confidence.h

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/* confidence.cpp :  confidence interval estimation routines
 * Copyright (C) 2020  Daniel Haley
 * 
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
#ifndef LIBATOMPROBE_CONFIDENCE_H
#define LIBATOMPROBE_CONFIDENCE_H

#include <gsl/gsl_rng.h>

namespace AtomProbe
{
//  uses chi-square estimates from
//     http://ms.mcmaster.ca/peter/s743/poissonalpha.html 
// - Counts: Observed counts
// - alpha : confidence level for bounds (0->1, exclusive)
// - lBound : lower bound
// - uBound : upper bound
// - Note upper and lower bounds are absolutes, not delta.
// - Poisson confidence limits of poisson rate parameter, given some observed counts
// - technically "counts" is integral
void poissonConfidenceObservation(float counts, float alpha, float &lBound, float &uBound);


bool numericalEstimatePoissRatioConf(float lambda1,float lambda2, float alpha, 
            unsigned int nTrials, gsl_rng *r, float &lBound, float &uBound );



bool numericalEstimateGaussRatioConf(float mu1,float mu2,float var1, float var2, float alpha, 
            unsigned int nTrials, gsl_rng *r,float &lBound, float &uBound );


bool numericalEstimateSkellamConf(float lambda1, float lambda2, float alpha,
            unsigned int nTrials, gsl_rng *r, float &lBound,float &uBound);

// are poisson distributed, summed together, you have observed the sum,
// but want to subtract the background.
bool zechConfidenceLimits(float lambdaBack, unsigned int observation, float alpha,
                float &estimate);

#ifdef DEBUG
bool runConfidenceTests();
#endif
}
#endif