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evidence.cpp
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evidence.cpp
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#include <algorithm>
#include <cmath>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <vector>
#include "acor.h"
#include "exception.h"
#include "int2str.h"
#include "mean.h"
#include "model.h"
#include "quicksort.h"
#include "preprocessors.h"
#include "rng.h"
#include "var.h"
using namespace std;
double CovInterval(const Model & model, size_t i, size_t j);
void refine (Model & model) {
model.level.LnPrims_r.resize(0);
model.level.LnPrims_r.push_back(0);
double Cx = 0; // This number determines "how much" of the level building part is to be "trusted"
for (size_t i = model.level.LnPrims_r.size(); i < model.level.num_level; ++i) {
model.level.LnPrims_r.push_back( model.level.LnPrims_r[i-1] + log ((static_cast<double>(model.Above_Visits[i-1]) + Cx * exp(model.level.LnPrims[i] - model.level.LnPrims[i-1])) / (static_cast<double>(model.Level_Visits[i-1]) + Cx)) );
}
//for (size_t i = 0; i < model.level.num_level-1; ++i) {
//cout << "refined " << model.level.LnPrims_r[i] << endl;
//cout << "unrefined " << model.level.LnPrims[i] << endl;
//cout << model.Level_Visits[i] << endl;
//cout << model.Above_Visits[i] << endl;
//}
}
// This routine calculates the standard deviation of primor mass intervals.
void stdev_pm (Model & model, const double tau) {
model.level.LnPrims_var.clear();
model.level.LnPrims_var.push_back(-1.7e308);
double var_xy, var_x, var_y, e_x, e_y;
double p;
for (size_t i = 1; i < model.level.num_level; ++i) {
p = static_cast<double>(model.Above_Visits[i-1])/static_cast<double>(model.Level_Visits[i-1]);
e_y = p;
e_x = 1.0; // scaled by exp(model.level.LnPrims_r[i-1])
var_y = p * (1-p) / static_cast<double>(model.Level_Visits[i-1]) * tau;
var_x = exp( model.level.LnPrims_var[i-1] - 2.0 * model.level.LnPrims_r[i-1] );
var_xy = var_x * var_y + var_x * e_y * e_y + var_y * e_x * e_x;
model.level.LnPrims_var.push_back( log(var_xy) + 2.0 * model.level.LnPrims_r[i-1] );
}
model.level.LnInterval_var.clear();
for (size_t i = 0; i < model.level.num_level-1; ++i) {
p = static_cast<double>(model.Above_Visits[i])/static_cast<double>(model.Level_Visits[i]);
e_y = 1. - p;
e_x = 1.0; // scaled by exp(model.level.LnPrims_r[i]);
var_y = p * (1-p) / static_cast<double>(model.Level_Visits[i]) * tau;
var_x = exp( model.level.LnPrims_var[i] - 2.0 * model.level.LnPrims_r[i-1] );
var_xy = var_x * var_y + var_x * e_y * e_y + var_y * e_x * e_x;
model.level.LnInterval_var.push_back( log(var_xy) + 2.0 * model.level.LnPrims_r[i-1] );
}
model.level.LnInterval_var.push_back(model.level.LnPrims_var.back());
for (size_t i = 0; i < model.level.num_level; ++i) {
cout << model.level.LnPrims_var[i] << " " << model.level.LnInterval_var[i] << endl;
}
}
double evidence (Model & model, size_t ens_size) {
model.level.LnThres.push_back(1.7e308);
model.level.LnPrims.push_back(-1.7e308);
vector< vector<double> > gaps(model.level.num_level);
for (size_t i = 0; i < model.chain_LnLikelihood.size(); ++i) {
for (size_t j = 0; j < model.level.num_level; ++j) {
if ( model.chain_LnLikelihood[i] >= model.level.LnThres[j] && model.chain_LnLikelihood[i] < model.level.LnThres[j+1] ) {
gaps[j].push_back(model.chain_LnLikelihood[i]);
break;
}
}
}
double mean, sigma, tau;
try {
acor(mean, sigma, tau, model.Quant_Ens_Mean, model.Quant_Ens_Mean.size());
}
catch( Exception & e ){
cout << e.ExceptionMessage() << endl;
fstream acorout;
acorout.open(("acor_err_"+model.model_name+"_"+model.time_label+"_"+int2str(model.Quant_Ens_Mean.size(),11)+".txt").c_str(), ios::out);
for (size_t i = 0; i < model.Quant_Ens_Mean.size(); ++i) {
acorout << model.Quant_Ens_Mean[i] << endl;
}
acorout.close();
tau = 1;
}
refine(model);
stdev_pm(model, tau);
double integral = 0;
double integral_r = 0;
double integral_err1 = 0; // caused by uncertainty of the integrand
double integral_err2 = 0; // caused by uncertainty of the prior masses
double integral_err3 = 0; // caused by uncertainty of the prior mass cross terms
vector< double > lml(gaps.size());
vector< double > lvl(gaps.size());
vector< double > Lvar(gaps.size());
for (size_t i = 0; i < lml.size(); ++i) {
if (gaps[i].size() == 0) {
lml[i] = -1e300;
cout << i << " empty!" << endl;
