A Simple Markov Model

A Markov model assumes that the current state contains the information from the past needed to determine the next-state distribution. Defining that state is part of the modeling task.

A Markov model assumes that, given the current state, earlier history adds no information about the probability distribution of the next state. The qualification matters: a state may need to include inventory, outstanding orders, or other remembered information. Calling something current does not make it sufficient.

For a finite model, transition probabilities can be placed in a matrix whose rows each sum to one. If the same matrix applies at every step, the chain is time-homogeneous, an additional assumption. Use the model to make a forecast and examine whether history still predicts errors. A compact state is valuable when it preserves relevant information, not because the past is inherently unimportant.

When to use it

When a sequential process can plausibly be represented by a manageable state and probabilistic transitions.

How it can help

Define states and transitions, make a forecast, and check whether omitted history materially improves prediction.