Bayes nets and probabilistic belief networks

What are Bayesian Networks or probablistic belief Nets?

Bayesian networks, sometimes known as belief nets, are probabilistic models of belief, knowledge, or data about the uncertain relationships among a set of variables. Each variable or node may represent something that may be true or false -- such as, whether it will rain tomorow -- or it may have several alternative values -- such as, the type of precipitation, none, rain, sleet, snow, or hail -- or it may be a continuous quantity -- such as inches of precipitation in the last 24 hours. The network is designed to estimate the probability distribution over each variable, based on evidence or observations of related variables -- such as the season, geographical location, or whether it is raining today.

The network consists of directed links or arrows depicting the existence of an "influence" of one variable on another. A Bayesian network must be acyclic -- that is with no directed cycles following the arrows. Usually, the beliefs are quantified as a probability distribution on each variable, conditioned on the values of its predecessors -- that is the variables from which it has incoming arrows or influences. Belief about a variable with no incoming arrows is expressed as a marginal probability distribution. Some people, notably Judea Pearl, one of the key developers of the concepts, refer to Bayesian networks as "causal networks" where the conditional probability distributions indicate underlying causal relationships. Most agree that influences may, but need not reflect causal relationships.

Does Analytica handle Bayesian Networks or Belief Nets?

Yes and no. Analytica can represent Bayesian networks. The influence diagrams provided by Analytica represent probabilistic relationships among variables, adding decision variables, and objectives (utilities), to standard chance variables of a belief network. Analytica provides fast, general methods, based on Monte Carlo and Latin hypercube sampling, for predictive inference -- that is computing probability distributions on downstream variables, based on the values or probability distributions over the upstream variables. However, it does not come with built-in algorithms for diagnostic inference -- that is computing probability distributions over upstream variables, based on observations of the values of downstream variables. For example, it does not calculate the probability of a disease given evidence on one or more symptoms that may be caused by that disease for which you have conditional probabilities of the symptom given the disease. For the majority of risk analysis and probabilistic applications, predictive inference is sufficient. If the network contains just one disease and its symptoms, diagnostic inference is relatively easy -- using Bayes rule to compute the posterior probability of the disease given the observed symptoms. But, for some important applications, notably in medicine and machine troubleshooting with a complex network of many conditions and observations, diagnostic inference is central, and you might be better off with another application that provides efficient diagnostic inference -- such as GenIe.