public function getLogNormalization()
{
$vars = $this->getVariables();
$marginal = $vars[0]->getValue();
$messages = $this->getMessages();
$message = $messages[0]->getValue();
$messageFromVariable = GaussianDistribution::divide($marginal, $message);
return -GaussianDistribution::logProductNormalization($messageFromVariable, $message) + log(GaussianDistribution::cumulativeTo(($messageFromVariable->getMean() - $this->_epsilon) / $messageFromVariable->getStandardDeviation()));
}
public static function wWithinMargin($teamPerformanceDifference, $drawMargin)
{
$teamPerformanceDifferenceAbsoluteValue = abs($teamPerformanceDifference);
$denominator = GaussianDistribution::cumulativeTo($drawMargin - $teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution::cumulativeTo(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue);
if ($denominator < 2.222758749E-162) {
return 1.0;
}
$vt = self::vWithinMargin($teamPerformanceDifferenceAbsoluteValue, $drawMargin);
return $vt * $vt + (($drawMargin - $teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution::at($drawMargin - $teamPerformanceDifferenceAbsoluteValue) - (-$drawMargin - $teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution::at(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue)) / $denominator;
}
public function getLogNormalization()
{
$variables =& $this->getVariables();
$marginal =& $variables[0]->getValue();
$messages =& $this->getMessages();
$message =& $messages[0]->getValue();
$messageFromVariable = GaussianDistribution::divide($marginal, $message);
$mean = $messageFromVariable->getMean();
$std = $messageFromVariable->getStandardDeviation();
$z = GaussianDistribution::cumulativeTo(($this->_epsilon - $mean) / $std) - GaussianDistribution::cumulativeTo((-$this->_epsilon - $mean) / $std);
return -GaussianDistribution::logProductNormalization($messageFromVariable, $message) + log($z);
}
public function testCumulativeTo()
{
// Verified with WolframAlpha
// (e.g. http://www.wolframalpha.com/input/?i=CDF%5BNormalDistribution%5B0%2C1%5D%2C+0.5%5D )
$this->assertEquals(0.691462, GaussianDistribution::cumulativeTo(0.5), '', GaussianDistributionTest::ERROR_TOLERANCE);
}
public function getPlayerWinProbability(GameInfo $gameInfo, $playerRating, $opponentRating)
{
$ratingDifference = $playerRating - $opponentRating;
// See equation 1.1 in the TrueSkill paper
return GaussianDistribution::cumulativeTo($ratingDifference / (sqrt(2) * $gameInfo->getBeta()));
}
