Merge pull request #74 from jethronap/book_examples

Add Markove chain Monte Carlo example

Author: pockerman

README.md

@@ -49,10 +49,13 @@ You can start using Jstat by adding the following dependency to your project:
 - <a href="src/main/java/examples/stats/example5/example.md">Example 5</a>: Calculate descriptive statistics metrics
 - <a href="src/main/java/examples/stats/example6/example.md">Example 6</a>: Hypothesis tests on the mean of a normal distribution with known variance
 - <a href="src/main/java/examples/stats/example7/example.md">Example 7</a>: Type II error and the sample size
+- <a href="src/main/java/examples/stats/example8/example.md">Example 8</a>: Simulate the Central Limit Theorem
 
 ### Monte Carlo 
 - <a href="src/main/java/examples/mc/example1/example.md">Example 1</a>: Monte Carlo Simulation for the Monty Hall Problem
 - <a href="src/main/java/examples/mc/example2/example.md">Example 2</a>: Calculate the area of a circle using Monte Carlo integration
+- <a href="src/main/java/examples/mc/example3/example.md">Example 3</a>: Markov chain Monte Carlo for pi calculation
+- <a href="src/main/java/examples/mc/example4/example.md">Example 4</a>: The Metropolis algorithm
 
 ### Plotting
 
@@ -66,5 +69,6 @@ You can start using Jstat by adding the following dependency to your project:
 - <a href="src/main/java/examples/es/example1/example.md">Example 1</a>: Load data from an Elasticsearch index
 
 
+
 
 

src/main/java/base/CommonConstants.java

@@ -1,10 +1,22 @@
 package base;
 
+import java.nio.file.Paths;
+
 public final class CommonConstants {
 
     public static double getTol(){return CommonConstants.tol;}
     public static void setTol(double tol){CommonConstants.tol = tol;}
 
+    public static String examplesPath(){
+        String path = "src/main/java/examples";
+        return path;
+    }
+
+    public static String mcExamplesPath(){
+        String path =  CommonConstants.examplesPath();
+        return path + "/mc";
+    }
+
     protected static double tol = 1.0e-8;
     private CommonConstants(){}
 

src/main/java/examples/mc/example3/Example3.java

@@ -0,0 +1,35 @@
+package examples.mc.example3;
+
+import java.util.concurrent.ThreadLocalRandom;
+
+public class Example3 {
+
+    static public void main(String[] args){
+
+
+
+        final  int N_ITERATIONS = 10000;
+        final double DELTA = 0.1;
+        double x = 1.0;
+        double y = 1.0;
+        double area_under_curve = 0.0;
+
+        for(int itr=0; itr < N_ITERATIONS; ++itr){
+
+            double del_x = ThreadLocalRandom.current().nextDouble(-DELTA, DELTA);
+            double del_y = ThreadLocalRandom.current().nextDouble(-DELTA, DELTA);
+
+            if(Math.abs(x + del_x) < 1.0 && Math.abs(y + del_y) < 1.0){
+                x += del_x;
+                y += del_y;
+            }
+
+            if(x*x + y*y < 1.0){
+                area_under_curve += 1;
+            }
+        }
+
+        System.out.println("Pi is: " + 4.0* area_under_curve/(double)N_ITERATIONS);
+
+    }
+}

