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Multilayer control of large Markov chains

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A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.


Maximum likelihood from incomplete data via the EM algorithm

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Wiley is a global provider of content and content-enabled workflow solutions in areas of scientific, technical, medical, and scholarly research; professional development; and education. Our core businesses produce scientific, technical, medical, and scholarly journals, reference works, books, database services, and advertising; professional books, subscription products, certification and training services and online applications; and education content and services including integrated online teaching and learning resources for undergraduate and graduate students and lifelong learners. Founded in 1807, John Wiley & Sons, Inc. has been a valued source of information and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Wiley has published the works of more than 450 Nobel laureates in all categories: Literature, Economics, Physiology or Medicine, Physics, Chemistry, and Peace. Wiley has partnerships with many of the world's leading societies and publishes over 1,500 peer-reviewed journals and 1,500 new books annually in print and online, as well as databases, major reference works and laboratory protocols in STMS subjects.


A Mathematical Theory of Evidence

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In the spring of 1971, I attended a course on statistical inference taught by Arthur Dempster at Harvard. In the fall of that same year Geoffrey Watson suggested I give a talk expositing Dempster's work on upper and lower probabilities to the Department of Statistics at Princeton. This essay is one of the results of the ensuing effort. It offers a reinterpretation of Dempster's work, a reinterpretation that identifies his "lower probabilities" as epistemic probabilities or degrees of belief, takes the rule for combining such degrees of belief as fundamental, and abandons the idea that they arise as lower bounds over classes of Bayesian probabilities.


Case grammar

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Lexical ambiguity can be syntactic if it involves more than one grammatical category for a single word, or semantic if more than one meaning can be associated with a word. In this article we discuss the application of a Bayesian-network model in the resolution of lexical ambiguities of both types. The network we propose comprises a parsing subnetwork, which can be constructed automatically for any context-free grammar, and a subnetwork for semantic analysis, which, in the spirit of Fillmore's (1968) case grammars, seeks to fulfill the required cases of all candidates for verb of the sentence. Solving for the highest joint probability of the variables conditioned upon the evidences to the network yields the most likely candidate with its meaning, along with its cases and respective meanings. This is achieved by fixing the values of all evidence nodes concurrently, and then performing a stochastic simulation in which the remaining nodes are updated probabilistically with a high degree of parallelism.


Computer-Based Medical Consultations: MYCIN

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This text is a description of a computer-based system designed to assist physicians with clinical decision-making. This system, termed MYCIN, utilizes computer techniques derived principally from the subfield of computer science known as artificial intelligence (AI). MYCIN's task is to assist with the decisions involved in the selection of appropriate therapy for patients with infections.

MYCIN contains considerable medical expertise and is also a novel application of computing technology. Thus, this text is addressed both to members of the medical community, who may have limited computer science backgrounds, and to computer scientists with limited knowledge of medical computing and clinical medicine. Some sections of the text may be of greater interest to one community than to the other. A guide to the text follows so that you may select those portions most pertinent to your particular interests and background.

The complete book in a single file.


A Model of Inexact Reasoning in Medicine

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Reprinted in Readings in Uncertain Reasoning, G. Shafer and J. Pearl, eds., pp. 259-273, San Mateo, CA: Morgan Kaufmann Publishers, Inc., 1990.See also: Stanford Center for Biomedical Informatics Research (BMIR).… quantifying confirmation and then manipulating the numbers as though they were probabilities quickly leads to apparent inconsistencies or paradoxes. Carl Hempel presented an early analysis of confirmation (Hempel, 1965), pointing out as we have that C[h,e] is a very different concept from P(hle ). His famous Paradox of the Ravens was presented early in his discussion of the logic of confirmation. Let hl be the statement that "all ravens are black" and h2 the statement that "all nonblack things are nonravens." Clearly hi is logically equivalent to h,2. If one were to draw an analogy with conditional probability, it might at first seem valid, therefore, to assert that C[hl,e] = C[h2,e] for all e. However, it appears counterintuitive to state that the observation of a green vase supports hi, even though the observation does seem to support h,2. C[h,e] is therefore different from P(hle) for it seems somehow wrong that an observation of a vase could logically support an assertion about ravens. Another characteristic of a quantitative approach to confirmation that distinguishes the concept from probability was well-recognized by Carnap (1950) and discussed by Barker (1957) and Harrd (1970). They note it is counterintuitive to suggest that the confirmation of the negation of a hypothesis is equal to one minus the confirmation of the hypothesis, i.e., C[h,e] is not 1 - C[-qh,e]. The streptococcal decision rule asserted that a gram-positive coccus growing in chains is a Streptococcus with a measure of support specified as 7 out of 10. This translates to C[h,e]=0.7 where h is "the organism is a Streptococcus" and e is the information that "the organism is a gram-positive coccus growing in chains." As discussed above, an expert does not necessarily believe that C[mh,e] = 0.3. The evidence is said to be supportive of the contention that the organism is a Streptococcus and can therefore hardly also support the contention that the organism is not a Streptococcus. Ch.13 of Mycin Book; revised from Math. Biosci. 23:351-379