/**
* Computes the Fisher scores for all the permutations in a single pass.
* The algorithm works by starting on one side (min a) and moving to the other side (max a).
* We compute all the probabilities that we encounter on the way incrementally.
* Then we sort the probabilities in increasing order and sum them up in that direction.
* The result is a mapping between the permutation probabilities and p-values.
* TODO - we may want to cache the resulting list in case of multiple calls
* */
public double[,] computeAllPermutationsScores()
{
int cPermutations = getMaxPossibleA() - getMinPossibleA() + 1;
List <double> alProbabilities = new List <double>();
double[,] adScores = new double[cPermutations, 2];
//We start from the table with the maximal value to avoid numeric computation problems
ContingencyTable ctMaxValue = getMaxValueTable();
ContingencyTable ctIterator = ctMaxValue;
double pStart = ctIterator.getHypergeometricProbability();
double pCurrent = pStart, dSum = 0.0;
int iCurrent = 0;
//iterate to the right side
while (ctIterator != null)
{
//Add the probability of the current permutation to the list
alProbabilities.Add(pCurrent);
//Increment the probability
pCurrent = ctIterator.incrementalHypergeometricProbability(pCurrent);
//Increment the table - will return null once a exceeds the max value
ctIterator = ctIterator.next();
}
//iterate to the left side
ctIterator = ctMaxValue;
pCurrent = ctIterator.decrementalHypergeometricProbability(pStart);
ctIterator = ctIterator.previous();
while (ctIterator != null)
{
//Add the probability of the current permutation to the list
alProbabilities.Add(pCurrent);
//Decrement the probability
pCurrent = ctIterator.decrementalHypergeometricProbability(pCurrent);
//Decrement the table - will return null once a drops below the min value
ctIterator = ctIterator.previous();
}
//Sort the observed probabilities in increasing order
alProbabilities.Sort();
//BUGBUG - suspecting that we do not handle well identical entries. Not sure if this bug is occuring.
dSum = 0.0;
//Sum the probabilities in increasing order, computing two sided p-values
//BUGBUG - Not sure how to make this work for one sided tests.
for (iCurrent = 0; iCurrent < alProbabilities.Count; iCurrent++)
{
pCurrent = (double)alProbabilities[iCurrent];
dSum += pCurrent;
if (dSum > 1.0)
{
dSum = 1.0;
}
adScores[iCurrent, 0] = pCurrent;
adScores[iCurrent, 1] = dSum;
}
return(adScores);
}
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;
}
}
private Map <double, FDRData> initFDRMap(List <ContingencyTable> actTables)
{
Map <double, FDRData> slFDR = new Map <double, FDRData>();
int iTable = 0;
ContingencyTable ctCurrent = null;
double dFisherScore = 0.0;
for (iTable = 0; iTable < actTables.Count; iTable++)
{
ctCurrent = (ContingencyTable)actTables[iTable];
dFisherScore = round(ctCurrent.getFisher2TailPermutationTest());
if (!slFDR.ContainsKey(dFisherScore))
{
slFDR.Add(dFisherScore, new FDRData(dFisherScore));
}
}
slFDR.Add(10.0, new FDRData(10.0)); // add a last entry with a huge fisher score
return(slFDR);
}
//Loading the contingency tables from the input file
//Implements the sampling techniques
private List <ContingencyTable> loadTables()
{
try
{
StreamReader sr = m_fiInput.OpenText();
ContingencyTable ctCurrent = null;
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportPhase("Loading data");
m_bContinue = m_prReport.reportMessage("Loading data from file " + m_fiInput.Name, true);
}
string sLine = "";
List <ContingencyTable> actTables = new List <ContingencyTable>();
int cTables = 0;
long cCharacters = 0;
bool bUseTable = true;
double dSampleProbability = 0.0, dProb = 0.0;
Random rnd = new Random();
int iLineNumber = 0;
if (m_bHuge)
{
m_ctcTableCounts = new ContingencyTableCache();
}
else
{
m_ctcTableCounts = null;
}
//On the first iteration go through the file to check the number of rows (tables)
if (m_cTables == -1)
{
m_cTables = 0;
sLine = sr.ReadLine();
initColumnHeaders(sLine);
while (!sr.EndOfStream)
{
sLine = sr.ReadLine();
m_cTables++;
if (m_bReportProgress)
{
if (m_cTables % MAX_REPROT_POINT == 0)
{
m_bContinue = m_prReport.reportMessage(".", false);
}
}
}
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportMessage("", true);
m_bContinue = m_prReport.reportMessage("Found " + m_cTables + " data rows.", true);
}
}
//Instead of enforcing a hard sample size, we sample the given the sample probability
dSampleProbability = m_iSampleSize / (double)m_cTables;
sr.Close();
sr = m_fiInput.OpenText();
if (m_bReportProgress)
{
if (m_bSampling)
{
m_bContinue = m_prReport.reportPhase("Sampling tables");
m_bContinue = m_prReport.reportMessage("Sampling " + m_iSampleSize + " tables.", true);
}
}
if (m_bHasColumnHeaders)
{
sr.ReadLine();
}
while (!sr.EndOfStream && m_bContinue)
{
sLine = sr.ReadLine().Trim();
iLineNumber++;
if (sLine.Length > 0)
{
bUseTable = true;//general use flag - sampling, validation, ...
