(10th-September-2020)
• For example, using particle filtering to compute P(Report|smoke) for the belief network of Figure 6.1. First generate the particles s1,...,s1000. For this example, we use the conditional probability of the variable being sampled given the particle as the proposal distribution. Suppose it first samples Fire. Out of the 1,000 particles, about 10 will have Fire=true and about 990 will have Fire=false (as P(fire)=0.01). It can then absorb the evidence Smoke=true. Those particles with Fire=true will be weighted by 0.9 [as P(smoke | fire ) = 0.9] and those particles with Fire=false will be weighted by 0.01 [as P(smoke | ¬fire ) = 0.01]. It can then resample; each particle can be chosen in proportion to its weight. The particles with Fire=true will be chosen in the ratio 990×0.01 : 10×0.9. Thus, about 524 particles will be chosen with Fire=true, and the remainder with Fire=false. The other variables can be sampled, in turn, until Report is sampled.
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