Proposal distribution is a crucial component in the Metropolis-Hastings algorithm used in Markov Chain Monte Carlo methods to sample from a probability distribution. It suggests new sample points based on a defined probability distribution, influencing the efficiency and convergence of the algorithm.

Proposal Distribution

Proposal distribution

The Metropolis-Hastings Algorithm is a Markov Chain Monte Carlo method used to generate a sequence of samples from a probability distribution for which direct sampling is difficult, often employed in Bayesian inference and statistical physics. It iteratively proposes a candidate state based on a proposal distribution and decides whether to accept or reject it based on an acceptance ratio, ensuring the samples converge to the target distribution over time.

Metropolis-Hastings algorithm

Markov Chain Monte Carlo methods

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. It is fundamental in statistics and data analysis, helping to model and predict real-world phenomena by describing how probabilities are distributed over values of a random variable.

probability distribution

sample points

Efficiency is the ability to achieve a desired outcome with the least amount of wasted resources, such as time, energy, or materials. It is a critical factor in both economic systems and engineering processes, driving innovation and competitiveness by maximizing output while minimizing input.

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