Bayes.Examples.Sampling

Example of sampling

Two samplers are availables : the discreteAncestralSampler and the gibbsSampler. Only the gibbsSampler can be used with evidence.

In this example, we have a very simple network.

    simple :: ([TDV Bool],SBN CPT)
    simple = runBN $ do 
        a <- variable "a" (t :: Bool)
        b <- variable "b" (t :: Bool) 
--        
        proba a ~~ [0.4,0.6]
        cpt b [a] ~~ [0.8,0.2,0.2,0.8]
--    
        return [a,b]

This network is representing a sensor b. We observe the value of b and we want to infer the value of a.

We use the gibbsSampler for this with an initial period of 200 samples which are dropped. The gibbsSampler is generate a stream of samples. From this stream, we need to compute a probability distribution. For this, we use the samplingHistograms histogram function which is generating a list : the probability values of each vertex.

    let (vars@[a,b],exampleG) = simple
    n <- runSampling 5000 200 (gibbsSampler exampleG [b =: True])
    let h = samplingHistograms n
    print $ h

Then, we compare this result with the exact one we get with a junction tree.

    let jt = createJunctionTree nodeComparisonForTriangulation exampleG
        jt' = changeEvidence [b =: True] jt
    mapM_ (x -> print . posterior jt' $ [x]) vars

We can also use the discreteAncestralSampler to compute the posterior but it is not supporting the use of evidence in this version. The syntax is similar.

    n <- runSampling 500 (discreteAncestralSampler exampleG)

Test function

testSampling :: IO ()