Markovketjupäättelyä

Markovketjupäättelyä, known in English as Markov chain inference, is a computational method used to analyze and predict the behavior of systems that can be modeled as Markov chains. A Markov chain is a stochastic model describing a sequence of possible events where the probability of each event depends only on the state attained in the previous event. This property is known as the Markov property. Markov chain inference involves using observed data to estimate the parameters of the Markov chain, such as transition probabilities between states, and then using this estimated model to make predictions about future states or to understand the long-term behavior of the system.

The process typically begins with collecting a sequence of observations representing the states of the system over time. These observations are then used to construct a transition matrix, which quantifies the likelihood of moving from any given state to any other state. Statistical techniques are employed to estimate these probabilities, often using maximum likelihood estimation. Once the transition matrix is estimated, various inference tasks can be performed. These include calculating the probability of a specific sequence of states occurring, determining the steady-state distribution of the system (the long-term probability of being in each state), or predicting the most likely future state given the current state. Markov chain inference finds applications in diverse fields such as natural language processing, bioinformatics, finance, and physics for modeling phenomena like word sequences, DNA evolution, stock market movements, and particle interactions.