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TheMetropolis-Hastings algorithm is a Monte Carlo method for generating random samples with a specific distribution. It can be used to get the probability distribution of a target sample function.

Here are the steps to get the target sample function using the Metropolis-Hastings algorithm:

1. Select a starting point, $x_0$, which can be any value in the target distribution function. < br / > $2, define a candidate distribution function q(x | y) $, $x $is new samples, $y $is the current sample. < br / > $3, from the candidate distribution function q(x | y) $sampling to get a new sample is $x '$. < br / > 4, calculating acceptance rate $\ alpha(x, y) = / min/left(1 \ frac {p(x ') q(y | x ')} {p(y) q(x '} \ | y) right) $, where $p(x) $is the target distribution function, $p(y) $is the distribution function of the current sample.5, accept the new sample $x'$with the probability of acceptance rate $\alpha(x,y)$, that is, generate a random number $u$, if $u \le \alpha(x,y)$, accept the new sample, otherwise continue to use the current sample $y$.

6. Repeat Steps 3-5 until you have the required number of samples. < br / > 7, Metropolis - Hastings algorithm is the key step is to define the candidate distribution function $q(x | y) $, its form can affect the performance of the algorithm. In general, you can use either a Gaussian or a uniform distribution as a candidate distribution function, depending on the shape of the target distribution function.

The resulting sample sequence can be used to estimate the expected value, variance, and other statistics of the target distribution function.