrase 'current state' does substantial work. Position alone may be insufficient, while position plus inventory or accumulated resources may capture the rule. A richer state can retain consequences of history without requiring the entire sequence.

Define transitions at a meaningful time step and check whether omitted history predicts what happens next. If duration in a state matters, a label such as 'waiting' may need an age component or a different model. Fixed transition probabilities are an additional time-homogeneity assumption, not part of every Markov process. A useful approximation still needs evaluation for the intended prediction.

When to use it

When representing sequential transitions and assessing whether a manageable current-state description is sufficient for the relevant prediction.

How it can help

Define a defensible state representation and test whether omitted history changes predicted transitions. Use the model for a specified sequential task while keeping approximation error and changing transition rules visible.