Mercurial > hg > camir-aes2014

diff toolboxes/FullBNT-1.0.7/nethelp3.3/metrop.htm @ 0:e9a9cd732c1e tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
parents
children
line wrap: on
line diff
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/nethelp3.3/metrop.htm	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,108 @@
+<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> uses
+the 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 and
+accepted or rejected according to the Metropolis criterion.
+
+<p><CODE>samples = metrop(f, x, options, [], p1, p2, ...)</CODE> allows
+additional arguments to be passed to <CODE>f()</CODE>.  The fourth argument is
+ignored, but is included for compatibility with <CODE>hmc</CODE> and the
+optimisers.
+
+<p><CODE>[samples, energies, diagn] = metrop(f, x, options)</CODE> also returns
+a log of the energy values (i.e. negative log probabilities) for the
+samples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containing
+diagnostic information (position and
+acceptance threshold) for each step of the chain in <CODE>diagn.pos</CODE> and
+<CODE>diagn.acc</CODE> respectively.  All candidate states (including rejected
+ones) are stored in <CODE>diagn.pos</CODE>.
+
+<p><CODE>s = metrop('state')</CODE> returns a state structure that contains the
+state 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> then
+it resets the generator to exactly the same state.
+
+<p>The optional parameters in the <CODE>options</CODE> vector have the following
+interpretations.
+
+<p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejection
+threshold at each step of the Markov chain. If the value is 2, then the
+position 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 the
+chain; 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 of
+weights 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 technical
+report 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>
\ No newline at end of file