public function getPartialUpdate(Rating $prior, Rating $fullPosterior, $updatePercentage)
{
$priorGaussian = new GaussianDistribution($prior->getMean(), $prior->getStandardDeviation());
$posteriorGaussian = new GaussianDistribution($fullPosterior->getMean(), $fullPosterior . getStandardDeviation());
// From a clarification email from Ralf Herbrich:
// "the idea is to compute a linear interpolation between the prior and posterior skills of each player
// ... in the canonical space of parameters"
$precisionDifference = $posteriorGaussian->getPrecision() - $priorGaussian->getPrecision();
$partialPrecisionDifference = $updatePercentage * $precisionDifference;
$precisionMeanDifference = $posteriorGaussian->getPrecisionMean() - $priorGaussian . getPrecisionMean();
$partialPrecisionMeanDifference = $updatePercentage * $precisionMeanDifference;
$partialPosteriorGaussion = GaussianDistribution::fromPrecisionMean($priorGaussian->getPrecisionMean() + $partialPrecisionMeanDifference, $priorGaussian->getPrecision() + $partialPrecisionDifference);
return new Rating($partialPosteriorGaussion->getMean(), $partialPosteriorGaussion->getStandardDeviation(), $prior->_conservativeStandardDeviationMultiplier);
}
public static function inverseCumulativeTo($x, $mean = 0.0, $standardDeviation = 1.0)
{
// From numerical recipes, page 320
return $mean - sqrt(2) * $standardDeviation * GaussianDistribution::inverseErrorFunctionCumulativeTo(2 * $x);
}
