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A better (less overflow-y) implementation of multinomialProbability(). 

git-svn-id: file:///humgen/gsa-scr1/gsa-engineering/svn_contents/trunk@579 348d0f76-0448-11de-a6fe-93d51630548a
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kiran 2009-05-01 06:28:16 +00:00
parent 4f818f5c1c
commit 16467ae7cf
1 changed files with 16 additions and 11 deletions
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27
java/src/org/broadinstitute/sting/utils/MathUtils.java
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@ -91,30 +91,35 @@ public class MathUtils {
* *
* where xi represents the number of times outcome i was observed, n is the number of total observations, and * where xi represents the number of times outcome i was observed, n is the number of total observations, and
* pi represents the probability of the i-th outcome to occur. In this implementation, the value of n is * pi represents the probability of the i-th outcome to occur. In this implementation, the value of n is
* inferred as the sum over i of xi; * inferred as the sum over i of xi.
* *
* @param x an int[] of counts, where each element represents the number of times a certain outcome was observed * @param x an int[] of counts, where each element represents the number of times a certain outcome was observed
* @param p a double[] of probabilities, where each element represents the probability a given outcome can occur * @param p a double[] of probabilities, where each element represents the probability a given outcome can occur
* @return the multinomial probability of the specified configuration. * @return the multinomial probability of the specified configuration.
*/ */
public static double multinomialProbability(int[] x, double[] p) { public static double multinomialProbability(int[] x, double[] p) {
int n = 0; // In order to avoid overflow in computing large factorials in the multinomial
for ( int obsCount : x ) { n += obsCount; } // coefficient, we split the calculation up into the product of a bunch of
double nfact = Arithmetic.factorial(n); // binomial coefficients.
double obsfact = 1.0, probs = 1.0, totalprob = 0.0; double multinomialCoefficient = 1.0;
for (int i = 0; i < x.length; i++) {
int n = 0;
for (int j = 0; j <= i; j++) { n += x[j]; }
double multinomialTerm = Arithmetic.binomial(n, x[i]);
multinomialCoefficient *= multinomialTerm;
}
double probs = 1.0, totalprob = 0.0;
for (int obsCountsIndex = 0; obsCountsIndex < x.length; obsCountsIndex++) { for (int obsCountsIndex = 0; obsCountsIndex < x.length; obsCountsIndex++) {
double ofact = Arithmetic.factorial(x[obsCountsIndex]);
obsfact *= ofact;
probs *= Math.pow(p[obsCountsIndex], x[obsCountsIndex]); probs *= Math.pow(p[obsCountsIndex], x[obsCountsIndex]);
totalprob += p[obsCountsIndex]; totalprob += p[obsCountsIndex];
} }
assert(MathUtils.compareDoubles(totalprob, 1.0, 0.01) == 0); assert(MathUtils.compareDoubles(totalprob, 1.0, 0.01) == 0);
return (nfact/obsfact)*probs; return multinomialCoefficient*probs;
} }
} }