Introduction

Date:	January 20, 2012
Authors:	Whit Armstrong
Contact:	[email protected]
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 5x to 10x faster than equivalent WinBugs and 3x to 5x faster than 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 in three steps.

• define the variable space
• implement a function which updates the deterministic variables
• add nodes to the model and define the parameters governing the stochastic variables

vec b(randn<vec>(4));
vec b_herd(randn<vec>(N_herd));
vec overdisp(randn<vec>(N));
vec phi;
double tau_overdisp(1), tau_b_herd(1), sigma_overdisp(1), sigma_b_herd(1);


std::function<void ()> model = [&]() {
  phi = fixed*b + indicator_matrix*b_herd + overdisp;
  phi = 1/(1+exp(-phi));
  sigma_overdisp = 1/sqrt(tau_overdisp);
  sigma_b_herd = 1/sqrt(tau_b_herd);
};

MCModel m(model);
m.normal(b).dnorm(0,0.001);
m.uniform(tau_overdisp).dunif(0,1000);
m.uniform(tau_b_herd).dunif(0,100);
m.normal(b_herd).dnorm(0, tau_b_herd);
m.normal(overdisp).dnorm(0,tau_overdisp);
m.binomial(incidence).dbinom(size,phi);
m.deterministic(sigma_overdisp);
m.deterministic(sigma_b_herd);
m.deterministic(phi);

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

#include <iostream>
#include <vector>
#include <armadillo>
#include <boost/random.hpp>
#include <cppbugs/cppbugs.hpp>
#include <cppbugs/mcmc.model.hpp>

using namespace arma;
using namespace cppbugs;
using std::cout;
using std::endl;

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;

  const ivec incidence(incidence_raw,N);
  const ivec size(size_raw,N);
  ivec herd(herd_raw,N); herd -= 1;
  const vec period2(period2_raw,N);
  const vec period3(period3_raw,N);
  const vec period4(period4_raw,N);

  mat indicator_matrix(N,N_herd);
  indicator_matrix.fill(0.0);
  for(uint i = 0; i < herd.n_elem; i++) {
    indicator_matrix(i,herd[i]) = 1.0;
  }

  mat fixed(N,4);
  fixed.col(0).fill(1);
  fixed.col(1) = period2;
  fixed.col(2) = period3;
  fixed.col(3) = period4;

  vec b(randn<vec>(4));
  vec b_herd(randn<vec>(N_herd));
  vec overdisp(randn<vec>(N));
  vec phi;
  double tau_overdisp(1), tau_b_herd(1), sigma_overdisp(1), sigma_b_herd(1);

  std::function<void ()> model = [&]() {
    phi = fixed*b + indicator_matrix*b_herd + overdisp;
    phi = 1/(1+exp(-phi));
    sigma_overdisp = 1/sqrt(tau_overdisp);
    sigma_b_herd = 1/sqrt(tau_b_herd);
  };

  MCModel m(model);
  m.normal(b).dnorm(0,0.001);
  m.uniform(tau_overdisp).dunif(0,1000);
  m.uniform(tau_b_herd).dunif(0,100);
  m.normal(b_herd).dnorm(0, tau_b_herd);
  m.normal(overdisp).dnorm(0,tau_overdisp);
  m.binomial(incidence).dbinom(size,phi);
  m.deterministic(sigma_overdisp);
  m.deterministic(sigma_b_herd);
  m.deterministic(phi);
  m.sample(1e6,1e5,1e4,50);

  cout << "samples: " << m.getNode(b).history.size() << endl;
  cout << "b: " << endl << m.getNode(b).mean() << endl;
  cout << "tau_overdisp: " << m.getNode(tau_overdisp).mean() << endl;
  cout << "tau_b_herd: " << m.getNode(tau_b_herd).mean() << endl;
  cout << "sigma_overdisp: " << m.getNode(sigma_overdisp).mean() << endl;
  cout << "sigma_b_herd: " << m.getNode(sigma_b_herd).mean() << endl;
  cout << "b_herd: " << endl << m.getNode(b_herd).mean() << endl;
  cout << "acceptance_ratio: " << m.acceptance_ratio() << endl;

  return 0;
}