# Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach

@article{Pearl1982ReverendBO, title={Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach}, author={Judea Pearl}, journal={Probabilistic and Causal Inference}, year={1982} }

This paper presents generalizations of Bayes likelihood-ratio updating rule which facilitate an asynchronous propagation of the impacts of new beliefs and/or new evidence in hierarchically organized inference structures with multi-hypotheses variables. The computational scheme proposed specifies a set of belief parameters, communication messages and updating rules which guarantee that the diffusion of updated beliefs is accomplished in a single pass and complies with the tenets of Bayes…

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## References

SHOWING 1-10 OF 11 REFERENCES

### Subjective Bayesian methods for rule-based inference systems

- Computer Science
- 1981

A subjective Bayesian inference method that realizes some of the advantages of both formal and informal approaches, and modifications needed to deal with the inconsistencies usually found in collections of subjective statements are described.

### On the Independence Assumption Underlying Subjective Bayesian Updating

- MathematicsArtif. Intell.
- 1981

### A Retrospective View of the Hearsay-II Architecture

- Computer ScienceIJCAI
- 1977

Experiences gained while successfully applying the Hearsay-II architecture to the problem of speech understanding are described, and the paradigm of viewing problem solving in terms of hypothesize-and-test actions distributed among distinct representations of the problem has been shown to be computationally feasible.

### Empirical Studies of Cascaded Inference in Jurisprudence: Methodological Consideration

- Empirical Studies of Cascaded Inference in Jurisprudence: Methodological Consideration

### Psychology Research Report

- Psychology Research Report
- 1980

### DDI Handbook for Decision Analysis, Decision and Design Inc

- DDI Handbook for Decision Analysis, Decision and Design Inc
- 1973

### Assuming now that P(A) is valid, let us examine the validity of q(B), where B is any child of A. By definition (Equation (11.6)), q(B) should satisfy: q(B i ) = P(B i | D u (B)) = ∑ P(B i | A j )P

### Chapter 11 Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach

### Belief Propagation in Hierarchical Inference Structures

- Belief Propagation in Hierarchical Inference Structures
- 1982