GEMMA-0.98.3/src/bslmmdap.cpp

/*
 Genome-wide Efficient Mixed Model Association (GEMMA)
 Copyright (C) 2011-2017, Xiang Zhou

 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/>.
*/

#include <fstream>
#include <iostream>
#include <sstream>

#include <algorithm>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iomanip>
#include <iostream>
#include <stdio.h>
#include <stdlib.h>

#include "gsl/gsl_blas.h"
#include "gsl/gsl_cdf.h"
#include "gsl/gsl_eigen.h"
#include "gsl/gsl_linalg.h"
#include "gsl/gsl_matrix.h"
#include "gsl/gsl_randist.h"
#include "gsl/gsl_roots.h"
#include "gsl/gsl_vector.h"

#include "bslmmdap.h"
#include "gemma_io.h"
#include "lapack.h"
#include "lm.h"
#include "lmm.h"
#include "logistic.h"
#include "mathfunc.h"
#include "param.h"

using namespace std;

void BSLMMDAP::CopyFromParam(PARAM &cPar) {
  file_out = cPar.file_out;
  path_out = cPar.path_out;

  time_UtZ = 0.0;
  time_Omega = 0.0;

  h_min = cPar.h_min;
  h_max = cPar.h_max;
  h_ngrid = cPar.h_ngrid;
  rho_min = cPar.rho_min;
  rho_max = cPar.rho_max;
  rho_ngrid = cPar.rho_ngrid;

  if (h_min <= 0) {
    h_min = 0.01;
  }
  if (h_max >= 1) {
    h_max = 0.99;
  }
  if (rho_min <= 0) {
    rho_min = 0.01;
  }
  if (rho_max >= 1) {
    rho_max = 0.99;
  }

  trace_G = cPar.trace_G;

  ni_total = cPar.ni_total;
  ns_total = cPar.ns_total;
  ni_test = cPar.ni_test;
  ns_test = cPar.ns_test;

  indicator_idv = cPar.indicator_idv;
  indicator_snp = cPar.indicator_snp;
  snpInfo = cPar.snpInfo;

  return;
}

void BSLMMDAP::CopyToParam(PARAM &cPar) {
  cPar.time_UtZ = time_UtZ;
  cPar.time_Omega = time_Omega;

  return;
}

// Read hyp file.
void ReadFile_hyb(const string &file_hyp, vector<double> &vec_sa2,
                  vector<double> &vec_sb2, vector<double> &vec_wab) {
  vec_sa2.clear();
  vec_sb2.clear();
  vec_wab.clear();

  igzstream infile(file_hyp.c_str(), igzstream::in);
  if (!infile) {
    cout << "error! fail to open hyp file: " << file_hyp << endl;
    return;
  }

  string line;
  char *ch_ptr;

  getline(infile, line);

  while (!safeGetline(infile, line).eof()) {
    ch_ptr = strtok_safe((char *)line.c_str(), " , \t");
    ch_ptr = strtok_safe(NULL, " , \t");

    ch_ptr = strtok_safe(NULL, " , \t");
    vec_sa2.push_back(atof(ch_ptr));

    ch_ptr = strtok_safe(NULL, " , \t");
    vec_sb2.push_back(atof(ch_ptr));

    ch_ptr = strtok_safe(NULL, " , \t");
    vec_wab.push_back(atof(ch_ptr));
  }

  infile.close();
  infile.clear();

  return;
}

// Read bf file.
void ReadFile_bf(const string &file_bf, vector<string> &vec_rs,
                 vector<vector<vector<double>>> &BF) {
  BF.clear();
  vec_rs.clear();

  igzstream infile(file_bf.c_str(), igzstream::in);
  if (!infile) {
    cout << "error! fail to open bf file: " << file_bf << endl;
    return;
  }

  string line, rs, block;
  vector<double> vec_bf;
  vector<vector<double>> mat_bf;
  char *ch_ptr;

  size_t bf_size = 0, flag_block;

  getline(infile, line);

  size_t t = 0;
  while (!safeGetline(infile, line).eof()) {
    flag_block = 0;

    ch_ptr = strtok_safe((char *)line.c_str(), " , \t");
    rs = ch_ptr;
    vec_rs.push_back(rs);

