Joint probability of Bayesian Network

[Anna Pan]

Hi,

I am new to Webppl. I wonder how can I infer the joint probability over a Bayesian Network (BN) with some observations as a single number? Assuming I have such a BN as below:

/**

var bn = function() {
    var Cloudy = sample(Discrete({ps:[0.5, 0.5]}));
    var Sprinkler = Cloudy ? sample(Discrete({ps: [0.9, 0.1]})) : sample(Discrete({ps: [0.5, 0.5]}));
    var Rain = Cloudy ? sample(Discrete({ps: [0.2, 0.8]})) : sample(Discrete({ps: [0.8, 0.2]}));
    var WetGrass = Sprinkler ? (Rain ? sample(Discrete({ps: [0.01, 0.99]})): sample(Discrete({ps: [0.1, 0.9]})))
                                                : (Rain ? sample(Discrete({ps: [0.1, 0.9]})): sample(Discrete({ps: [1.0, 0.0]})));
    condition(WetGrass,1);
    //return [Cloudy, Rain, Sprinkler, WetGrass];
    //return sum([Cloudy, Rain, Sprinkler, WetGrass]);
    return {"WetGrass": WetGrass, "Rain": Rain, "Sprinkler": Sprinkler, "Cloudy": Cloudy};
}

var dist = Infer(
  {method: 'enumerate', maxExecutions: 1000000},
  bn);

print(dist);
viz.table(dist);

**/

Also, although this returns me a distribution table, this distribution table seems to be normalized. I wonder how should I do if I want a unnormalized one? 

Thank you so much for help!

Kind regards,

Jingwen

[Tom Lieber]

For your first question, I wonder if you're looking for distributions' score method?

dist.score({'WetGrass': 1, 'Rain': 1, 'Sprinkler': 1, 'Cloudy': 1});
// => -2.7936717238027855

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[null-a]

> how can I infer the joint probability over a Bayesian Network (BN) with some observations as a single number?

I might be able to help, but I'm not sure I understand the question, in particular the "with some observations as a single number" bit.

One guess is you're imagining a scenario in which you have multiple random variables (sample statements), and you'd like to condition on the result of combining these in some way. Here's an example of that kind of thing:

```

var xor = function(a,b) { return a != b; };
var myflip = function() { return flip(0.1); };
var model = function() {
  var xs = repeat(3, myflip);
  var parity = reduce(xor, false, xs)
  condition(parity == true)
  return xs;
};
var d = Infer(model);
viz.table(d);

```

If that doesn't help, maybe try asking the question in another way, and I'll try again.

Best,

Paul

[Anna Pan]

Thank you for all the replies.

I have now resolved this issue now.