/** Return the most likely distance between two contigs and the number
* of pairs that support that estimate. */
static pair<int, unsigned>
maximumLikelihoodEstimate(int first, int last,
const Histogram& samples,
const PMF& pmf,
unsigned len0, unsigned len1)
{
int filterSize = 2 * (int)(0.05 * pmf.mean()) + 3; // want an odd filter size
first = max(first, (int)pmf.minValue() - samples.maximum()) - filterSize/2;
last = min(last, (int)pmf.maxValue() - samples.minimum()) + filterSize/2 + 1;
/* When randomly selecting fragments that span a given point,
* longer fragments are more likely to be selected than
* shorter fragments.
*/
WindowFunction window(len0, len1);
unsigned nsamples = samples.size();
double bestLikelihood = -numeric_limits<double>::max();
int bestTheta = first;
unsigned bestn = 0;
vector<double> le;
vector<unsigned> le_n;
vector<int> le_theta;
for (int theta = first; theta <= last; theta++) {
// Calculate the normalizing constant of the PMF, f_theta(x).
double c = 0;
for (int i = pmf.minValue(); i <= (int)pmf.maxValue(); ++i)
c += pmf[i] * window(i - theta);
double likelihood;
unsigned n;
tie(likelihood, n) = computeLikelihood(theta, samples, pmf);
likelihood -= nsamples * log(c);
le.push_back(likelihood);
le_n.push_back(n);
le_theta.push_back(theta);
}
HannWindow filter(filterSize);
for (int i = filterSize / 2; i < (int)le.size()-(filterSize / 2); i++) {
double likelihood = 0;
for (int j = -filterSize / 2; j <= filterSize / 2; j++) {
assert((unsigned)(i + j) < le.size() && i + j >= 0);
likelihood += filter(j) * le[i + j];
}
if (le_n[i] > 0 && likelihood > bestLikelihood) {
bestLikelihood = likelihood;
bestTheta = le_theta[i];
bestn = le_n[i];
}
}
return make_pair(bestTheta, bestn);
}
/** Estimate the distance between two contigs using the difference of
* the population mean and the sample mean.
* @param numPairs [out] the number of pairs that agree with the
* expected distribution
* @return the estimated distance
*/
static int estimateDistanceUsingMean(
const std::vector<int>& samples, const PMF& pmf,
unsigned& numPairs)
{
Histogram h(samples.begin(), samples.end());
int d = (int)round(pmf.mean() - h.mean());
// Count the number of samples that agree with the distribution.
unsigned n = 0;
for (Histogram::const_iterator it = h.begin();
it != h.end(); ++it)
if (pmf[it->first + d] > pmf.minProbability())
n += it->second;
numPairs = n;
return d;
}