    ch_ptr = strtok_safe(NULL, " , \t");
    if (t == 0) {
      block = ch_ptr;
    } else {
      if (strcmp(ch_ptr, block.c_str()) != 0) {
        flag_block = 1;
        block = ch_ptr;
      }
    }

    ch_ptr = strtok(NULL, " , \t");
    while (ch_ptr != NULL) {
      vec_bf.push_back(atof(ch_ptr));
      ch_ptr = strtok(NULL, " , \t");
    }

    if (t == 0) {
      bf_size = vec_bf.size();
    } else {
      if (bf_size != vec_bf.size()) {
        cout << "error! unequal row size in bf file." << endl;
      }
    }

    if (flag_block == 0) {
      mat_bf.push_back(vec_bf);
    } else {
      BF.push_back(mat_bf);
      mat_bf.clear();
    }
    vec_bf.clear();

    t++;
  }

  infile.close();
  infile.clear();

  return;
}

// Read category files.
// Read both continuous and discrete category file, record mapRS2catc.
void ReadFile_cat(const string &file_cat, const vector<string> &vec_rs,
                  gsl_matrix *Ac, gsl_matrix_int *Ad, gsl_vector_int *dlevel,
                  size_t &kc, size_t &kd) {
  igzstream infile(file_cat.c_str(), igzstream::in);
  if (!infile) {
    cout << "error! fail to open category file: " << file_cat << endl;
    return;
  }

  string line;
  char *ch_ptr;

  string rs, chr, a1, a0, pos, cm;

  // Read header.
  HEADER header;
  safeGetline(infile, line).eof();
  ReadHeader_io(line, header);

  // Use the header to determine the number of categories.
  kc = header.catc_col.size();
  kd = header.catd_col.size();

  // set up storage and mapper
  map<string, vector<double>> mapRS2catc;
  map<string, vector<int>> mapRS2catd;
  vector<double> catc;
  vector<int> catd;

  // Read the following lines to record mapRS2cat.
  while (!safeGetline(infile, line).eof()) {
    ch_ptr = strtok_safe((char *)line.c_str(), " , \t");

    if (header.rs_col == 0) {
      rs = chr + ":" + pos;
    }

    catc.clear();
    catd.clear();

    for (size_t i = 0; i < header.coln; i++) {
      enforce(ch_ptr);
      if (header.rs_col != 0 && header.rs_col == i + 1) {
        rs = ch_ptr;
      } else if (header.chr_col != 0 && header.chr_col == i + 1) {
        chr = ch_ptr;
      } else if (header.pos_col != 0 && header.pos_col == i + 1) {
        pos = ch_ptr;
      } else if (header.cm_col != 0 && header.cm_col == i + 1) {
        cm = ch_ptr;
      } else if (header.a1_col != 0 && header.a1_col == i + 1) {
        a1 = ch_ptr;
      } else if (header.a0_col != 0 && header.a0_col == i + 1) {
        a0 = ch_ptr;
      } else if (header.catc_col.size() != 0 &&
                 header.catc_col.count(i + 1) != 0) {
        catc.push_back(atof(ch_ptr));
      } else if (header.catd_col.size() != 0 &&
                 header.catd_col.count(i + 1) != 0) {
        catd.push_back(atoi(ch_ptr));
      } else {
      }

      ch_ptr = strtok(NULL, " , \t");
    }

    if (mapRS2catc.count(rs) == 0 && kc > 0) {
      mapRS2catc[rs] = catc;
    }
    if (mapRS2catd.count(rs) == 0 && kd > 0) {
      mapRS2catd[rs] = catd;
    }
  }

