马尔科夫链Matlab程序

% MCMC -- Markov Chain Monte Carlo Tools % Copyright (c) 1998, Harvard University. Full copyright in the file Copyright % % There are three parts to this library of routines. % 1. *[rnd,pdf,lpr].m - distribution function tools to complement Matlab's % 2. mcmc*.m - routines to calculate and display summaries of MCMC output % 3. other - other useful routines % % 1. Distribution Function Tools % % These function help in random number generation and % various calculations involving density functions. % The names attempt to match those that MatLab uses, % namely, *pdf, *cdf, and *rnd. Those that end in % "lpr" are for "Log. Probability Ratio", which are % useful for a Metropolis-Hastings algorithm. % % Note: there are two random number generators in Matlab % one for normals and the other for everything else. % For reseting the normal random seed use randn('state', ...) % and for all others use rand('state', ...). % % randrand - randomize both random number chains off the clock % % mvnormrnd - random multivariate normal - different from Matlab's mvnrnd % % wishrnd - random Wishart value % wishirnd - random Wishart value - integer df only % invwishrnd - random inverse Wishart value % invwishirnd - random inverse Wishart value - integer df only % invwishpdf - inverse Wishart density % % metrop - a general Metropolis-Hastings step % % betalpr - log probability ratio for beta distribution % gamlpr - log probability ratio for gamma distribution % invwishlpr - log probability ratio for inverse wishart distribution % mvnormlpr - log probability ratio for multivariate normal distribution % % 2. MCMC Summaries % % These routines use the last dimension of an array as the % sample index. So an array with dimension (nr,nc,ns) % will be a collection of ns samples of an nr by nc matrix of % parameters. An array with dimension (nr,nc) will % be nc samples of an nr-vector of parameters. % When the summary statistics are calculated, the last dimension % is dropped. % % Note: Matlab routines tend to collapse over the first dimension % instead of the last. I chose to use the last dimension for % an aesthetic reason, when simply displaying a 3+ dimensional % array, Matlab displays the first two dimensions as a matrix % and splits over the 3rd+ dimensions. To see what I mean % enter 'x = zeros(2,3,4)'. % % mcmclt - lower triangle - for symmetric matricies - to use with mcmctrace % mcmcsumm - calculate summary statistics % (includes autocorrelations and Gelman-Rubin statistics) % mcmctrace - matrix of trace plots % mcmcacf - to plot autocorrelations % mcmcgr - Gelman-Rubin R statistic for convergence % % mcmcdemo - short demonstration program % % 3. Other % % ltvec - convert a lower-triangular matrix into a vector % veclt - convert a vector into a lower-triangular matrix % ltindex - convert row and column index into lt-index % % % Bug reports and suggestions are welcome, but quick % response is not guaranteed. % % David Shera - shera@hsph.harvard.edu % http://www.biostat.harvard.edu/~shera/mcmc