if (m_bSampling)
{
dProb = rnd.NextDouble();
if (dProb > dSampleProbability)
{
bUseTable = false;
}
}
if (bUseTable)
{
ctCurrent = new ContingencyTable(sLine, m_cTableNamesColumns);
bUseTable = ctCurrent.validate();
}
if (bUseTable)
{
if (m_bHuge)//instead of maintaining all the tables try to see whether we already loaded a table with the same counts
{
double dCount = m_ctcTableCounts.getCachedValue(ctCurrent);
if (double.IsNaN(dCount))//First time table was observed
{
dCount = 0;
actTables.Add(ctCurrent);
}
m_ctcTableCounts.setCachedValue(ctCurrent, dCount + 1);//increment the table count
}
else//not huge - maintain all tables (including duplicates)
{
actTables.Add(ctCurrent);
}
}
cTables++;
}
if ((cTables > 0) && (cTables % MAX_REPROT_POINT == 0))
{
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportProcessedTables(cTables, m_cTables);
m_bContinue = m_prReport.reportMessage("Loaded " + cTables + " tables.", false);
if (m_bHuge)
{
m_bContinue = m_prReport.reportMessage(" Found " + actTables.Count + " distinct tables.", false);
}
m_bContinue = m_prReport.reportMessage("", true);
}
}
cCharacters += sLine.Length + 2;
}
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportMessage("Done loading data. Found " + actTables.Count + " distinct tables.", true);
}
sr.Close();
return(actTables);
}
catch (Exception e)
{
m_bContinue = m_prReport.reportError("Could not load data : " + e.Message);
}
return(null);
}
/*
* Computing pi in the filtering case.
* In this case we compute a different pi for each p-value
* A table is considered relevant for the pi computation of a p-value p only if its marginals support a p-value that is more extreme than p.
* */
private Map <double, double> computeFilteringPi(List <ContingencyTable> actTables, List <double> lPValues)
{
Map <double, List <ContingencyTable> > slRelevantTables = new Map <double, List <ContingencyTable> >();
double dSumObservedPValuesInRange = 0.0, dCurrentTableFisherTestPValue = 0.0;
int cObservedTablesInRange = 0;
double dFisherScore = 0.0, dHyperProbability = 0.0, dMinimalPossiblePValue = 0.0, dFirstLargerKey = 0.0;
double dSumExpectedNullsInRange = 0;
double dSumNullProbsInRange = 0.0;
int cNullsInRange = 0;
int iTable = 0;
Map <double, double> slPi = new Map <double, double>();
ContingencyTable ctCurrent = null;
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportPhase("Computing relevant tables.");
m_bContinue = m_prReport.reportMessage("Started computing relevant tables for PI computation.", true);
}
//We first compute the list of relevant tables.
//For each table we compute its minimal achievable p-value and add it to the next p-value on the list.
//Now, the relevant tables are all the tables that belong to a p-value that is more exterme than the current one.
for (iTable = 0; iTable < actTables.Count && m_bContinue; iTable++)
{
ctCurrent = (ContingencyTable)actTables[iTable];
dMinimalPossiblePValue = ctCurrent.getMinimalAchievablePValue();
dFirstLargerKey = getNextKey(lPValues, dMinimalPossiblePValue);
if (!slRelevantTables.ContainsKey(dFirstLargerKey))
{
slRelevantTables.Add(dFirstLargerKey, new List <ContingencyTable>());
}
slRelevantTables[dFirstLargerKey].Add(ctCurrent);
if (m_bReportProgress && (iTable > 0) && (iTable % 1000 == 0))
{
m_bContinue = m_prReport.reportProcessedTables(iTable, actTables.Count);
}
}
//We iterate from smallest p-value to largest. The order is important because we want the relevant tables list to grow all the time.
