# 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 “diagnosis.”

### Observational Inference

• One of the central benefits of Bayesian networks is that they represent the Joint Probability Distribution and can therefore carry out inference “omnidirectionally.”

• Given an observation with any type of evidence on any of the networks’ 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.

• Pearl’s Graph Surgery and Jouffe’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

• BayesiaLab’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. BayesiaLab’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. BayesiaLab’s Genetic Target Optimization will search, within the specified constraints, for those scenarios that optimize the target criterion.

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