# Edit in JSFiddle

```/**
* A demonstration of using re-estimation and the forward algorithm with a Hidden Markov Model.
*/

var alphabetSize = 20,
numStates = 20,
isFirstConditioning = true,
model;
var sp = [
[]
],
tp = [
[]
],
ep = [
[]
];
var p = ProbabilityAPI.HiddenMarkovModel;
var outputDiv = document.getElementById("output");
var model = p.getModel();

//random distribution of initial values
//pass one: create random variables at each index
var stp, sep;
var stpArr = [],
sepArr = [];
for (var i = 0; i < numStates; i++) {
sp[i] = Math.random();
tp[i] = [];
ep[i] = [];
stp = 0;
sep = 0;
//one loop for state to state transition
for (var j = 0; j < numStates; j++) {
tp[i].push(Math.random());
stp += tp[i][j];
}
//...and another for observation dependent on state transition
for (var j = 0; j < alphabetSize; j++) {
ep[i].push(Math.random());
sep += ep[i][j];
}
stpArr.push(stp);
sepArr.push(sep);
}

//pass two:normalize random variables so a row sums to 1
for (var i = 0; i < numStates; i++) {
for (var j = 0; j < numStates; j++) {
tp[i][j] /= stpArr[i];
}
for (var j = 0; j < alphabetSize; j++) {
ep[i][j] = 1 / alphabetSize; //keep the emissions uniform
}
}

/**d= A dummy data array. Play around with the individual indices, and try passing the forward algorithm various numeric arrays after re-estimation to see how it scores them.
*/
var d = [0, 0, 1, 1, 0, 3, 2, 0, 1];
var n1 = logScore(p.forward(d, sp, tp, ep)[1]);
model = p.reestimation(d, sp, tp, ep);
//evens out probability distribution so there are no rows with absolute 0 probability, which causes problems
model[0] = p.redistProbability(model[0]);
model[1] = p.redistProbability(model[1]);
model[2] = p.redistProbability(model[2]);
var n2 = logScore(p.forward(d, model[0], model[1], model[2])[1]);

var output = "<p>Normalized closeness of data average to model before re-estimation: " + n1 + " ...and after: " + n2 + "</p>";
outputDiv.innerHTML = output;

//used to make the forward algorithm output easier to read
function logScore(v) {
return 100 + (Math.log(v) / Math.log(1.5));
}```
`<div id="output"></div>`