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<html><head><title>Netlab Reference Manual metrop</title></head><body><H1> metrop</H1><h2>Purpose</h2>Markov Chain Monte Carlo sampling with Metropolis algorithm.<p><h2>Synopsis</h2><PRE>samples = metrop(f, x, options)samples = metrop(f, x, options, [], P1, P2, ...)[samples, energies, diagn] = metrop(f, x, options)s = metrop('state')metrop('state', s)</PRE><p><h2>Description</h2><CODE>samples = metrop(f, x, options)</CODE> usesthe Metropolis algorithm to sample from the distribution<CODE>p ~ exp(-f)</CODE>, where <CODE>f</CODE> is the first argument to <CODE>metrop</CODE>. The Markov chain starts at the point <CODE>x</CODE> and each candidate state is picked from a Gaussian proposal distribution andaccepted or rejected according to the Metropolis criterion.<p><CODE>samples = metrop(f, x, options, [], p1, p2, ...)</CODE> allowsadditional arguments to be passed to <CODE>f()</CODE>. The fourth argument isignored, but is included for compatibility with <CODE>hmc</CODE> and theoptimisers.<p><CODE>[samples, energies, diagn] = metrop(f, x, options)</CODE> also returnsa log of the energy values (i.e. negative log probabilities) for thesamples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containingdiagnostic information (position andacceptance threshold) for each step of the chain in <CODE>diagn.pos</CODE> and<CODE>diagn.acc</CODE> respectively. All candidate states (including rejectedones) are stored in <CODE>diagn.pos</CODE>.<p><CODE>s = metrop('state')</CODE> returns a state structure that contains thestate of the two random number generators <CODE>rand</CODE> and <CODE>randn</CODE>.These are contained in fields<CODE>randstate</CODE>, <CODE>randnstate</CODE>.<p><CODE>metrop('state', s)</CODE> resets the state to <CODE>s</CODE>. If <CODE>s</CODE> is an integer,then it is passed to <CODE>rand</CODE> and <CODE>randn</CODE>.If <CODE>s</CODE> is a structure returned by <CODE>metrop('state')</CODE> thenit resets the generator to exactly the same state.<p>The optional parameters in the <CODE>options</CODE> vector have the followinginterpretations.<p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejectionthreshold at each step of the Markov chain. If the value is 2, then theposition vectors at each step are also displayed.<p><CODE>options(14)</CODE> is the number of samples retained from the Markov chain;default 100. <p><CODE>options(15)</CODE> is the number of samples omitted from the start of thechain; default 0.<p><CODE>options(18)</CODE> is the variance of the proposal distribution; default 1.<p><h2>Examples</h2>The following code fragment samples from the posterior distribution ofweights for a neural network.<PRE>w = mlppak(net);[samples, energies] = metrop('neterr', w, options, 'netgrad', net, x, t);</PRE><p><h2>Algorithm</h2>The algorithm follows the procedure outlined in Radford Neal's technicalreport CRG-TR-93-1 from the University of Toronto.<p><h2>See Also</h2><CODE><a href="hmc.htm">hmc</a></CODE><hr><b>Pages:</b><a href="index.htm">Index</a><hr><p>Copyright (c) Ian T Nabney (1996-9)</body></html>⌨️ 快捷键说明
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