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README.md

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+## Examples of Applying Bayes Rule in Processing
+
+This repository collects a series of Processing sketches demonstrating the use Bayes Rule. It was created as part of [Makematics at ITP in Fall 2012](http://makematics.com/syllabus/2012-fall).
+
+What follows is a description of the sketches contained herein:
+
+### A Basic Demonstration of Bayes Rule
+
+Expressed in the classic form of an imperfect test for a rare disease. Calculates all four probabilities possible with the two different test results.
+
+### Bayesian Localization
+
+A demonstration of determining the position of a "robot" in 1 dimension given a set of uncertain sensor readings.
+
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+
+This was adapted from Unit 1 of Sebastian Thrun's [Udacity Self-Driving Car class](http://www.udacity.com/overview/Course/cs373/CourseRev/apr2012)
+
+### Bayesian Spam Filtering
+
+An implementation of Paul Graham's classic technique from [A Plan for Spam](http://www.paulgraham.com/spam.html). Adapted from [this java implementation by Dan Shiffman](http://www.shiffman.net/teaching/a2z/bayesian/).

basic_bayes_rule/basic_bayes_rule.pde

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+float frequencyOfDisease = 0.01;
+
+float accuracyOfTest = 0.95;
+
+float totalPositiveProbability = (accuracyOfTest*frequencyOfDisease) + (1-accuracyOfTest)*(1-frequencyOfDisease);
+
+float probabilityOfDisesaeGivenPositiveTest = (accuracyOfTest*frequencyOfDisease)/totalPositiveProbability;
+float probabilityOfHealthGivenPositiveTest = ((1-accuracyOfTest)*(1-frequencyOfDisease))/totalPositiveProbability;
+
+float totalNegativeProbability = (accuracyOfTest * (1- frequencyOfDisease)) + (1-accuracyOfTest)*(frequencyOfDisease);
+
+
+float probabilityOfDiseaseGivenNegativeTest = ((1-accuracyOfTest)*frequencyOfDisease)/totalNegativeProbability;
+float probabilityOfHealthGivenNegativeTest = (accuracyOfTest*(1-frequencyOfDisease))/totalNegativeProbability;
+
+println("probabilityOfDisesaeGivenPositiveTest: " + probabilityOfDisesaeGivenPositiveTest);
+println("probabilityOfHealthGivenPositiveTest: " + probabilityOfHealthGivenPositiveTest);
+println(probabilityOfHealthGivenPositiveTest + probabilityOfDisesaeGivenPositiveTest);
+
+println("probabilityOfDiseaseGivenNegativeTest: " + probabilityOfDiseaseGivenNegativeTest);
+println("probabilityOfHealthGivenNegativeTest: " + probabilityOfHealthGivenNegativeTest);
+println(probabilityOfDiseaseGivenNegativeTest + probabilityOfHealthGivenNegativeTest);

bayesian_localization/bayesian_localization.pde

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+boolean[] cells;
+float[] probabilities;
+
+int numCells = 10;
+int currentPosition;
+int doorWidth = 20;
+int doorHeight = 50;
+// inaccurate senor probabilites
+float hitError = 0.6;
+float missError = 0.2;
+
+boolean showPosition = false;
+
+void setup() {
+  size(400, 400);
+  cells = new boolean[numCells];
+  probabilities = new float[numCells];
+  for (int i = 0; i < cells.length; i++) {
+    cells[i] = (random(1) > 0.7);
+    probabilities[i] = 1.0/cells.length;
+  }
+
+  currentPosition = (int)random(numCells);
+}
+
+void draw() {
+  background(255);
+  drawSensorReading();
+
+  if(showPosition){
+    fill(0);
+    text("True position: " + currentPosition, 50, 200);
+  }
+
+  translate(10, 10);
+  drawCells();
+
+  translate(0, 150);
+  drawProbabilities();
+}
+void sense(boolean sensorReading){
+  float[] newProbs = new float[probabilities.length];
+
+  for(int i = 0; i < cells.length; i++) {
+    if(cells[i] == sensorReading){
+      newProbs[i] = probabilities[i] * hitError;
+    } else {
+      newProbs[i] = probabilities[i] * missError;
+    }
+  }
+
+  probabilities = newProbs;
+
+  // now we have to normalize, i.e.
+  // make sure all the probabilities add up to 1
+  float sum = 0;
+  for(float i : probabilities){
+    sum += i;
+  }
+
+  for(int i = 0; i < probabilities.length; i++){
+    probabilities[i] /= sum;
+  }
+}
+
+void move(int move){
+  boolean[] newCells = new boolean[cells.length];
+
+  for(int i = 0; i < cells.length; i++){
+    int j = (i+(cells.length + move)) % cells.length;
+
+    newCells[i] = cells[j];
+  }
+
+  cells = newCells;
+}
+
+
+
+void drawProbabilities(){
+  pushMatrix();
+  pushStyle();
+  stroke(0);
+  noFill();
+  float scale = 0.8;
+  scale(scale);
+
+  beginShape();
+  for(int i = 0; i < cells.length; i++) {
+    float doorX = (doorWidth+5) * i * 1/scale;
+    vertex(doorX+doorWidth/2, probabilities[i]*-100);
+    pushStyle();
+    fill(125);
+    text(nf(probabilities[i],1,2), doorX, 15); 
+    popStyle(); 
+  }
+  endShape();
+  popStyle();
+  popMatrix();
+}
+
+void drawSensorReading() {
+  pushMatrix();
+  pushStyle();
+  translate(width-100, 10); 
+
+  fill(0);
+  text("SENSOR", 0, 10);
+  noFill();
+  stroke(0);
+  rect(0, 20, 90, 100);
+
+  if (takeSensorReading()) {
+    pushMatrix();
+    translate(30, 30);
+    drawDoor();
+    popMatrix();
+  }
+
+  popStyle();
+  popMatrix();
+}
+
+boolean takeSensorReading() {
+  // perfect measurement
+  return cells[currentPosition];
+}
+
+void drawCells() {
+
+  pushStyle();
+
+  pushMatrix();
+  for (int i = 0; i < cells.length; i++) {
+    int doorX = (doorWidth+5) * i;
+
+    if (cells[i]) {
+      pushMatrix();
+      translate(doorX, 0);
+      drawDoor();
+      popMatrix();
+    }
+    fill(0);
+    text(i, doorX-5+doorWidth/2, + doorHeight+15);
+  }
+  popMatrix();
+  popStyle();
+}
+
+void drawDoor() {
+  pushMatrix();
+  pushStyle();
+    fill(110, 50, 50);
+  stroke(0);
+  rect(0, 0, doorWidth, doorHeight);
+  popStyle();
+  popMatrix();
+}
+
+void keyPressed(){
+  if(key == ' '){
+    sense(takeSensorReading());
+  }
+
+  if(key == '='){
+    move(1);
+  }
+  if(key == '-'){
+    move(-1);
+  }
+
+  if(key == 'r'){
+    showPosition = !showPosition;
+  }
+  saveFrame("bayesian-localization-####.png");
+}