public double getCachedValue(ContingencyTable ct)
{
int[] aKey = new int[] { ct.getA(), ct.getB(), ct.getC(), ct.getD() };
if (m_slContingencyTables.ContainsKey(aKey))
{
return(m_slContingencyTables[aKey]);
}
return(double.NaN);
}
/**
* Computes the hypergeometric probablity using the following factorization:
* (a+b)!(a+c)!(b+d)!(c+d)! (a+b)! (a+c)! (c+d)! (b+d)!
* ------------------------ = ------- * ------- * -------- * --------
* a!b!c!d!n! a!b! c! d! n!
* The assumption is that (a+b) is the smallest marginal.
* A better implementation would check for the smallest marginal and factor according to it, but the current implementation seems fast enough.
* */
public static double pr(ContingencyTable ct)
{
double pt = 1;
double iFactorial = 0;
int a = ct.getA(), b = ct.getB(), c = ct.getC(), d = ct.getD();
double iDenominator = a + b + c + d;
double iMinDenominator = b + d;
for (iFactorial = a + 1; iFactorial <= a + b; iFactorial++) // (a+b)!/a!b!
{
pt *= iFactorial / (iFactorial - a);
while ((pt > 1) && (iDenominator > iMinDenominator))
{
pt /= iDenominator;
iDenominator--;
}
}
for (iFactorial = c + 1; iFactorial <= a + c; iFactorial++) // (a+c)!/c!
{
pt *= iFactorial;
while ((pt > 1) && (iDenominator > iMinDenominator))
{
pt /= iDenominator;
iDenominator--;
}
}
for (iFactorial = d + 1; iFactorial <= c + d; iFactorial++) // (c+d)!/d!
{
pt *= iFactorial;
while ((pt > 1) && (iDenominator > iMinDenominator))
{
pt /= iDenominator;
iDenominator--;
}
}
if (pt == 0.0) //underflow
{
return(double.Epsilon);
}
while ((iDenominator > iMinDenominator) && (pt > 0.0))
{
pt /= iDenominator;
if (pt == 0.0) //underflow
{
return(double.Epsilon);
}
iDenominator--;
}
if (pt > 1.0) //numerical error
{
pt = 1.0;
}
return(pt);
}
public void setCachedValue(ContingencyTable ct, double dValue)
{
int[] aKey = new int[] { ct.getA(), ct.getB(), ct.getC(), ct.getD() };
if (!m_slContingencyTables.ContainsKey(aKey))
{
m_slContingencyTables.Add(aKey, dValue);
}
else
{
m_slContingencyTables[aKey] = dValue;
}
}
/**
* Computes the Fisher 2 sided p-value.
* We iterate over all the premutations and sum the ones that have a lower probability (more extreme).
* We compute from scratch only a single hypergeometric probability - the probability of the "real" table.
* Then we iterate by incrementing the table and the probability (right side) and by decrementing the table and the probability (left side).
* The algorithm has the complexity of O(n), but usually runs much faster.
* Adding another possible optimization - when the p-value exceeds a cutoff - return 1. This is useful when we only need to know whether one value is larger than the other.
* When the values are too small to be represented by a double (less than 1-E302) the computation returns an upper bound on the real value.
