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The Metropolis-Hastings algorithm sampling a normal one-dimensional posterior probability distribution. In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. New ...
Gibbs sampling can be viewed as a special case of Metropolis–Hastings algorithm with acceptance rate uniformly equal to 1. When drawing from the full conditional distributions is not straightforward other samplers-within-Gibbs are used (e.g., see [8] [9]). Gibbs sampling is popular partly because it does not require any 'tuning'.
Gibbs sampling is named after the physicist Josiah Willard Gibbs, in reference to an analogy between the sampling algorithm and statistical physics.The algorithm was described by brothers Stuart and Donald Geman in 1984, some eight decades after the death of Gibbs, [1] and became popularized in the statistics community for calculating marginal probability distribution, especially the posterior ...
When sampling from a full-conditional density is not easy, a single iteration of slice sampling or the Metropolis-Hastings algorithm can be used within-Gibbs to sample from the variable in question. If the full-conditional density is log-concave, a more efficient alternative is the application of adaptive rejection sampling (ARS) methods.
In statistics and physics, multicanonical ensemble (also called multicanonical sampling or flat histogram) is a Markov chain Monte Carlo sampling technique that uses the Metropolis–Hastings algorithm to compute integrals where the integrand has a rough landscape with multiple local minima.
Gibbs sampling is a special case of the Metropolis-Hastings sampler, with the a proposal distribution that at each iteration, updates one element of the parameter vector from the distribution of that element conditional on the current value of all of the others: (′ |) = (|), resulting in an acceptance probability that is always 1, and hence ...
Compared to using a Gaussian random walk proposal distribution in the Metropolis–Hastings algorithm, Hamiltonian Monte Carlo reduces the correlation between successive sampled states by proposing moves to distant states which maintain a high probability of acceptance due to the approximate energy conserving properties of the simulated ...
Key papers include Albert and Chib (1993) [1] which introduced an approach for binary and categorical response models based on latent variables that simplifies the Bayesian analysis of categorical response models; Chib and Greenberg (1995) [2] which provided a derivation of the Metropolis-Hastings algorithm from first principles, guidance on ...