for (iTable = 0; iTable < actTables.Count && m_bContinue; iTable++)
{
ctCurrent = (ContingencyTable)actTables[iTable];
dCurrentTableFisherTestPValue = round(ctCurrent.getFisher2TailPermutationTest());
if (slRelevantTables.ContainsKey(dCurrentTableFisherTestPValue))
{
//Now we iterate over the list of relevant tables
//Note - a table never becomes irrelevant. Therefore we always accumulate more observations and remove any.
foreach (ContingencyTable ctRelevant in slRelevantTables[dCurrentTableFisherTestPValue])
{
dFisherScore = ctRelevant.getFisher2TailPermutationTest();
dSumObservedPValuesInRange += dFisherScore;
cObservedTablesInRange++;
//TODO - calling computeAllPermutationsScores twice - inefficient
double[,] adScores = ctRelevant.computeAllPermutationsScores();
for (int iCurrent = 0; iCurrent < adScores.GetLength(0); iCurrent++)
{
dHyperProbability = adScores[iCurrent, 0];
dFisherScore = adScores[iCurrent, 1];
dSumNullProbsInRange += dHyperProbability;
dSumExpectedNullsInRange += dFisherScore * dHyperProbability;
cNullsInRange++;
}
}
slRelevantTables.Remove(dCurrentTableFisherTestPValue);
}
//After iterating over all the relevant tables we compute the PI for that p-value
//using the weighted sum method
slPi[dCurrentTableFisherTestPValue] = (dSumObservedPValuesInRange / cObservedTablesInRange) /
(dSumExpectedNullsInRange / dSumNullProbsInRange);
if (m_bReportProgress && (iTable > 0) && (iTable % 1000 == 0))
{
m_bContinue = m_prReport.reportProcessedTables(iTable, actTables.Count);
}
}
slPi[10.0] = 1.0;
return(slPi);
}
/*
* Main FDR computation function.
* Takes as input an array of tables, already sorted by Fisher scores.
* Outputs a map from p-value to FDR.
* */
private Map <double, FDRData> computeFDR(List <ContingencyTable> actTables)
{
int iTable = 0, cTables = actTables.Count;
ContingencyTable ctCurrent = null;
double dFirstLargerKey = 0.0;
double dHyperProbability = 0.0, dFisherScore = 0.0;
DateTime dtBefore = DateTime.Now, dtAfter = DateTime.Now;
TimeSpan tsCurrent = TimeSpan.Zero, tsTotal = TimeSpan.Zero;
int cTableCount = 1;
int cReprotInterval = 0;
Map <double, FDRData> slFDR = null;
double dSumObservedPValues = 0.0, dCurrentTableFisherTestPValue = 0.0;
double dSumNullPValues = 0.0, dExpectedNullPValue = 0.0;
double dEPhiNull = 0.0, dEPhiObserved = 0.0;
int cNullPValues = 0;
int cObservedPValues = 0;
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportPhase("Computing pooled p-values.");
m_bContinue = m_prReport.reportMessage("Started computing pooled p-values values.", true);
}
slFDR = initFDRMap(actTables);
cReprotInterval = Math.Min(actTables.Count / 10, MAX_REPROT_POINT);
for (iTable = 0; iTable < cTables && m_bContinue; iTable++)
{
ctCurrent = (ContingencyTable)actTables[iTable];
dCurrentTableFisherTestPValue = ctCurrent.getFisher2TailPermutationTest();
dSumObservedPValues += dCurrentTableFisherTestPValue;
//dEPhiObserved += -Math.Log(1 - 0.99999999 * dCurrentTableFisherTestPValue);
dEPhiObserved += Math.Sqrt(dCurrentTableFisherTestPValue);
cObservedPValues++;
double[,] adScores = ctCurrent.computeAllPermutationsScores();
int iCurrent = 0;
if (m_bHuge)
{