continue;
}
lml[i] = logMeanLog(gaps[i]);
lvl[i] = logVarLog(gaps[i]);
Lvar[i] = lvl[i] + log(tau) - log(static_cast<double>(gaps[i].size()));
}
double max_lml = *max_element( lml.begin(), lml.end() );
for (size_t j = 0; j < model.level.num_level; ++j) {
//cout << j << endl;
if (j < model.level.num_level-1) {
integral += exp( lml[j]-max_lml ) * ( exp( model.level.LnPrims[j]-model.level.LnPrims[j+1] ) - 1 ) * exp( model.level.LnPrims[j+1] );
integral_r += exp( lml[j]-max_lml ) * ( exp( model.level.LnPrims_r[j]-model.level.LnPrims_r[j+1] ) - 1 ) * exp( model.level.LnPrims_r[j+1] );
integral_err1 += exp(Lvar[j] - 2.0 * max_lml) * (exp(model.level.LnPrims_r[j]-model.level.LnPrims_r[j+1]) - 1) * exp(model.level.LnPrims_r[j+1]) * (exp(model.level.LnPrims_r[j]-model.level.LnPrims_r[j+1]) - 1) * exp(model.level.LnPrims_r[j+1]);
integral_err2 += exp(2.0 * (lml[j]-max_lml)) * exp(model.level.LnInterval_var[j]);
}
else {
integral += exp(lml[j]-max_lml) * (exp(model.level.LnPrims[j]) - 0);
integral_r += exp(lml[j]-max_lml) * (exp(model.level.LnPrims_r[j]) - 0);
integral_err1 += exp(Lvar[j] - 2.0 * max_lml) * (exp(model.level.LnPrims_r[j]) - 0) * (exp(model.level.LnPrims_r[j]) - 0);
integral_err2 += exp(2.0 * (lml[j]-max_lml)) * exp(model.level.LnInterval_var[j]);
}
}
for (size_t i = 0; i < model.level.num_level - 1; ++i) {
for (size_t j = i + 1; j < model.level.num_level; ++j) {
integral_err3 += 2.0*exp( lml[i] + lml[j] - 2.0*max_lml ) * CovInterval(model, i, j) ;
cout << "i = " << i << " j = " << j << " Cov = " << CovInterval(model, i, j) << endl;
}
}
cout << "log unrefined evi = " << log(integral)+max_lml << endl;
cout << "log refined evi = " << log(integral_r)+max_lml << endl;
cout << "err1 " << exp(log(integral_err1)+2.0*max_lml) << endl;
cout << "err2 " << exp(log(integral_err2)+2.0*max_lml) << endl;
cout << "err3 " << exp(log(integral_err3)+2.0*max_lml) << endl;
model.evidence = log(integral)+max_lml;
model.evidence_r = log(integral_r)+max_lml;
model.evidence_err1 = log(integral_err1)+2.0*max_lml;
model.evidence_err2 = log(integral_err2)+2.0*max_lml;
model.evidence_err3 = log(integral_err3)+2.0*max_lml;
fstream out;
//////////////////////////////////////////////////////
out.open(("refines_"+model.model_name+"_"+model.time_label+".txt").c_str(), ios::out);
//////////////////////////////////////////////////////
out << setprecision(17) << "log unrefined evi = " << log(integral)+max_lml << endl;
out << setprecision(17) << "log refined evi = " << log(integral_r)+max_lml << endl;
out << setprecision(17) << "log err1 = " << log(integral_err1)+2.*max_lml << endl;
out << setprecision(17) << "log err2 = " << log(integral_err2)+2.*max_lml << endl;
out << setprecision(17) << "log err3 = " << log(integral_err3)+2.*max_lml << endl;
out << setprecision(17) << "autocorrelation t = " << tau << endl;
out << "Level, LnThres, LnPrims, LnPrims_r, Visits, Lvar, Above" << endl;
for (size_t j = 0; j < model.level.num_level; ++j) {
out << j << " ";
out << setprecision(17) << model.level.LnThres[j] << " ";
out << setprecision(17) << model.level.LnPrims[j] << " ";
out << setprecision(17) << model.level.LnPrims_r[j] << " ";
out << setprecision(17) << model.Level_Visits[j] << " ";
out << setprecision(17) << Lvar[j] << " ";
if (j < model.level.num_level - 1) {
out << setprecision(17) << model.Above_Visits[j] << " ";
}
out << endl;
}
model.level.LnThres.pop_back();
model.level.LnPrims.pop_back();
return model.evidence_r;
}
double CovInterval(const Model & model, size_t i, size_t j) {
if ( i == j ) {
return 0;
}
if ( i > j ) {
double temp = j;
j = i;
i = temp;
}
double Cov = 0;
if ( i == 0 ) {
Cov = exp( model.level.LnPrims_var[i+1] - model.level.LnPrims_r[i+1] ) * ( - 1.0 + exp ( model.level.LnPrims_r[j+1] - model.level.LnPrims_r[j] ) ) * exp( model.level.LnPrims_r[j] );
return Cov;
}
if ( j == model.level.num_level - 1 ) {
Cov = ( exp( model.level.LnPrims_var[i] - model.level.LnPrims_r[i] ) - exp( model.level.LnPrims_var[i+1] - model.level.LnPrims_r[i+1] ) ) * exp( model.level.LnPrims_r[j] );
return Cov;
}
Cov = ( exp(model.level.LnPrims_var[i] - model.level.LnPrims_r[i]) - exp(model.level.LnPrims_var[i+1] - model.level.LnPrims_r[i+1]) ) * ( 1.0 - exp ( model.level.LnPrims_r[j+1] - model.level.LnPrims_r[j] )) * exp( model.level.LnPrims_r[j] );
return Cov;
}