Markov Models
Markov models describe systems in which the future state depends only on the current state, not on past states. This memoryless property makes them tractable for various sequential tasks.
Example: A board game where only the current position matters for the next move. They are used for forecasting, stock market analysis, and other time-dependent phenomena.
Hidden Markov Models (HMMs) model sequential data with a series of hidden states that produce observable outputs. They solve evaluation, decoding, and learning problems for sequences.
Key concept: HMMs have a hidden state process (which follows the Markov property) and an observation process dependent on the current state. Example: Inferring the weather in a windowless room by observing people’s clothing.
Markov chains model sequences where only the current state determines the next state. Over time, they often settle into a stationary distribution that reflects long-term probabilities.
Everyday example: Weather patterns where if today is sunny, there is an 80% chance tomorrow will also be sunny. Applications include stock market predictions and website navigation analysis.