cTableCount = (int)m_ctcTableCounts.getCachedValue(ctCurrent);
}
else
{
cTableCount = 1;
}
for (iCurrent = 0; iCurrent < adScores.GetLength(0); iCurrent++)
{
dHyperProbability = adScores[iCurrent, 0];
dFisherScore = adScores[iCurrent, 1];
dSumNullPValues += dHyperProbability;
dExpectedNullPValue += dFisherScore * dHyperProbability;
//dEPhiNull += -Math.Log(1 - 0.99999999 * dFisherScore) * dHyperProbability;
dEPhiNull += Math.Sqrt(dFisherScore) * dHyperProbability;
cNullPValues++;
dFirstLargerKey = getNextKey(slFDR.KeyList, dFisherScore);
slFDR[dFirstLargerKey].PooledPValue += (dHyperProbability * cTableCount);
}
if ((iTable > 0) && (iTable % cReprotInterval == 0))
{
if (m_bReportProgress)
{
dtAfter = DateTime.Now;
tsCurrent = dtAfter.Subtract(dtBefore);
tsTotal += tsCurrent;
m_bContinue = m_prReport.reportProcessedTables(iTable, cTables);
m_bContinue = m_prReport.reportMessage("Done " + iTable + " tables, avg time (ms) " + Math.Round(tsTotal.TotalMilliseconds / (iTable + 1)) +
", total time " + tsTotal, true);
}
}
}
double dPi = 1.0;
if ((m_pmEvaluatePi == PiMethod.WeightedSum) || (m_pmEvaluatePi == PiMethod.DoubleAverage))
{
if (m_pmEvaluatePi == PiMethod.WeightedSum)
{
dPi = (dSumObservedPValues / cObservedPValues) / (dExpectedNullPValue / dSumNullPValues); // \pi_0 = (\sum_T p(T))/(\sum_T p(T)pr(T|H=0))
}
else if (m_pmEvaluatePi == PiMethod.DoubleAverage)
{
dPi = 2.0 * (dSumObservedPValues / cObservedPValues); // \pi_0 = 2 * avg(p)
}
double dPhiPi = dEPhiObserved / dEPhiNull;
m_bContinue = m_prReport.reportMessage("Estimating PI = " + dPi, true);
}
else if (m_pmEvaluatePi == PiMethod.Filtering)
{
Map <double, double> slPi = computeFilteringPi(actTables, slFDR.KeyList);
List <double> lKeys = new List <double>(slFDR.Keys);
foreach (double dKey in lKeys)
{
slFDR[dKey].FilteringPi = slPi[dKey];
}
}
m_dPi = dPi;
sumFDRs(actTables, slFDR, dPi);
return(slFDR);
}
/*
* Writes the results of the computation to a file.
* First line is the headers (if exist) with the new columns added.
* Each following line is the contingency table with the Fisher scores, FDR and q-value
* */
private List <string> getResults(List <ContingencyTable> actTables
, Map <double, FDRData> slFDR)
{
int iTable = 0;
ContingencyTable ctCurrent = null;
double dFisherTest = 0.0, dCurrentQValue = 0.0;
double dNextKey = 0;
string sHeader = "";
FDRData fdCurrent = null;
string sOutputLine = "";
List <string> lResults = new List <string>();
bool bFiltering = m_pmEvaluatePi == PiMethod.Filtering;
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportPhase("Writing results.");
}
sHeader = m_sColumnHeaders + "\tp-value";
if (m_bFullOutput)
{
sHeader += "\tpooled p-value\t";
if (bFiltering)
{
sHeader += "filtering pi\t";
}
if (m_bPositiveFDR)
{
sHeader += "pr(R(p)>0)\tpFDR";
}
else
{
sHeader += "FDR";
}
}
sHeader += "\tq-value";
lResults.Add(sHeader);
List <KeyValuePair <double, double> > lPToQMappings = new List <KeyValuePair <double, double> >();
//When the huge flag is used, the tables are not kept.
//We now have to go over the entire input file, read each table,
//compute p-value for it, and map it into FDR and q-value.
