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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 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 ...
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:
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.
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.
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.
Simulation: Drawing one pseudo-random uniform variable from the interval [0,1] can be used to simulate the tossing of a coin: If the value is less than or equal to 0.50 designate the outcome as heads, but if the value is greater than 0.50 designate the outcome as tails. This is a simulation, but not a Monte Carlo simulation.
Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator .