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The Marsaglia polar method [1] is a pseudo-random number sampling method for generating a pair of independent standard normal random variables. [2]Standard normal random variables are frequently used in computer science, computational statistics, and in particular, in applications of the Monte Carlo method.
A diagram of an alias table that represents the probability distribution〈0.25, 0.3, 0.1, 0.2, 0.15〉 In computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by Alastair J. Walker.
A blocked Gibbs sampler groups two or more variables together and samples from their joint distribution conditioned on all other variables, rather than sampling from each one individually. For example, in a hidden Markov model , a blocked Gibbs sampler might sample from all the latent variables making up the Markov chain in one go, using the ...
The basic form as given by Box and Muller takes two samples from the uniform distribution on the interval (0,1) and maps them to two standard, normally distributed samples. The polar form takes two samples from a different interval, [−1,+1], and maps them to two normally distributed samples without the use of sine or cosine functions.
Publicly available dynamic nested sampling software packages include: dynesty - a Python implementation of dynamic nested sampling which can be downloaded from GitHub. [15] dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions. [16] dyPolyChord is available on GitHub.
For an exponential distribution, the tail looks just like the body of the distribution. One way is to fall back to the most elementary algorithm E = −ln(U 1) and let x = x 1 − ln(U 1). Another is to call the ziggurat algorithm recursively and add x 1 to the result. For a normal distribution, Marsaglia suggests a compact algorithm:
Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution.The method is based on the observation that to sample a random variable one can sample uniformly from the region under the graph of its density function.
Gibbs sampling: generates a sequence of samples from the joint probability distribution of two or more random variables; Hybrid Monte Carlo: generates a sequence of samples using Hamiltonian weighted Markov chain Monte Carlo, from a probability distribution which is difficult to sample directly.