  // Load into Ad and Ac.
  if (kc > 0) {
    Ac = gsl_matrix_alloc(vec_rs.size(), kc);
    for (size_t i = 0; i < vec_rs.size(); i++) {
      if (mapRS2catc.count(vec_rs[i]) != 0) {
        for (size_t j = 0; j < kc; j++) {
          gsl_matrix_set(Ac, i, j, mapRS2catc[vec_rs[i]][j]);
        }
      } else {
        for (size_t j = 0; j < kc; j++) {
          gsl_matrix_set(Ac, i, j, 0);
        }
      }
    }
  }

  if (kd > 0) {
    Ad = gsl_matrix_int_alloc(vec_rs.size(), kd);

    for (size_t i = 0; i < vec_rs.size(); i++) {
      if (mapRS2catd.count(vec_rs[i]) != 0) {
        for (size_t j = 0; j < kd; j++) {
          gsl_matrix_int_set(Ad, i, j, mapRS2catd[vec_rs[i]][j]);
        }
      } else {
        for (size_t j = 0; j < kd; j++) {
          gsl_matrix_int_set(Ad, i, j, 0);
        }
      }
    }

    dlevel = gsl_vector_int_alloc(kd);
    map<int, int> rcd;
    int val;
    for (size_t j = 0; j < kd; j++) {
      rcd.clear();
      for (size_t i = 0; i < Ad->size1; i++) {
        val = gsl_matrix_int_get(Ad, i, j);
        rcd[val] = 1;
      }
      gsl_vector_int_set(dlevel, j, rcd.size());
    }
  }

  infile.clear();
  infile.close();

  return;
}

void BSLMMDAP::WriteResult(const gsl_matrix *Hyper, const gsl_matrix *BF) {
  string file_bf, file_hyp;
  file_bf = path_out + "/" + file_out;
  file_bf += ".bf.txt";
  file_hyp = path_out + "/" + file_out;
  file_hyp += ".hyp.txt";

  ofstream outfile_bf, outfile_hyp;

  outfile_bf.open(file_bf.c_str(), ofstream::out);
  outfile_hyp.open(file_hyp.c_str(), ofstream::out);

  if (!outfile_bf) {
    cout << "error writing file: " << file_bf << endl;
    return;
  }
  if (!outfile_hyp) {
    cout << "error writing file: " << file_hyp << endl;
    return;
  }

  outfile_hyp << "h"
              << "\t"
              << "rho"
              << "\t"
              << "sa2"
              << "\t"
              << "sb2"
              << "\t"
              << "weight" << endl;
  outfile_hyp << scientific;
  for (size_t i = 0; i < Hyper->size1; i++) {
    for (size_t j = 0; j < Hyper->size2; j++) {
      outfile_hyp << setprecision(6) << gsl_matrix_get(Hyper, i, j) << "\t";
    }
    outfile_hyp << endl;
  }

  outfile_bf << "chr"
             << "\t"
             << "rs"
             << "\t"
             << "ps"
             << "\t"
             << "n_miss";
  for (size_t i = 0; i < BF->size2; i++) {
    outfile_bf << "\t"
               << "BF" << i + 1;
  }
  outfile_bf << endl;

  size_t t = 0;
  for (size_t i = 0; i < ns_total; ++i) {
    if (indicator_snp[i] == 0) {
      continue;
    }

    outfile_bf << snpInfo[i].chr << "\t" << snpInfo[i].rs_number << "\t"
               << snpInfo[i].base_position << "\t" << snpInfo[i].n_miss;

    outfile_bf << scientific;
    for (size_t j = 0; j < BF->size2; j++) {
      outfile_bf << "\t" << setprecision(6) << gsl_matrix_get(BF, t, j);
    }
    outfile_bf << endl;

    t++;
  }

  outfile_hyp.close();
  outfile_hyp.clear();
  outfile_bf.close();
  outfile_bf.clear();
  return;
}

void BSLMMDAP::WriteResult(const vector<string> &vec_rs,
                           const gsl_matrix *Hyper, const gsl_vector *pip,
                           const gsl_vector *coef) {
  string file_gamma, file_hyp, file_coef;
  file_gamma = path_out + "/" + file_out;
  file_gamma += ".gamma.txt";
  file_hyp = path_out + "/" + file_out;
  file_hyp += ".hyp.txt";
  file_coef = path_out + "/" + file_out;
  file_coef += ".coef.txt";

  ofstream outfile_gamma, outfile_hyp, outfile_coef;

  outfile_gamma.open(file_gamma.c_str(), ofstream::out);
  outfile_hyp.open(file_hyp.c_str(), ofstream::out);
  outfile_coef.open(file_coef.c_str(), ofstream::out);

