Im working on a script that uses the bayesian theorem and the inverse chi squared function to retrieve the probability that any given text belongs in a specific category.

I've read up on the inverse chi squared function and i know it shouldnt give a negative value, but for some reason im getting negative values from the function.

PHP Code:

        $N = 0;
        $H = $S = 1;
        foreach($ngrams as $k => $v) {
            if ( !isset($knowledge[$k]) ) continue;

            $N++;
            $value = $knowledge[$k] * $v; 
            $H *= $value;
            $S *= (float)( 1 - ( ($value>=1) ? 0.99 : $value) );
        } 


So after calculating the above the values are as follows:

H: 4
S: 1.0E-20
N = 10

These values are now passed into the inverse chi squared function with 2 degress of freedom.

PHP Code:

        $H = $this->chi2Q( -2 * log( $N *  $H), 2 * $N);
        $S = (float)$this->chi2Q( -2 * log( $N *  $S), 2 * $N); 


Inverse Chi Squared Function:

PHP Code:

    function chi2Q($x, $v) {
        $m = $x / 2;
        
        $sum = $term = exp(-$m);

        for($i=1; $i < ($v/2);$i++) {
            $term *= $m/$i;
            $sum += $term;
        }
        echo 'Sum: '.$sum;
        return ($sum < 1.0) ? $sum : 1.0;
    } 


The results from the function are as follows:

H: -2.8299816393601
S: 2.0228764578537E-10

Then going back to the original function we can calculate the probability that its in H or S.

PHP Code:

        $I = (( 1 + ($H - $S)) / 2) * 100;
        return is_finite($I) ? $I : 100; 


Because H is alot smaller that S it causes the final probability to be -91.499081978121, obviously you shouldnt get an inverse number from a chi square distribution, so im not sure where its gone wrong. Maybe i haven't got enough information, and if so how would i go about detecting this?

S: 2.0228764578537E-10

isn't a negative number, just a tiny positive number ( 1<>0 )

0.000 000 000 20228764578537



<pedantic>BTW it should be Bayesian theorem </pedantic>

Spelling mistake... Sorry.

The S is a postive number but because its so small when calculating the probability using the code below, the probability will be negative as H+S isn't enough to generate a postive number:

PHP Code:

        $I = (( 1 + ($H - $S)) / 2) * 100;
        return is_finite($I) ? $I : 100; 


I know you can't get a negative number from the inverse chi squared function, but as it stands i do. I was just wondering if there were any limitations to using the function and whether any one has prior knowledge who might be able to sport any mistakes etc...

Yes, but you do have $H - $S in your formulae.

Yeah, but surely both $H and $S should be positive numbers first.

Originally Posted by evans123

Yeah, but surely both $H and $S should be positive numbers first.

Trying (and failing) to cast my mind back to college for statistical analysis lessons.