Markoff chain
Noun: A Markov chain is a specific type of stochastic (random) process. It is defined by the property that the probability of transitioning to any particular future state depends only on the current state of the process, not on the sequence of events that preceded it. This is known as the "memoryless" property or Markov property. The "chain" refers to the sequence of states generated by this process over discrete time steps.
This term is used primarily in mathematics, statistics, computer science, and fields involving probabilistic modeling. - It describes a mathematical system that undergoes transitions from one state to another according to specific probabilistic rules. - The defining characteristic is its lack of memory; only the present state influences the future.
- In Mathematics/Statistics:
- The researcher used a Markov chain to model the random movement of a particle.
- Analyzing the Markov chain revealed the long-term behavior of the system.
- In Computer Science:
- The algorithm is based on a Markov chain for generating realistic text sequences.
- In General Context:
- Weather patterns are sometimes approximated using a Markov chain, where today's weather is the state that predicts tomorrow's.
- "to model something as a Markov chain": To represent a system using the principles of a Markov chain.
- We can model the board game as a Markov chain where each square is a state.
- "stationary distribution of a Markov chain": A key concept referring to the long-run, stable probability distribution of states.
- Calculating the stationary distribution tells us the proportion of time the chain spends in each state.
- Markov process (n): A more general term for a process with the Markov property, which can be in continuous time. A Markov chain is a type of Markov process with discrete time.
- State (n): A possible condition or position in the chain.
- Transition probability (n): The probability of moving from one state to another.
- Memoryless property (n): The defining characteristic of a Markov chain.
- Stochastic process with Markov property: A more descriptive technical synonym.
- State machine (probabilistic): A related concept in computer science, though not always identical.
- Hidden Markov Model (HMM) (n): A statistical model where the system being modeled is assumed to be a Markov process with unobserved (hidden) states.
- Speech recognition software often relies on Hidden Markov Models.
- Markov Chain Monte Carlo (MCMC) (n): A class of algorithms for sampling from probability distributions, using Markov chains.
- Markov Chain Monte Carlo methods are essential in Bayesian statistics.
- a Markov process for which the parameter is discrete time values