src/main/java/examples/mc/example3/example.md

@@ -0,0 +1,64 @@
+# Markov Chain Monte Carlo For Pi Calculation
+
+## Contents
+ * [Overview](#overview) 
+ * [Import files](#include_files)
+ * [The main function](#m_func)
+ * [Results](#results)
+ * [Source Code](#source_code)
+
+## <a name="overview"></a> Overview
+
+## <a name="include_files"></a> Import files
+
+ ```
+package examples.mc.example3;
+
+import java.util.concurrent.ThreadLocalRandom;
+ ```
+
+## <a name="m_func"></a> The main function
+
+```
+public class Example3 {
+
+    static public void main(String[] args){
+
+
+
+        final  int N_ITERATIONS = 10000;
+        final double DELTA = 0.1;
+        double x = 1.0;
+        double y = 1.0;
+        double area_under_curve = 0.0;
+
+        for(int itr=0; itr < N_ITERATIONS; ++itr){
+
+            double del_x = ThreadLocalRandom.current().nextDouble(-DELTA, DELTA);
+            double del_y = ThreadLocalRandom.current().nextDouble(-DELTA, DELTA);
+
+            if(Math.abs(x + del_x) < 1.0 && Math.abs(y + del_y) < 1.0){
+                x += del_x;
+                y += del_y;
+            }
+
+            if(x*x + y*y < 1.0){
+                area_under_curve += 1;
+            }
+        }
+
+        System.out.println("Pi is: " + 4.0* area_under_curve/(double)N_ITERATIONS);
+        
+    }
+}
+```
+
+## <a name="results"></a> Results
+
+```
+Pi is: 3.0244
+```
+
+ ## <a name="source_code"></a> Source Code
+ 
+ <a href="Example3.java">Example3.java</a>

src/main/java/examples/mc/example4/Example4.java

@@ -0,0 +1,55 @@
+package examples.mc.example4;
+
+import base.CommonConstants;
+import io.CSVFileWriter;
+import org.apache.commons.math3.distribution.AbstractRealDistribution;
+import org.apache.commons.math3.distribution.NormalDistribution;
+
+import java.util.ArrayList;
+import java.util.List;
+
+public class Example4 {
+
+
+    public static double target(double x){
+
+        if(x < 0.){
+            return 0.0;
+        }
+
+        return Math.exp(-x);
+    }
+
+    public static void main(String[] args){
+
+        final int N_ITERATIONS = 10000;
+        List<Double> pos = new ArrayList<>(N_ITERATIONS);
+        for(int i=0; i<N_ITERATIONS; ++i){
+            pos.add(0.0);
+        }
+
+        CSVFileWriter writer = new CSVFileWriter(CommonConstants.mcExamplesPath()+"/example4/positions.csv");
+        writer.writeColumnNames("ITERATION", "POSITION");
+        pos.set(0, 2.0);
+
+        writer.writeRow(0, pos.get(0));
+
+        AbstractRealDistribution normal = new NormalDistribution(0.0, 1.0);
+
+        for(int i=1; i<N_ITERATIONS; ++i){
+            double xk = pos.get(i-1);
+            double xkPlusOne = xk + normal.sample();
+
+            double A = Example4.target(xkPlusOne/xk);
+
+            if(A < 1.0 ){
+                pos.set(i, xkPlusOne);
+            }
+            else{
+                pos.set(i, xk);
+            }
+
+            writer.writeRow(i, pos.get(i));
+        }
+    }
+}

src/main/java/examples/mc/example4/example.md

@@ -0,0 +1,40 @@
+# Example 4: The Metropolis Algorithm
+ 
+ ## Contents
+ * [Acknowledgements](#acknowledgement) 
+ * [Overview](#overview) 
+     * [Metropolis algorithm](#goodness_of_fit)
+ * [Import files](#include_files)
+ * [The main function](#m_func)
+ * [Results](#results)
+ * [Source Code](#source_code)
+ 
+ ## <a name="acknowledgement"></a> Acknowledgements
+ This example was taken from <a href="https://stephens999.github.io/fiveMinuteStats/index.html">fiveMinuteStats</a>.
+ ## <a name="overview"></a> Overview
+ 
+ ### <a name="goodness_of_fit"></a> Metropolis algorithm
+ 
+
+ ## <a name="include_files"></a> Import files
+ 
+ ```
+
+ ```
+ 
+ ## <a name="m_func"></a> The main function
+ 
+ ```
+ 
+     
+ ```
+ 
+ ## <a name="results"></a> Results
+ 
+ ```
+
+ ```
+ 
+ ## <a name="source_code"></a> Source Code
+ 
+ <a href="Example4.java">Example4.java</a>