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simplemcmc.cpp
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simplemcmc.cpp
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#include <random>
#include <string>
#include <math.h>
#include "matplotlibcpp.h"
using namespace std;
namespace plt = matplotlibcpp;
double true_mean = 0.5;
double true_sigma = 0.1;
std::vector<double> data_x;
std::vector<double> data_y;
int data_size = 150;
void find_mean_stdev(vector<double>* c) {
double sum = std::accumulate(c->begin(), c->end(), 0.0);
double mean = sum / c->size();
double sq_sum = std::inner_product(c->begin(), c->end(), c->begin(), 0.0);
double stdev = std::sqrt(sq_sum / c->size() - mean * mean);
std::cout << "Mean is " << mean << std::endl;
std::cout << "Var is " << stdev << std::endl;
}
double normal_custom(double x) {
double mean = 4;
double sigma = 0.1;
return exp(-(x-mean)*(x-mean)/(2*sigma*sigma))/(sigma*sqrt(2*M_PI));
}
double log_normal_custom(double x, double mean, double sigma) {
//return log(1/(2*sigma*sigma)) + (-(x-mean)*(x-mean));
return log(normal_custom(x, mean, sigma));
}
int main()
{
int n = 5000; // number of data points
std::random_device rd;
std::mt19937 gen(rd());
//Data
for (int i = 0; i < data_size; i++) {
data_x.push_back(random_(0, 1));
data_y.push_back(normal_custom(data_x.at(i), true_mean, true_sigma));
}
// Monte Carlo
std::normal_distribution<> norm(5.0, 0.1);
vector<double> c(n);
for(int i=0; i<n; ++i) {
c.at(i) = norm(gen);
}
find_mean_stdev(&c);
plt::hist(c, 50);
plt::show();
// Metropolis-Hastings Algorithm
double initial = 2.0;
vector<double> x(n);
x.at(0) = initial + 1; // JLT
for(int i=1; i<n; ++i) {
std::normal_distribution<> proposal(x.at(i-1), 0.1);
double y = proposal(gen);
// Its ok to use the same generator, but you have to recreate the distribution each time.
double r = min(normal_custom(y)/normal_custom(x.at(i-1)), 1.0);
if (rand() / double(RAND_MAX) < r)
x.at(i) = y;
else
x.at(i) = x.at(i-1);
// Could do log likelihood here to avoid divisions, but it works!
}
find_mean_stdev(&x);
plt::hist(x, 50);
plt::show();
}