if (m_bHuge)
{
StreamReader sr = m_fiInput.OpenText();
string sLine = "";
double dFisherScoreCutoff = 0.0;
bool bUseTable = true;
if (m_dFDRCutoff > 0.0)
{
dFisherScoreCutoff = mapFDR2FisherScore(slFDR, m_dFDRCutoff);
}
iTable = 0;
while (!sr.EndOfStream)
{
sLine = sr.ReadLine();
if (sLine.Length > 0)
{
ctCurrent = new ContingencyTable(sLine, m_cTableNamesColumns);
bUseTable = ctCurrent.validate();
if (bUseTable)
{
dFisherTest = round(ctCurrent.getFisher2TailPermutationTest(dFisherScoreCutoff));
dNextKey = getNextKey(slFDR.KeyList, dFisherTest);
fdCurrent = slFDR[dNextKey];
dCurrentQValue = round(fdCurrent.QValue);
if (dCurrentQValue <= m_dFDRCutoff)
{
sOutputLine = ctCurrent.ToString() + "\t";
sOutputLine += fdCurrent.getData(m_bFullOutput, bFiltering, m_bPositiveFDR);
lResults.Add(sOutputLine);
lPToQMappings.Add(new KeyValuePair <double, double>(dNextKey, dCurrentQValue));//will not work for huge because multiple tables will be missed
}
}
iTable++;
if (m_bReportProgress && (iTable % MAX_REPROT_POINT == 0))
{
m_bContinue = m_prReport.reportProcessedTables(iTable, m_cTables);
m_bContinue = m_prReport.reportMessage("Written " + iTable + " tables.", true);
}
}
}
sr.Close();
}
else//Not huge - all data is already in memory - just write the tables.
{
for (iTable = 0; iTable < actTables.Count; iTable++)
{
ctCurrent = (ContingencyTable)actTables[iTable];
dFisherTest = ctCurrent.getFisher2TailPermutationTest();
dNextKey = getNextKey(slFDR.KeyList, dFisherTest);
fdCurrent = slFDR[dNextKey];
dCurrentQValue = floor(fdCurrent.QValue);
if (dCurrentQValue <= m_dFDRCutoff)
{
sOutputLine = ctCurrent.ToString() + "\t";
sOutputLine += fdCurrent.getData(m_bFullOutput, bFiltering, m_bPositiveFDR);
lPToQMappings.Add(new KeyValuePair <double, double>(dNextKey, dCurrentQValue));
lResults.Add(sOutputLine);
}
if (m_bReportProgress && (iTable % MAX_REPROT_POINT == 0))
{
m_bContinue = m_prReport.reportProcessedTables(iTable, actTables.Count);
}
//swMarginalPValues.WriteLine(fdCurrent.PValue);
}
}
PToQMapping = lPToQMappings;
if (m_bReportProgress)
{
m_bContinue = m_prReport.reportMessage("Done writing results", true);
}
//swMarginalPValues.Close();
return(lResults);
}
/**
* When computing we only add the probabilities of the permutations to the closest higher p-value table
* Now, we need to go over all these tables and sum everything that has smaller p-value (more significant)
* We take a mapping from p-value to single appearance probabilities
* and teturn a mapping from p-value to sum of all more significant probabilities
* */
private void sumFDRs(List <ContingencyTable> actTables, Map <double, FDRData> slFDR, double dPiEstimation)
{
double dSum = 0;
int iTable = 0;
long cAllTables = actTables.Count;
long cTables = 0;
ContingencyTable ctCurrent = null, ctNext = null;
double dFisherScore = 0.0, dNextFisherScore = 0.0;
int iSample = 0;
//First, sum all the pooled p-values that are lower than the current table
foreach (FDRData data in slFDR.Values)
{
dSum += data.PooledPValue;
data.PooledPValue = dSum;
data.PooledPValue /= cAllTables;
if (data.FilteringPi > 0.0)
{
data.FDR = dSum * data.FilteringPi;
}
else
{
data.FDR = dSum * dPiEstimation;
}
if (m_bPositiveFDR)
{
data.RejectionAreaProb = OneMinusOneMinuXToTheM(data.PooledPValue, cAllTables);
data.FDR /= data.RejectionAreaProb;
}
iSample++;
}
dSum = 0;
//We now have to divide by the number of more significant tables to move from pooled p-values to FDR
for (iTable = 0; iTable < actTables.Count; iTable++)
{
ctCurrent = (ContingencyTable)actTables[iTable];
if (iTable < actTables.Count - 1)
{
ctNext = (ContingencyTable)actTables[iTable + 1];
}
else
{
ctNext = null;
}
dFisherScore = round(ctCurrent.getFisher2TailPermutationTest());
if (m_bHuge)//special case to huge datasets where the same table can appear multiple times
{
cTables += (long)m_ctcTableCounts.getCachedValue(ctCurrent);
}
else
{
cTables++;
}
if (ctNext != null)
{
dNextFisherScore = round(ctNext.getFisher2TailPermutationTest());
}
if ((ctNext == null) || (dFisherScore != dNextFisherScore))
{
slFDR[dFisherScore].FDR /= cTables;
}
}
}
/**
* 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);
}