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<h1>fig8_2
</h1>

<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="box"><strong>Local Regression and Likelihood, Figure 8.2.</strong></div>

<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="box"><strong>This is a script file. </strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="fragment"><pre class="comment"> Local Regression and Likelihood, Figure 8.2.

 Discrimination/Classification, simple example using
 density estimation.

 First, compute density estimates fit0, fit1 ('family','rate'
 - output is in events per unit area) for each class in the
 training sample. The ratio fit1/(fit1+fit0) estimates the
 posterior probability that an observation comes from population 1.

 plotting the classification boundary is slightly tricky - it depends
 on both fits, so lfplot() can't be used. Instead, both fits must be
 evaluated on the same grid of values, which is then used to make a
 contour plot.

 Author: Catherine Loader</pre></div>

<!-- crossreference -->
<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../../../matlabicon.gif)">
<li><a href="../../../chronux_2_10/locfit/m/locfit.html" class="code" title="function fit=locfit(varargin)">locfit</a>	Smoothing noisy data using Local Regression and Likelihood.</li><li><a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>	Interpolate a fit produced by locfit().</li></ul>
This function is called by:
<ul style="list-style-image:url(../../../matlabicon.gif)">
<li><a href="runbook.html" class="code" title="">runbook</a>	</li></ul>
<!-- crossreference -->


<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="fragment"><pre>0001 <span class="comment">% Local Regression and Likelihood, Figure 8.2.</span>
0002 <span class="comment">%</span>
0003 <span class="comment">% Discrimination/Classification, simple example using</span>
0004 <span class="comment">% density estimation.</span>
0005 <span class="comment">%</span>
0006 <span class="comment">% First, compute density estimates fit0, fit1 ('family','rate'</span>
0007 <span class="comment">% - output is in events per unit area) for each class in the</span>
0008 <span class="comment">% training sample. The ratio fit1/(fit1+fit0) estimates the</span>
0009 <span class="comment">% posterior probability that an observation comes from population 1.</span>
0010 <span class="comment">%</span>
0011 <span class="comment">% plotting the classification boundary is slightly tricky - it depends</span>
0012 <span class="comment">% on both fits, so lfplot() can't be used. Instead, both fits must be</span>
0013 <span class="comment">% evaluated on the same grid of values, which is then used to make a</span>
0014 <span class="comment">% contour plot.</span>
0015 <span class="comment">%</span>
0016 <span class="comment">% Author: Catherine Loader</span>
0017 
0018 load cltrain;
0019 u0 = find(y==0);
0020 u1 = find(y==1);
0021 fit0 = <a href="../../../chronux_2_10/locfit/m/locfit.html" class="code" title="function fit=locfit(varargin)">locfit</a>([x1(u0) x2(u0)],y(u0),<span class="string">'family'</span>,<span class="string">'rate'</span>,<span class="string">'scale'</span>,0);
0022 fit1 = <a href="../../../chronux_2_10/locfit/m/locfit.html" class="code" title="function fit=locfit(varargin)">locfit</a>([x1(u1) x2(u1)],y(u1),<span class="string">'family'</span>,<span class="string">'rate'</span>,<span class="string">'scale'</span>,0);
0023 
0024 v0 = -3+6*(0:50)'/50;
0025 v1 = -2.2+4.2*(0:49)'/49;
0026 <span class="comment">% predict returns log(rate)</span>
0027 z = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit0,{v0 v1})-<a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit1,{v0 v1});
0028 z = reshape(z,51,50);
0029 figure(<span class="string">'Name'</span>,<span class="string">'fig8_2: classification'</span>);
0030 contour(v0,v1,z',[0 0]);
0031 hold on;
0032 plot(x1(u0),x2(u0),<span class="string">'.'</span>);
0033 plot(x1(u1),x2(u1),<span class="string">'.'</span>,<span class="string">'color'</span>,<span class="string">'red'</span>);
0034 hold off;
0035 
0036 p0 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit0,[x1 x2]);
0037 p1 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit1,[x1 x2]);
0038 py = (p1 &gt; p0);
0039 disp(<span class="string">'Classification table for training data'</span>);
0040 tabulate(10*y+py);
0041 
0042 load cltest;
0043 p0 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit0,[x1 x2]);
0044 p1 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit1,[x1 x2]);
0045 py = (p1 &gt; p0);
0046 disp(<span class="string">'Classification table for test data'</span>);
0047 tabulate(10*y+py);
0048</pre></div>
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