Bayesian Decision Analysis: Principles and Practice by Jim Q. Smith

By Jim Q. Smith

Bayesian determination research helps principled choice making in advanced domain names. This textbook takes the reader from a proper research of straightforward choice difficulties to a cautious research of the occasionally very complicated and information wealthy buildings faced through practitioners. The booklet comprises easy fabric on subjective likelihood conception and multi-attribute software concept, occasion and selection bushes, Bayesian networks, effect diagrams and causal Bayesian networks. the writer demonstrates whilst and the way the idea could be effectively utilized to a given determination challenge, how facts will be sampled and professional decisions elicited to help this research, and while and the way a good Bayesian determination research may be applied. Evolving from a third-year undergraduate direction taught by means of the writer over decades, the entire fabric during this publication can be obtainable to a pupil who has accomplished introductory classes in chance and mathematical facts.

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Finding an EMV strategy is then not quite such a transparent task. 10. A laboratory has to test the blood of 2n people for a rare disease having a probability p of appearing in any one individual. The laboratory can either test each person’s blood separately [decision d0 ] or randomly pool the blood of the subjects into 2n−r groups of size x = 2r , r = 1, 2, . . , n [decision dr ] and test each pooled sample of blood. If a pool gives a negative result then this would mean that each member of the pool did not have the disease.

Thus the tree has to be sufficiently refined for the full consequences of any possible unfolding of history will be known by the DM. In a problem represented by a tree it is essential that two different unfoldings of history giving rise to different consequences – and so in particular their associated rewards – are distinguished by different root to leaf paths. On the other hand, although it is sometimes computationally convenient or more transparent to express two outfoldings with the same sequence of decisions and associated distributions on consequences by different root to leaf paths it is not technically necessary to keep these separate.

So the reason for the diagnosis can be fed back to the doctor: that “the unlikely absence of the 4th symptom and the relatively better explanation of this observation provided by illness 3 outweighs in strength all other evidence pointing in the other direction”. This might be acceptable to the doctor or the external auditor. Alternatively she or he may question whether the elicited small probabilities of this symptom were possibly inaccurate or not apposite to this particular patient. A reasoned and supported argument for adjusting these probabilities could then lead to a documented revision of the diagnosis.

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