The Bayes.php class implements the Bayes theorem calculation. The getPosterior method is where most of the mathematically interesting code resides.
Listing 5. Implementing the calculation with the Bayes.php class
<?php
/**
* Bayes
*
* Calculates posterior probabilities for m hypotheses and n evidence
* alternatives. The code was inspired by a procedural TrueBasic version
* (Bayes.tru) bundled with Grimstead and Snell's excellent online
* textbook "Introduction to Probability".
*/
class Bayes {
/**
* Number of evidence alternatives (that is, number of rows).
*/
var $m;
/**
* Number of hypothesis alternatives (that is, number of columns).
*/
var $n;
/**
* Output labels for evidence alternatives.
*/
var $row_labels = array();
/**
* Output labels for hypothesis alternatives.
*/
var $column_labels = array();
/**
* Vector container for prior probabilities.
*/
var $priors = array();
/**
* Matrix container for likelihood of evidence e given hypothesis h.
*/
var $likelihoods = array();
/**
* Matrix container for posterior probabilties.
*/
var $posterior = array();
/**
* Vector container for evidence probabilties.
*/
var $evidence = array();
/**
* Initialize the Bayes algorithm by setting the priors, likelihoods
* and dimensions of the likelihood and posterior matrices.
*/
function Bayes($priors, $likelihoods) {
$this->priors = $priors;
$this->likelihoods = $likelihoods;
$this->m = count($this->likelihoods); // num rows
$this->n = count($this->likelihoods[0]); // num cols
return true;
}
/**
* Output method for setting row labels prior to display.
*/
function setRowLabels($row_labels) {
$this->row_labels = $row_labels;
return true;
}
/**
* Output method for setting column labels prior to display.
*/
function setColumnLabels($column_labels) {
$this->column_labels = $column_labels;
return true;
}
/**
* Compute the posterior probability matrix given the priors and
* likelihoods.
*
* The first set of loops computes the denominator of the canonical
* Bayes equation. The probability appearing in the denominator
* serves a normalizing role in the computation - it ensures that
* posterior probabilities sum to 1.
*
* The second set of loops:
*
* 1. multiplies the prior[$h] by the likelihood[$h][$e]
* 2. divides the result by the denominator
* 3. assigns the result to the posterior[$e][$h] probability matrix
*/
function getPosterior() {
// Find probability of evidence e
for($e=0; $e < $this->n; $e++) {
for ($h=0; $h < $this->m; $h++) {
$this->evidence[$e] += $this->priors[$h]
* $this->likelihoods[$h][$e];
}
}
// Find probability of hypothesis given evidence
for($e=0; $e < $this->n; $e++) {
for ($h=0; $h < $this->m; $h++) {
$this->posterior[$e][$h] = $this->priors[$h
* $this->likelihoods[$h][$e] / $this->evidence[$e];
}
}
return true;
}
/**
* Output method for displaying posterior probability matrix
*/
function toHTML($number_format="%01.3f") {
?>
<table border='1' cellpadding='5' cellspacing='0'>
<tr>
<td> </td>
<?php
for ($h=0; $h < $this->m; $h++) {
?>
<td align='center'>
<b><?php echo $this->column_labels[$h] ?></b>
</td>
<?php
}
?>
</tr>
<?php
for($e=0; $e < $this->n; $e++) {
?>
<tr>
<td><b><?php echo $this->row_labels[$e] ?></b></td>
<?php
for ($h=0; $h < $this->m; $h++) {
?>
<td align='right'>
<?php printf($number_format, $this->posterior[$e][$h]) ?>
</td>
<?php
}
?>
</tr>
<?php
}
?>
</table>
<?php
}
}
?>