  if (!outfile_gamma) {
    cout << "error writing file: " << file_gamma << endl;
    return;
  }
  if (!outfile_hyp) {
    cout << "error writing file: " << file_hyp << endl;
    return;
  }
  if (!outfile_coef) {
    cout << "error writing file: " << file_coef << endl;
    return;
  }

  outfile_hyp << "h"
              << "\t"
              << "rho"
              << "\t"
              << "sa2"
              << "\t"
              << "sb2"
              << "\t"
              << "weight" << endl;
  outfile_hyp << scientific;
  for (size_t i = 0; i < Hyper->size1; i++) {
    for (size_t j = 0; j < Hyper->size2; j++) {
      outfile_hyp << setprecision(6) << gsl_matrix_get(Hyper, i, j) << "\t";
    }
    outfile_hyp << endl;
  }

  outfile_gamma << "rs"
                << "\t"
                << "gamma" << endl;
  for (size_t i = 0; i < vec_rs.size(); ++i) {
    outfile_gamma << vec_rs[i] << "\t" << scientific << setprecision(6)
                  << gsl_vector_get(pip, i) << endl;
  }

  outfile_coef << "coef" << endl;
  outfile_coef << scientific;
  for (size_t i = 0; i < coef->size; i++) {
    outfile_coef << setprecision(6) << gsl_vector_get(coef, i) << endl;
  }

  outfile_coef.close();
  outfile_coef.clear();
  outfile_hyp.close();
  outfile_hyp.clear();
  outfile_gamma.close();
  outfile_gamma.clear();
  return;
}

double BSLMMDAP::CalcMarginal(const gsl_vector *Uty, const gsl_vector *K_eval,
                              const double sigma_b2, const double tau) {
  gsl_vector *weight_Hi = gsl_vector_alloc(Uty->size);

  double logm = 0.0;
  double d, uy, Hi_yy = 0, logdet_H = 0.0;
  for (size_t i = 0; i < ni_test; ++i) {
    d = gsl_vector_get(K_eval, i) * sigma_b2;
    d = 1.0 / (d + 1.0);
    gsl_vector_set(weight_Hi, i, d);

    logdet_H -= log(d);
    uy = gsl_vector_get(Uty, i);
    Hi_yy += d * uy * uy;
  }

  // Calculate likelihood.
  logm = -0.5 * logdet_H - 0.5 * tau * Hi_yy + 0.5 * log(tau) * (double)ni_test;

  gsl_vector_free(weight_Hi);

  return logm;
}

double BSLMMDAP::CalcMarginal(const gsl_matrix *UtXgamma, const gsl_vector *Uty,
                              const gsl_vector *K_eval, const double sigma_a2,
                              const double sigma_b2, const double tau) {
  clock_t time_start;
  double logm = 0.0;
  double d, uy, P_yy = 0, logdet_O = 0.0, logdet_H = 0.0;

  gsl_matrix *UtXgamma_eval =
      gsl_matrix_alloc(UtXgamma->size1, UtXgamma->size2);
  gsl_matrix *Omega = gsl_matrix_alloc(UtXgamma->size2, UtXgamma->size2);
  gsl_vector *XtHiy = gsl_vector_alloc(UtXgamma->size2);
  gsl_vector *beta_hat = gsl_vector_alloc(UtXgamma->size2);
  gsl_vector *weight_Hi = gsl_vector_alloc(UtXgamma->size1);

  gsl_matrix_memcpy(UtXgamma_eval, UtXgamma);

  logdet_H = 0.0;
  P_yy = 0.0;
  for (size_t i = 0; i < ni_test; ++i) {
    gsl_vector_view UtXgamma_row = gsl_matrix_row(UtXgamma_eval, i);
    d = gsl_vector_get(K_eval, i) * sigma_b2;
    d = 1.0 / (d + 1.0);
    gsl_vector_set(weight_Hi, i, d);

    logdet_H -= log(d);
    uy = gsl_vector_get(Uty, i);
    P_yy += d * uy * uy;
    gsl_vector_scale(&UtXgamma_row.vector, d);
  }

