Inference

• Can use the BBN to infer the value of a target variable given the observed values of the other variables.
• Infer not a single value but the probability distribution for the target variable which specifies the probability it will take on each possible value given the observed values of the other variables.
• Generally, we may wish to infer the probability distribution of a variable (e.g., ) given observed values for only a subset of the other variables (e.g., and are the only observed values available).
• Exact inference of probabilities (and even some approximate methods) for an arbitrary BBN is known to be NP-hard.
• Monte Carlo methods provide approximate solutions by randomly sampling the distributions of the unobserved variables.