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@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\W}[1]{ \; #1 \; }@)@This is dismod_at-20221105 documentation: Here is a link to its current documentation .
Metropolis MCMC Algorithm

Syntax
log_f
m
x0
s
     Vector Case
     Float Case
a
c
Example

Syntax
(a, c) = dismod_at.metropolis(log_f, m, x0, s)
log_f
Given a numpy float vector of length n , the syntax
 d = log_f(x)
 sets the float d to the log of the un-normalized density corresponding to the positive function @(@ f(x) @)@ mapping @(@ \B{R}^n @)@ to the non-negative real values. If @(@ f(x) @)@ is zero, the corresponding log-density value should equal - float("inf").

m
is the int number of vectors in the MCMC chain.

x0
is a numpy float vector of length n that specifies the initial vector in the chain (denoted by @(@ x^0 @)@ below).

s
is a float or, a numpy float vector of length n , that specifies the scaling for each of the components of @(@ x @)@.

Vector Case
If s is a vector, for @(@ i = 1 , \ldots, m-1 @)@, and @(@ j = 0 , \ldots, n-1 @)@, the j-th component of the i-th proposal vector @(@ y^i @)@ is given by @[@ y_j^i = x_j^{i-1} + w_j^{i-1} s_j @]@ where @(@ w_j^i \sim \B{N}(0, 1) @)@ are all independent.

Float Case
If s is a float, @[@ y_j^i = x_j^{i-1} + w_j^{i-1} s @]@

a
is the int acceptance count; i.e. the number of indices @(@ i @)@ such that @(@ x^i = y^i @)@ (for the other indices @(@ x^i = x^{i-1} @)@).

c
is an @(@ m \times n @)@ numpy float array that contains the components of the Markov Chain. We use the notation @(@ x_j^i @)@ for c[i, j] . For any smooth function @(@ g : \B{R}^n \rightarrow \B{R} @)@, the Metropolis algorithm provides the following approximation as @(@ m \rightarrow \infty @)@, @[@ \frac{1}{m} \sum_{i=0}^{m-1} g( x^i ) \rightarrow \frac{ \int g( x ) f ( x ) \B{d} x }{ \int f( x ) \B{d} x } @]@

Example
The file user_metropolis.py contains an example and test of this routine.
Input File: python/dismod_at/metropolis.py