  // Calculate Omega.
  gsl_matrix_set_identity(Omega);

  time_start = clock();
  lapack_dgemm((char *)"T", (char *)"N", sigma_a2, UtXgamma_eval, UtXgamma, 1.0,
               Omega);
  time_Omega += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0);

  // Calculate beta_hat.
  gsl_blas_dgemv(CblasTrans, 1.0, UtXgamma_eval, Uty, 0.0, XtHiy);

  logdet_O = CholeskySolve(Omega, XtHiy, beta_hat);

  gsl_vector_scale(beta_hat, sigma_a2);

  gsl_blas_ddot(XtHiy, beta_hat, &d);
  P_yy -= d;

  gsl_matrix_free(UtXgamma_eval);
  gsl_matrix_free(Omega);
  gsl_vector_free(XtHiy);
  gsl_vector_free(beta_hat);
  gsl_vector_free(weight_Hi);

  logm = -0.5 * logdet_H - 0.5 * logdet_O - 0.5 * tau * P_yy +
         0.5 * log(tau) * (double)ni_test;

  return logm;
}

double BSLMMDAP::CalcPrior(class HYPBSLMM &cHyp) {
  double logprior = 0;
  logprior =
      ((double)cHyp.n_gamma - 1.0) * cHyp.logp +
      ((double)ns_test - (double)cHyp.n_gamma) * log(1.0 - exp(cHyp.logp));
  return logprior;
}

// Where A is the ni_test by n_cat matrix of annotations.
void BSLMMDAP::DAP_CalcBF(const gsl_matrix *U, const gsl_matrix *UtX,
                          const gsl_vector *Uty, const gsl_vector *K_eval,
                          const gsl_vector *y) {
  clock_t time_start;

  // Set up BF.
  double tau, h, rho, sigma_a2, sigma_b2, d;
  size_t ns_causal = 10;
  size_t n_grid = h_ngrid * rho_ngrid;
  vector<double> vec_sa2, vec_sb2, logm_null;

  gsl_matrix *BF = gsl_matrix_alloc(ns_test, n_grid);
  gsl_matrix *Xgamma = gsl_matrix_alloc(ni_test, 1);
  gsl_matrix *Hyper = gsl_matrix_alloc(n_grid, 5);

  // Compute tau by using yty.
  gsl_blas_ddot(Uty, Uty, &tau);
  tau = (double)ni_test / tau;

  // Set up grid values for sigma_a2 and sigma_b2 based on an
  // approximately even grid for h and rho, and a fixed number
  // of causals.
  size_t ij = 0;
  for (size_t i = 0; i < h_ngrid; i++) {
    h = h_min + (h_max - h_min) * (double)i / ((double)h_ngrid - 1);
    for (size_t j = 0; j < rho_ngrid; j++) {
      rho = rho_min + (rho_max - rho_min) * (double)j / ((double)rho_ngrid - 1);

      sigma_a2 = h * rho / ((1 - h) * (double)ns_causal);
      sigma_b2 = h * (1.0 - rho) / (trace_G * (1 - h));

      vec_sa2.push_back(sigma_a2);
      vec_sb2.push_back(sigma_b2);
      logm_null.push_back(CalcMarginal(Uty, K_eval, 0.0, tau));

      gsl_matrix_set(Hyper, ij, 0, h);
      gsl_matrix_set(Hyper, ij, 1, rho);
      gsl_matrix_set(Hyper, ij, 2, sigma_a2);
      gsl_matrix_set(Hyper, ij, 3, sigma_b2);
      gsl_matrix_set(Hyper, ij, 4, 1 / (double)n_grid);
      ij++;
    }
  }

  // Compute BF factors.
  time_start = clock();
  cout << "Calculating BF..." << endl;
  for (size_t t = 0; t < ns_test; t++) {
    gsl_vector_view Xgamma_col = gsl_matrix_column(Xgamma, 0);
    gsl_vector_const_view X_col = gsl_matrix_const_column(UtX, t);
    gsl_vector_memcpy(&Xgamma_col.vector, &X_col.vector);

    for (size_t ij = 0; ij < n_grid; ij++) {
      sigma_a2 = vec_sa2[ij];
      sigma_b2 = vec_sb2[ij];

      d = CalcMarginal(Xgamma, Uty, K_eval, sigma_a2, sigma_b2, tau);
      d -= logm_null[ij];
      d = exp(d);

      gsl_matrix_set(BF, t, ij, d);
    }
  }
  time_Proposal = (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0);

