# file priors/cauchy.hpp #

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## Namespaces #

Name
Gambit
TODO: see if we can use this one:
Gambit::Priors

## Classes #

Name
classGambit::Priors::Cauchy
Multi-dimensional Cauchy prior.

## Detailed Description #

Author:

Date:

• 2013 Dec
• Feb 2014
• August 2020

Multivariate Cauchy prior

Authors (add name and date if you modify):

## Source code #

//  GAMBIT: Global and Modular BSM Inference Tool
//  *********************************************
///  \file
///
///  Multivariate Cauchy prior
///
///  *********************************************
///
///  Authors (add name and date if you modify):
///
///  \author Ben Farmer
///    (benjamin.farmer@monash.edu.au)
///  \date 2013 Dec
///
///  \author Gregory Martinez
///    (gregory.david.martinez@gmail.com)
///  \date Feb 2014
///
///  \author Andrew Fowlie
///    (andrew.j.fowlie@qq.com)
///  \date August 2020
///
///  *********************************************

#ifndef __PRIOR_CAUCHY_HPP__
#define __PRIOR_CAUCHY_HPP__

#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <vector>

#include "gambit/ScannerBit/cholesky.hpp"
#include "gambit/ScannerBit/priors.hpp"
#include "gambit/ScannerBit/scanner_utils.hpp"

namespace Gambit {
namespace Priors {
/**
* @brief  Multi-dimensional Cauchy prior
*
* This is a [multivariate \f$t\f$-distribution](https://en.wikipedia.org/wiki/Multivariate_t-distribution)
* with \f$\nu = 1\f$ degree of freedom.
*
* Defined by a scale matrix, \f$\Sigma\f$, and a location vector.
*
* If the scale matrix is diagonal,it may instead be specified by the square-roots of its
* diagonal entries, denoted \f$\gamma\f$.
*/
class Cauchy : public BasePrior
{
private:
std::vector<double> location;
mutable Cholesky col;

public:
// Constructor defined in cauchy.cpp
Cauchy(const std::vector<std::string>& param, const Options& options);

/** @brief Transformation from unit interval to the Cauchy */
void transform(const std::vector<double>& unitpars, std::unordered_map<std::string, double>& outputMap) const override
{
std::vector<double> vec(unitpars.size());

auto v_it = vec.begin();
for (auto elem_it = unitpars.begin(), elem_end = unitpars.end(); elem_it != elem_end; elem_it++, v_it++)
{
*v_it = std::tan(M_PI * (*elem_it - 0.5));
}

col.ElMult(vec);

v_it = vec.begin();
auto m_it = location.begin();
for (auto str_it = param_names.begin(), str_end = param_names.end(); str_it != str_end; str_it++)
{
outputMap[*str_it] = *(v_it++) + *(m_it++);
}
}

std::vector<double> inverse_transform(const std::unordered_map<std::string, double> &physical) const override
{
// subtract location
std::vector<double> central;
for (int i = 0, n = this->size(); i < n; i++)
{
central.push_back(physical.at(param_names[i]) - location[i]);
}

// invert rotation by Cholesky matrix
std::vector<double> rotated = col.invElMult(central);

// now diagonal; invert Cauchy CDF
std::vector<double> u;
for (const auto& v : rotated)
{
u.push_back(std::atan(v) / M_PI + 0.5);
}
return u;
}

double operator()(const std::vector<double>& vec) const override
{
static double norm = std::log(M_PI * col.DetSqrt());
return -std::log1p(col.Square(vec, location)) - norm;
}
};