Markov Chain Monte Carlo: Simulating changes in a system to find the underlying distribution of states

Markov Chain Monte Carlo is a set of algorithms that simulate changes in a system to determine the underlying distribution of states at an equilibrium point. It uses Markov Chains, which describe the relationship between the current and previous states in a system using a transition matrix. By understanding these relationships, complex systems like the variation in produce available at a supermarket can be modeled. Monte Carlo sampling is used to determine the probability distribution, where random numbers between 0 and 1 are generated to decide the next state in the chain. This method has practical applications such as predicting customer movement in wineries or determining popular locations for advertising or city planning.