  // Save results.
  WriteResult(Hyper, BF);

  // Free matrices and vectors.
  gsl_matrix_free(BF);
  gsl_matrix_free(Xgamma);
  gsl_matrix_free(Hyper);
  return;
}

void single_ct_regression(const gsl_matrix_int *Xd,
                          const gsl_vector_int *dlevel,
                          const gsl_vector *pip_vec, gsl_vector *coef,
                          gsl_vector *prior_vec) {

  map<int, double> sum_pip;
  map<int, double> sum;

  int levels = gsl_vector_int_get(dlevel, 0);

  for (int i = 0; i < levels; i++) {
    sum_pip[i] = sum[i] = 0;
  }

  for (size_t i = 0; i < Xd->size1; i++) {
    int cat = gsl_matrix_int_get(Xd, i, 0);
    sum_pip[cat] += gsl_vector_get(pip_vec, i);
    sum[cat] += 1;
  }

  for (size_t i = 0; i < Xd->size1; i++) {
    int cat = gsl_matrix_int_get(Xd, i, 0);
    gsl_vector_set(prior_vec, i, sum_pip[cat] / sum[cat]);
  }

  for (int i = 0; i < levels; i++) {
    double new_prior = sum_pip[i] / sum[i];
    gsl_vector_set(coef, i, log(new_prior / (1 - new_prior)));
  }

  return;
}

// Where A is the ni_test by n_cat matrix of annotations.
void BSLMMDAP::DAP_EstimateHyper(
    const size_t kc, const size_t kd, const vector<string> &vec_rs,
    const vector<double> &vec_sa2, const vector<double> &vec_sb2,
    const vector<double> &wab, const vector<vector<vector<double>>> &BF,
    gsl_matrix *Ac, gsl_matrix_int *Ad, gsl_vector_int *dlevel) {
  // clock_t time_start;

  // Set up BF.
  double h, rho, sigma_a2, sigma_b2, d, s, logm, logm_save = nan("");
  size_t t1, t2;
  size_t n_grid = wab.size(), ns_test = vec_rs.size();

  gsl_vector *prior_vec = gsl_vector_alloc(ns_test);
  gsl_matrix *Hyper = gsl_matrix_alloc(n_grid, 5);
  gsl_vector *pip = gsl_vector_alloc(ns_test);
  gsl_vector *coef = gsl_vector_alloc(kc + kd + 1);

  // Perform the EM algorithm.
  vector<double> vec_wab, vec_wab_new;

  // Initial values.
  for (size_t t = 0; t < ns_test; t++) {
    gsl_vector_set(prior_vec, t, (double)BF.size() / (double)ns_test);
  }
  for (size_t ij = 0; ij < n_grid; ij++) {
    vec_wab.push_back(wab[ij]);
    vec_wab_new.push_back(wab[ij]);
  }

  // EM iteration.
  size_t it = 0;
  double dif = 1;
  while (it < 100 && dif > 1e-3) {

    // Update E_gamma.
    t1 = 0, t2 = 0;
    for (size_t b = 0; b < BF.size(); b++) {
      s = 1;
      for (size_t m = 0; m < BF[b].size(); m++) {
        d = 0;
        for (size_t ij = 0; ij < n_grid; ij++) {
          d += vec_wab_new[ij] * BF[b][m][ij];
        }
        d *=
            gsl_vector_get(prior_vec, t1) / (1 - gsl_vector_get(prior_vec, t1));

        gsl_vector_set(pip, t1, d);
        s += d;
        t1++;
      }

      for (size_t m = 0; m < BF[b].size(); m++) {
        d = gsl_vector_get(pip, t2) / s;
        gsl_vector_set(pip, t2, d);
        t2++;
      }
    }

