Is This Bathroom Occupied?

bathroom.js

// underscore.js helpers
var _ = require('underscore');

// State aliases
var OCCUPIED = true;
var VACANT = false;

// Sample a current state
var knock = function(state) {
	var correct = state.sign === state.bathroom;
	if (correct && state.sign === OCCUPIED) {
		return _({}).extend(state, { truePositive: state.truePositive + 1 });
	}
	if (correct && state.sign === VACANT) {
		return _({}).extend(state, { trueNegative: state.trueNegative + 1 });
	}
	if (state.sign && !state.bathroom) {
		return _({}).extend(state, { falsePositive: state.falsePositive + 1 });
	}
	return _({}).extend(state, { falseNegative: state.falseNegative + 1 });
};

// Define behaviors as modifying the current state of the bathroom. Can be invoked as entering or exiting.

// Don't change the state of the sign
var unobservant = function(state, exit) {
	return _({}).extend(state, {
		sign: state.sign,
		bathroom: !exit
	});
};
// Change the sign when entering, but not on leaving
var forgetful = function(state, exit) {
	return _({}).extend(state, {
		sign: OCCUPIED,
		bathroom: !exit
	});
};
// Make sure that the sign reflects the actual state of the bathroom
var conscientious = function(state, exit) {
	return _({}).extend(state, {
		sign: !exit,
		bathroom: !exit
	});
};
// Each behavior is as likely to appear
var chooseBehavior = _(_.sample).partial([unobservant, forgetful, conscientious]);

// Create a person, randomly choosing a behavior
var Person = function() {
	var behavior = chooseBehavior();
	this.enterBehavior = behavior;
	// Behavior functionality is based on the exit flag, so we can reuse and partially apply that flag to the exit behavior
	this.exitBehavior = _(behavior).partial(_, true);
};
// Enter bathroom
Person.prototype.enterBathroom = function(state) {
	return this.enterBehavior(state);
};
// Exit bathroom
Person.prototype.exitBathroom = function(state) {
	return this.exitBehavior(state);
};
Person.prototype.useBathroom = function(state) {
	// Enter the bathroom and sample the result
	var enterState = knock(this.enterBathroom(state));
	// Exit the bathroom and sample the result
	return knock(this.exitBathroom(enterState));
};

// Set number of runs for the model
var numberOfRuns = 500000;
// Sample twice per run
var samples = numberOfRuns * 2;

// Initial starting state
var initialState = {
	sign: VACANT,
	bathroom: VACANT,
	truePositive: 0,
	trueNegative: 0,
	falsePositive: 0,
	falseNegative: 0
};

// Get the results
var results = _(numberOfRuns).chain()
	// Get a list with length numberOfRuns
	.range()
	// Generate as many people as runs
	.map(function() { return new Person(); })
	// Work through the runs, returning a final state
	.reduce(function(state, person) { return person.useBathroom(state); }, initialState)
	.value();

var tp = results.truePositive / samples;
var tn = results.trueNegative / samples;
var fp = results.falsePositive / samples;
var fn = results.falseNegative / samples;

// Reporting
console.log('Results after ' + numberOfRuns + ' runs:');
console.log('Probability of the bathroom being occupied when the sign reads occupied: ' + (tp / (tp + fp)).toPrecision(4));
console.log('Probability of the bathroom being vacant when the sign reads vacant: ' + (tn / (tn + fn)).toPrecision(4));