Inference: Diagnosis, Prediction, and Simulation

  • The inherent ability of Bayesian networks to explicitly model uncertainty makes them suitable for a broad range of real-world applications.

  • In the Bayesian network framework, diagnosis, prediction, and simulation are identical computations. They all consist of observational inference conditional upon evidence:

    • Inference from observed effects to causes: diagnosis or abduction.

    • Inference from observed causes to effects: simulation or prediction.

  • This distinction, however, only exists from the perspective of the researcher, who would presumably see the symptom of a disease as the effect and the disease itself as the cause. Hence, carrying out inference based on observed symptoms is interpreted as a โ€œdiagnosis.โ€

Observational Inference

  • One of the central benefits of Bayesian networks is that they represent the Joint Probability Distribution and can therefore carry out inference โ€œomnidirectionally.โ€

  • Given an observation with any type of evidence on any of the networksโ€™ nodes (or a subset of nodes), BayesiaLab computes the posterior probabilities of all other nodes in the network, regardless of arc directions.

  • Both exact and approximate observational inference algorithms are implemented in BayesiaLab.

Types of Evidence

  • Hard Evidence: no uncertainty regarding the state of the variable (node).

  • Likelihood/Virtual Evidence is defined by likelihoods associated with each variable state.

  • Probabilistic/Soft Evidence, defined by marginal probability distributions.

  • Numerical Evidence, for numerical variables or for categorical/symbolic variables that have associated numerical values.

Causal Inference

  • Beyond observational inference, BayesiaLab can also perform causal inference for computing the impact of intervening on a subset of variables instead of merely observing these variables.

  • Pearlโ€™s Graph Surgery and Jouffeโ€™s Likelihood Matching are available for this purpose.

Effects Analysis

  • Many research activities focus on estimating the size of an effect, e.g., to establish the treatment effect of a new drug or to determine the sales boost from a new advertising campaign. Other studies attempt to decompose observed effects into their causes, i.e., they perform attribution.

  • BayesiaLab performs simulations to compute effects, as parameters as such do not exist in this nonparametric framework.

  • As all the domain dynamics are encoded in discrete Conditional Probability Tables (CPT), effect sizes only manifest themselves when different conditions are simulated.

  • Total Effects Analysis, Target Mean Analysis, and several other functions offer ways to study effects, including nonlinear and variable interactions.

Optimization

  • BayesiaLabโ€™s ability to perform inference over all possible states of all nodes in a network also provides the basis for searching for node values that optimize a target criterion. BayesiaLabโ€™s Target Optimization is a set of tools for this purpose.

  • Using these functions in combination with Direct Effects is of particular interest when searching for the optimum combination of variables that have a nonlinear relationship with the target, plus co-relations between them.

  • A typical example would be searching for the optimum mix of marketing expenditures to maximize sales. BayesiaLabโ€™s Genetic Target Optimization will search, within the specified constraints, for those scenarios that optimize the target criterion.

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