    // Update E_wab.
    s = 0;
    for (size_t ij = 0; ij < n_grid; ij++) {
      vec_wab_new[ij] = 0;

      t1 = 0;
      for (size_t b = 0; b < BF.size(); b++) {
        d = 1;
        for (size_t m = 0; m < BF[b].size(); m++) {
          d += gsl_vector_get(prior_vec, t1) /
               (1 - gsl_vector_get(prior_vec, t1)) * vec_wab[ij] * BF[b][m][ij];
          t1++;
        }
        vec_wab_new[ij] += log(d);
      }

      s = max(s, vec_wab_new[ij]);
    }

    d = 0;
    for (size_t ij = 0; ij < n_grid; ij++) {
      vec_wab_new[ij] = exp(vec_wab_new[ij] - s);
      d += vec_wab_new[ij];
    }

    for (size_t ij = 0; ij < n_grid; ij++) {
      vec_wab_new[ij] /= d;
    }

    // Update coef, and pi.
    if (kc == 0 && kd == 0) {

      // No annotation.
      s = 0;
      for (size_t t = 0; t < pip->size; t++) {
        s += gsl_vector_get(pip, t);
      }
      s = s / (double)pip->size;
      for (size_t t = 0; t < pip->size; t++) {
        gsl_vector_set(prior_vec, t, s);
      }

      gsl_vector_set(coef, 0, log(s / (1 - s)));
    } else if (kc == 0 && kd != 0) {

      // Only discrete annotations.
      if (kd == 1) {
        single_ct_regression(Ad, dlevel, pip, coef, prior_vec);
      } else {
        logistic_cat_fit(coef, Ad, dlevel, pip, 0, 0);
        logistic_cat_pred(coef, Ad, dlevel, prior_vec);
      }
    } else if (kc != 0 && kd == 0) {

      // Only continuous annotations.
      logistic_cont_fit(coef, Ac, pip, 0, 0);
      logistic_cont_pred(coef, Ac, prior_vec);
    } else if (kc != 0 && kd != 0) {

      // Both continuous and categorical annotations.
      logistic_mixed_fit(coef, Ad, dlevel, Ac, pip, 0, 0);
      logistic_mixed_pred(coef, Ad, dlevel, Ac, prior_vec);
    }

    // Compute marginal likelihood.
    logm = 0;

    t1 = 0;
    for (size_t b = 0; b < BF.size(); b++) {
      d = 1;
      s = 0;
      for (size_t m = 0; m < BF[b].size(); m++) {
        s += log(1 - gsl_vector_get(prior_vec, t1));
        for (size_t ij = 0; ij < n_grid; ij++) {
          d += gsl_vector_get(prior_vec, t1) /
               (1 - gsl_vector_get(prior_vec, t1)) * vec_wab[ij] * BF[b][m][ij];
        }
      }
      logm += log(d) + s;
      t1++;
    }

    if (it > 0) {
      dif = logm - logm_save;
    }
    logm_save = logm;
    it++;

    cout << "iteration = " << it << "; marginal likelihood = " << logm << endl;
  }

  // Update h and rho that correspond to w_ab.
  for (size_t ij = 0; ij < n_grid; ij++) {
    sigma_a2 = vec_sa2[ij];
    sigma_b2 = vec_sb2[ij];

    d = exp(gsl_vector_get(coef, coef->size - 1)) /
        (1 + exp(gsl_vector_get(coef, coef->size - 1)));
    h = (d * (double)ns_test * sigma_a2 + 1 * sigma_b2) /
        (1 + d * (double)ns_test * sigma_a2 + 1 * sigma_b2);
    rho = d * (double)ns_test * sigma_a2 /
          (d * (double)ns_test * sigma_a2 + 1 * sigma_b2);

    gsl_matrix_set(Hyper, ij, 0, h);
    gsl_matrix_set(Hyper, ij, 1, rho);
    gsl_matrix_set(Hyper, ij, 2, sigma_a2);
    gsl_matrix_set(Hyper, ij, 3, sigma_b2);
    gsl_matrix_set(Hyper, ij, 4, vec_wab_new[ij]);
  }

  // Obtain beta and alpha parameters.

  // Save results.
  WriteResult(vec_rs, Hyper, pip, coef);

  // Free matrices and vectors.
  gsl_vector_free(prior_vec);
  gsl_matrix_free(Hyper);
  gsl_vector_free(pip);
  gsl_vector_free(coef);
  return;
}