Markov Chain Monte Carlo (MCMC) is a simulation-based computational method employed in a wide variety of areas such as physics, biology and civil engineering etc. The method is based on randomly sampling possible answers to a given problem until a solution that is close enough to the desired answer is obtained.
MCMC was first proposed by Andrei Andreevich Markov in the early 20th century as a means of modelling a stochastic process. The basic idea is to construct a Markov Chain consisting of a large number of possible states and use it to explore the probability space of the problem. Each state is assigned a certain probability and by randomly sampling the possible states, a solution is obtained.
MCMC is a popular method in statistics and has been widely used in Bayesian analysis since the mid-1950s. The basic idea of MCMC is to draw samples from the posterior distribution of the parameters of interest in order to make inferences. This is done by constructing a Markov Chain with a stationary distribution that approximates the posterior distribution. The samples obtained from the chain can be used to estimate the parameters and make inferences about the underlying process.
In addition to being a powerful technique in statistics, MCMC has also been applied to computer science. It has been used for Bayesian optimization, which is the process of optimizing a set of parameters by minimizing the expected value of an objective function. MCMC has also seen use in artificial intelligence and machine learning, where it has been used to approximate intractable probabilities.
Overall, Markov Chain Monte Carlo (MCMC) is a powerful simulation-based method which is used in a wide variety of areas to obtain approximate solutions to complex problems. It is a popular technique in statistics and more recently in computer science as well. The method is particularly useful for approximating intractable probabilities and can be employed for Bayesian optimization and other machine learning tasks.