* */
private double computeFisher2TailPermutationTest(double dObservedTableProbability, double dCutoff)
{
double p0 = dObservedTableProbability;
double p0Epsilon = p0 * 0.00001;
double p = p0, pt = 0, pAbove = 0.0, pLeft = p0, pRight = 0.0;
ContingencyTable ctIterator = null;
int cPermutations = 0, cRemiaingPermutations = getMaxPossibleA() - getMinPossibleA();
m_dMinimalPValue = p0;
if (p0 == double.Epsilon)
{
return(p0 * cRemiaingPermutations); //an upper bound estimation
}
//Iterate to the right side - increasing values of a
if (g_ttTestType == TestType.Right || g_ttTestType == TestType.TwoSided)
{
ctIterator = next();
pt = incrementalHypergeometricProbability(p0);
while (ctIterator != null)
{
if (pt < m_dMinimalPValue)
{
m_dMinimalPValue = pt;
}
cPermutations++;
if (p0 + p0Epsilon >= pt)
{
p = p + pt;
pLeft += pt;
if (p > dCutoff)
{
return(1.0);
}
}
else
{
pAbove += pt;
}
pt = ctIterator.incrementalHypergeometricProbability(pt);
ctIterator = ctIterator.next();
if ((ctIterator != null) && (pt <= p0Epsilon))
{
pt *= (getMaxPossibleA() - ctIterator.getA() + 1);
p += pt;
pLeft += pt;
ctIterator = null;
}
}
}
//Iterate to the left side - decreasing values of a
if (g_ttTestType == TestType.Left || g_ttTestType == TestType.TwoSided)
{
ctIterator = previous();
pt = decrementalHypergeometricProbability(p0);
double dBackward = pt;
while (ctIterator != null)
{
if (pt < m_dMinimalPValue)
{
m_dMinimalPValue = pt;
}
cPermutations++;
if (p0 + p0Epsilon >= pt)
{
p = p + pt;
pRight += pt;
if (p > dCutoff)
{
return(1.0);
}
}
else
{
pAbove += pt;
}
double dBefore = pt;
pt = ctIterator.decrementalHypergeometricProbability(pt);
ctIterator = ctIterator.previous();
if ((ctIterator != null) && (pt <= p0Epsilon))
{
pt *= (ctIterator.getA() - getMinPossibleA());
p += pt;
pRight += pt;
ctIterator = null;
}
}
}
m_cComputedFisherScores++;
return(p);
}
public double[] computeAllFisherStatistics(double[] adResults, ref bool bApproximated)
{
double p0 = getHypergeometricProbability();// probability of seeing the actual data
double p0Epsilon = p0 * 0.00001;
double p = p0, pt = 0, ptMax = 0.0, pLeft = p0, pRight = p0;
ContingencyTable ctMaxTable = getMaxValueTable(), ctIterator = ctMaxTable;
int iMaxA = getMaxPossibleA(), iMinA = getMinPossibleA();
int cPermutations = 0, cRemiaingPermutations = iMaxA - iMinA;
int iCurrentA = 0;
double[] adMapping = new double[iMaxA + 1];
adResults[0] = p0;
ptMax = ctIterator.getHypergeometricProbability();
pt = ptMax;
while (ctIterator != null)
{
cPermutations++;
iCurrentA = ctIterator.getA();
adMapping[iCurrentA] = pt;
if (iCurrentA > m_iA)
{
pRight += pt;
}
if (iCurrentA < m_iA)
{
pLeft += pt;
}
if (p0 + p0Epsilon >= pt && iCurrentA != m_iA)
{
p = p + pt;
}
pt = ctIterator.incrementalHypergeometricProbability(pt);
ctIterator = ctIterator.next();
if ((ctIterator != null) && (pt == double.Epsilon))
{
pt *= (iMaxA - ctIterator.getA() + 1);
p += pt;
pRight += pt;
bApproximated = true;
for (iCurrentA = ctIterator.getA(); iCurrentA <= iMaxA; iCurrentA++)
{
adMapping[iCurrentA] = double.Epsilon;
}
ctIterator = null;
}
}
//Iterate to the left side - decreasing values of a
ctIterator = ctMaxTable.previous();
pt = ctMaxTable.decrementalHypergeometricProbability(ptMax);
while (ctIterator != null)
{
cPermutations++;
iCurrentA = ctIterator.getA();
adMapping[iCurrentA] = pt;
if (iCurrentA > m_iA)
{
pRight += pt;
}
if (iCurrentA < m_iA)
{
pLeft += pt;
}
if (p0 + p0Epsilon >= pt && iCurrentA != m_iA)
{
p = p + pt;
}
pt = ctIterator.decrementalHypergeometricProbability(pt);
ctIterator = ctIterator.previous();
if ((ctIterator != null) && (pt == double.Epsilon))
{
pt *= (ctIterator.getA() - getMinPossibleA());
p += pt;
pLeft += pt;
bApproximated = true;
for (iCurrentA = ctIterator.getA(); iCurrentA >= iMinA; iCurrentA--)
{
adMapping[iCurrentA] = double.Epsilon;
}
ctIterator = null;
}
}
for (iCurrentA = iMinA - 1; iCurrentA >= 0; iCurrentA--)
{
adMapping[iCurrentA] = 0.0;
}
adResults[1] = pLeft;
adResults[2] = pRight;
adResults[3] = p;
return(adMapping);
}
