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Introduction

Date: October 1, 2010
Authors: Whit Armstrong
Contact: armstrong.whit@gmail.com
Web site:http://github.com/armstrtw/CppBugs
License:GPL-3

Purpose

CppBugs is a c++ library designed for MCMC sampling.

Features

CppBugs attempts to make writing mcmc models as painless as possible. It incorporates features from both WinBugs and PyMC and requires users only to implment an update method which resembles the model section of a WinBUGS script.

  • CppBugs is extremely fast. Typically between 20x and 100x faster than equivalent WinBugs or PyMC models.
  • Common statistical distributions are supported drawing heavily on Boost libraries. Many more will be implemented to eventually be as feature complete as WinBugs/PyMC.

Usage

Starting with a bugs model:

model {
 for(i in 1:n){
   incidence[i] ~ dbin(phi2[i], size[i])
   logit(phi[i]) <- B.0 + B.period2*period2[i] + B.period3*period3[i] + B.period4*period4[i] + b.herd[herd[i]] + overdisp[i]
   phi2[i] <- max(0.00001, min(phi[i], 0.9999999))
   overdisp[i] ~ dnorm(0,tau.overdisp)
 }
 B.0 ~ dnorm(0,0.001)
 B.period2 ~ dnorm(0, 0.001)
 B.period3 ~ dnorm(0, 0.001)
 B.period4 ~ dnorm(0, 0.001)

 tau.overdisp <- pow(sigma.overdisp, -2)
 sigma.overdisp ~ dunif(0, 1000)
 for(j in 1:n.herd){
   b.herd[j] ~ dnorm(0, tau.b.herd)
 }
 tau.b.herd <- pow(sigma.b.herd, -2)
 sigma.b.herd ~ dunif(0, 100)
}

This mode can be converted to a CppBugs model by implementing an update function which encapsulates the bugs model:

void update() {
  phi.value = b0.value + b_period2.value*period2 + b_period3.value*period3 + b_period4.value*period4 + sum(permutation_matrix*b_herd.value,1) + overdisp.value;
  phi.value = 1/(1+exp(-phi.value));
  sigma_overdisp.value = 1/sqrt(tau_overdisp.value);
  sigma_b_herd.value = 1/sqrt(tau_b_herd.value);
  b0.dnorm(0,0.001);
  b_period2.dnorm(0,0.001);
  b_period3.dnorm(0,0.001);
  b_period4.dnorm(0,0.001);
  tau_overdisp.dunif(0,1000);
  tau_b_herd.dunif(0,100);
  b_herd.dnorm(0, tau_b_herd.value);
  overdisp.dnorm(0,tau_overdisp.value);
  likelihood.dbinom(size,phi.value);
}

That's it. The model can be compiled and run as follows:

int main() {
  int incidence_raw[] = {2,3,4,0,3,1,1,8,2,0,2,2,0,2,0,5,0,0,1,3,0,0,1,8,1,3,0,12,2,0,0,0,1,1,0,2,0,5,3,1,2,1,0,0,1,2,0,0,11,0,0,0,1,1,1,0};
  int size_raw[] = {14,12,9,5,22,18,21,22,16,16,20,10,10,9,6,18,25,24,4,17,17,18,20,16,10,9,5,34,9,6,8,6,22,22,18,22,25,27,22,22,10,8,6,5,21,24,19,23,19,2,3,2,19,15,15,15};
  int herd_raw[] = {1,1,1,1,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,15};
  double period2_raw[] = {0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0};
  double period3_raw[] = {0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0};
  double period4_raw[] = {0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1};

  int N = 56;
  int N_herd = 15;

  ivec incidence(incidence_raw,N);
  ivec size(size_raw,N);
  ivec herd(herd_raw,N); herd -= 1;
  vec period2(period2_raw,N);
  vec period3(period3_raw,N);
  vec period4(period4_raw,N);
  HerdModel m(incidence,size,herd,period2,period3,period4,N,N_herd);
  m.sample(1e6,1e5,50);

  cout << "samples: " << m.b0.history.size() << endl;
  cout << "b0: " << m.b0.mean() << endl;
  cout << "b_period2: " << m.b_period2.mean() << endl;
  cout << "b_period3: " << m.b_period3.mean() << endl;
  cout << "b_period4: " << m.b_period4.mean() << endl;
  cout << "tau_overdisp: " << m.tau_overdisp.mean() << endl;
  cout << "tau_b_herd: " << m.tau_b_herd.mean() << endl;
  cout << "sigma_overdisp: " << m.sigma_overdisp.mean() << endl;
  cout << "sigma_b_herd: " << m.sigma_b_herd.mean() << endl;
  cout << "b_herd: " << endl << m.b_herd.mean() << endl;

  return 0;
}
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