Markov chain
Noun: A Markov chain is a specific type of stochastic (random) process. It models a sequence of possible events where the probability of each event depends only on the state attained in the previous event. It is characterized by the "Markov property," meaning the future state is independent of the past states given the present state. The "chain" refers to this linked sequence of states.
A Markov chain is used to model systems that transition from one state to another among a finite or countable number of possible states. The transitions are probabilistic, not deterministic.
Examples: * The weather pattern was modeled as a Markov chain, where each day's weather depended only on the previous day's. * In the board game simulation, the player's movement was treated as a Markov chain. * Analyzing the sequence of words in a sentence often uses a Markov chain model.
- "Hidden Markov Model": A statistical model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states.
- Speech recognition software frequently relies on Hidden Markov Models.
- "Markov Chain Monte Carlo (MCMC)": A class of algorithms for sampling from probability distributions based on constructing a Markov chain.
- The researcher used Markov Chain Monte Carlo methods to estimate the complex statistical model.
- Markov process (n): A more general stochastic process with the Markov property, of which a Markov chain is a type (specifically one with a discrete state space and often discrete time).
- Markovian (adj): Having the properties of a Markov process; exhibiting the Markov property.
- The system's behavior is Markovian.
- State machine (in certain contexts, particularly deterministic ones)
- Stochastic process (this is the broader category)
- Transition matrix: A square matrix used to describe the probabilities of moving from one state to another in a Markov chain.
- Stationary distribution: A probability distribution that remains unchanged as the Markov chain evolves over time.
- State space: The set of all possible states in the Markov chain.
- a Markov process for which the parameter is discrete time values