mcmcpoisson.cc

使用R语言的马尔科夫链蒙特卡洛模拟（MCMC）源代码程序。

// MCMCpoisson.cc is C++ code to estimate a Poisson regression model with
//   a multivariate normal prior
//
// Andrew D. Martin
// Dept. of Political Science
// Washington University in St. Louis
// [e-mail]
//
// Kevin M. Quinn
// Dept. of Government
// Harvard University
// [e-mail]
// 
// This software is distributed under the terms of the GNU GENERAL
// PUBLIC LICENSE Version 2, June 1991.  See the package LICENSE
// file for more information.
//
// Copyright (C) 2004 Andrew D. Martin and Kevin M. Quinn
// 
// updated to the new version of Scythe 7/26/2004 KQ
// updated to Scythe 1.0.X 7/7/2007 ADM
//
#ifndef MCMCPOISSON_CC
#define MCMCPOISSON_CC

#include "MCMCrng.h"
#include "MCMCfcds.h"
#include "matrix.h"
#include "distributions.h"
#include "stat.h"
#include "la.h"
#include "ide.h"
#include "smath.h"
#include "rng.h"
#include "mersenne.h"
#include "lecuyer.h"

#include <R.h>           // needed to use Rprintf()
#include <R_ext/Utils.h> // needed to allow user interrupts

using namespace std;
using namespace scythe;

static double poisson_logpost(const Matrix<>& Y, 
			      const Matrix<>& X, 
			      const Matrix<>& beta,
			      const Matrix<>& beta_prior_mean,
			      const Matrix<>& beta_prior_prec){
  
  // likelihood
  const Matrix<> eta = X * beta;
  const Matrix<> mu = exp(eta);
  double loglike = 0.0;
  for (unsigned int i=0; i<Y.rows(); ++i) 
    loglike += -mu[i] + Y[i] * eta[i];
  
  // prior
  double logprior = 0.0;
  if (beta_prior_prec(0,0) != 0){
    logprior = lndmvn(beta, beta_prior_mean, invpd(beta_prior_prec));
  }
  
  return (loglike + logprior);
}


/* MCMCpoisson implementation.  Takes Matrix<> reference and fills with the
 * posterior.
 */
template <typename RNGTYPE>      
void MCMCpoisson_impl (rng<RNGTYPE>& stream, const Matrix<>& Y,
   const Matrix<>& X, const Matrix<>& tune, Matrix<>& beta, const Matrix<>& b0,
   const Matrix<>& B0,  const Matrix<>& V, unsigned int burnin,
   unsigned int mcmc, unsigned int thin, unsigned int verbose,  Matrix<>& result) {

    // define constants
    const unsigned int tot_iter = burnin + mcmc;  // total number iterations
    const unsigned int nstore = mcmc / thin;      // number of draws to store
    const unsigned int k = X.cols();
    
    // storage matrix or matrices
    Matrix<> storemat(nstore, k);
    
    // proposal parameters
    const Matrix<> propV = tune * invpd(B0 + invpd(V)) * tune;
    const Matrix<> propC = cholesky(propV) ;
    
    double logpost_cur = poisson_logpost(Y, X, beta, b0, B0);
    
    // MCMC loop
    int count = 0;
    int accepts = 0;
    for (unsigned int iter = 0; iter < tot_iter; ++iter){

       // sample beta
       const Matrix<> beta_can = gaxpy(propC, stream.rnorm(k,1,0,1), beta);
       const double logpost_can = poisson_logpost(Y,X,beta_can, b0, B0);
       const double ratio = ::exp(logpost_can - logpost_cur); 
      
       if (stream.runif() < ratio){
	      beta = beta_can;
	      logpost_cur = logpost_can;
	      ++accepts;
       }
      
      // store values in matrices
	  if (iter >= burnin && (iter % thin==0)){
	     storemat(count,_) = beta;
	     ++count;
	  }
      
      // print output to stdout
      if(verbose > 0 && iter % verbose == 0){
	     Rprintf("\n\nMCMCpoisson iteration %i of %i \n", (iter+1), tot_iter);
	     Rprintf("beta = \n");
	     for (unsigned int j=0; j<k; ++j)
	        Rprintf("%10.5f\n", beta[j]);
	     Rprintf("Metropolis acceptance rate for beta = %3.5f\n\n", 
		 static_cast<double>(accepts) / 
		 static_cast<double>(iter+1));	
      }
      
      R_CheckUserInterrupt(); // allow user interrupts   
   }// end MCMC loop
   result = storemat;
     
   Rprintf("\n\n@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@\n");
   Rprintf("The Metropolis acceptance rate for beta was %3.5f", 
	   static_cast<double>(accepts) / static_cast<double>(tot_iter));
   Rprintf("\n@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@\n");
}

extern "C"{
void MCMCpoisson(double *sampledata, const int *samplerow, 
		   const int *samplecol, const double *Ydata, 
		   const int *Yrow, const int *Ycol, const double *Xdata, 
		   const int *Xrow, const int *Xcol, const int *burnin, 
		   const int *mcmc, const int *thin, const double *tunedata, 
		   const int *tunerow, const int *tunecol, const int *uselecuyer, 
		   const int *seedarray, const int *lecuyerstream, 
		   const int *verbose, const double *betastartdata, 
		   const int *betastartrow, const int *betastartcol, 
		   const double *b0data, const int *b0row, const int *b0col, 
		   const double *B0data, const int *B0row, const int *B0col, 
		   const double *Vdata, const int *Vrow, const int *Vcol) {  
    
   // pull together Matrix objects
   const Matrix <> Y(*Yrow, *Ycol, Ydata);
   const Matrix <> X(*Xrow, *Xcol, Xdata);
   const Matrix <> tune(*tunerow, *tunecol, tunedata);
   Matrix <> beta(*betastartrow, *betastartcol, 
      betastartdata);
   const Matrix <> b0(*b0row, *b0col, b0data);
   const Matrix <> B0(*B0row, *B0col, B0data);
   const Matrix <> V(*Vrow, *Vcol, Vdata);
    
   Matrix<> storagematrix;
   MCMCPACK_PASSRNG2MODEL(MCMCpoisson_impl, Y, X, tune, beta, b0, B0,
      V, *burnin, *mcmc, *thin, *verbose, storagematrix);
 
   const unsigned int size = *samplerow * *samplecol;
   for (unsigned int i=0; i<size; ++i)
      sampledata[i] = storagematrix(i);
   }
}

#endif