Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Probability Theory”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 recordsLinked to original sources
PubMed1992

Clusters galore: insights about environmental clusters from probability theory.

The posterior probability of a causal explanation given that an environmental cancer cluster is statistically significant depends on the prior probability of an environmentally caused cluster, the sensitivity of the statistical test and its specificity. The prior probability is low, because it is rare to have enough carcinogen in the general environment to cause a relative risk of cancer high enough to achieve statistical significance in a small geographic area. The sensitivity and specificity are not great. The likelihood that a census tract escapes statistically significant elevations in all 80 types of cancer can be calculated. Many of the thousands of census tracts will, by chance alone, have at least one type of cancer whose elevation is statistically significant. Actual observation from a large cancer registry confirms this probabilistic prediction. Applying the principles of Bayes' Theorem would suggest that most statistically significant environmental cancer clusters are not due to environmental carcinogens. One would have to investigate hundreds of environmental cancer clusters to find one with a true environmental cause.

Bayes Theorem↗
PubMed1985

Use of the average antibody-antigen bond concept and probability theory to simplify modeling of linear and circular antibody-antigen complex formation.

We illustrate use of a simple approach to describe the equilibrium interactions of mixtures of monoclonal antibodies and antigens. This procedure is based on elementary concepts in probability theory and is readily suited to describing interactions of antibodies and antigens which form circular as well as linear complexes. The method is also suited to describing the inhibitory effects of antibodies which compete for overlapping epitopes and an example is provided to show how the procedure can be used to describe the interactions of antibodies which inhibit circular complex formation. We also outline simple strategies for preparing computer programs to simulate binding of antigens to defined antibody mixtures. The methods described should facilitate design of immunoassay procedures based on the use of defined mixtures of monoclonal antibodies.

Antibodies, Monoclonal↗
PubMed1990

An application of probability theory to a group of breath-alcohol and blood-alcohol data.

Many jurisdictions have "per se" driving-while-intoxicated (DWI) status expressed in terms of a blood-alcohol concentration (BAC) standard (in grams per 100 mL or the equivalent). Since breath-alcohol (BrAC) analysis is typically employed to determine BAC, there is often challenge to the use of an assumed 2100:1 conversion ratio. This concern may be relevant in light of considerable data that show a low percentage of cases in which BrAC greater than BAC, and this concern increases when the BrAC is used to predict BAC in the context of "per se" legislation. Probability theory provides a basis for estimating the likelihood of an individual having a BrAC greater than or equal to g/210 L with a corresponding BAC less than 0.10 g/100 mL. Actual field data from the state of Wisconsin (n = 404) were evaluated to determine the probability of this occurrence. The probability for this occurrence involves the multiplication law for independent events. The computed probability from the data was 0.018. The actual number of occurrences where BrAC greater than or equal to 0.10 g/210 L and BAC less than 0.10 g/100 mL was 5, resulting in a probability of 0.012. The concern of having BrAC greater than BAC at the critical "per se" level has a very low probability of occurrence, which thus supports the reasonableness of "per se" DWI legislation based upon a blood-alcohol standard determined by breath-alcohol analysis.

Alcoholic Intoxication↗
PubMed1986

Probability theory in the use of diagnostic tests. An introduction to critical study of the literature.

The purpose of this article is to provide an understanding of methods that are useful in formulating advice about when to use diagnostic tests. If the clinician expresses diagnostic uncertainty as the probability of a disease in a patient, Bayes' theorem may be used to predict the effect of doing various tests and their impact on patient management. To use Bayes' theorem wisely, one must be aware of pitfalls in estimating probability and must understand the limitations of most studies of the sensitivity and specificity of diagnostic tests.

Bayes Theorem↗
PubMedDate not supplied

The feasibility of axiomatically-based expert systems.

We distinguish axiomatically-based expert systems, whose design and implementation are guided by one or more axiomatically-based theories of decision-making (e.g., decision theory, Bayesian probability theory, maximum entropy theory), from traditional expert systems. An analysis of the knowledge acquisition and computational needs of axiomatically-based expert systems is presented. An explicit quantitative comparison is made between the actual knowledge acquisition effort required to build an existing expert system, and the effort that would be required to build an analogous axiomatically-based advice system. The costs and benefits of the axiomatic approach are discussed. The analysis suggests that the small additional cost of knowledge acquisition for the axiomatic approach are outweighed by the long-term benefits this approach provides.

Computer Simulation↗
PubMed1992

Expert systems in histopathology. V. DS theory, certainty factors and possibility theory.

Uncertainty management for the evaluation of evidence based on linguistic and conceptual data is taking advantage of developments in the Dempster-Shafer (DS) theory of evidence, possibility theory and fuzzy logic. The DS theory offers the capability to assess the uncertainty of different subsets of assertions in a domain and the way in which uncertainty is affected by accumulating evidence. The DS theory goes beyond probability theory in its ability to represent ignorance about certain aspects of a situation. However, the theory is very sensitive to the numerical assessments provided by users and can lead to intuitively unexpected and even undesirable results. Certainty factors are widely used in various expert systems. Their definition and updating may follow either a probabilistic model or fuzzy set theoretic concept.

Data Interpretation, Statistical↗
PubMed1991

Reasoning in uncertainties. An analysis of five strategies and their suitability in pathology.

In reasoning systems, uncertainty plays a crucial part, especially for those fields in which judgements are essential, as in pathology. Uncertainty has several aspects, such as prevalence of diseases, occurrence of findings and the sensitivity and predictive value of findings. For the functioning of a reasoning system, two aspects are crucial: (1) the internal representation of the uncertainty and (2) the way in which the uncertainty is propagated in the reasoning process when combining formal statements. Five well-known reasoning strategies (Bayes' probability theory, MYCIN's certainty factor model, fuzzy set theory, the theory of Dempster-Shafer and Pathfinder's scoring mechanism) are compared, with particular attention to: (1) Under what conditions will the model function? In particular, what information is to be specified a priori to the system? (2) Can the different aspects of uncertainty be dealt with as separate entities? (3) How are unknown uncertainties dealt with? (4) How is evidence in favor of a hypothesis combined with evidence against it? (5) How does the model treat the simultaneous occurrence of more than one disorder, that is, how does the model support reasoning with compound hypotheses? It is preliminarily concluded that the different aspects of uncertainty are expressed as separate entities only in Pathfinder and probability theory. Hence, the other models do not accurately represent uncertain knowledge. Also, such theoretically attractive models as the Bayes, MYCIN and Dempster-Shafer theory can only function properly under the tight condition of mutual exclusiveness of hypotheses, which is not always suited for broader areas of pathology. They may, however, be suited for smaller areas, with a limited number of defined diseases and a limited number of features. All models but the Bayes model lack a predictable performance since there is no (or only a partial) underlying theory to guarantee minimization of the overall error.

Humans↗
PubMed1979

Probability and the brain.

Probability theory asserts the lawfulness of seemingly random events in large populations and seems to be a reasonable approach to a general understanding of the structure and function of the nervous system. The brain, by virtue of the number of its components, the multiplicity of their possible interconnections, and the range and rapidity of their outputs, is almost implausably complex in its over-all design. Probability theory, therefore, is usually applied to (a) descriptions of the behavior of large neuronal populations, (b) statistical analysis of neuronal spike trains, and (c) theoretical models of neuronal interaction. A consideration of each of these subjects is presented, as is a discussion of the most fundamental level of application of the theory to the nervous system: (d) the assertion that the neuron and/or brain is inherently nondeterministic. In practical terms this is shown to be a "nonissue," the uncertainty principle that follows has rather definite philosophical implications.

Auditory Perception↗
PubMed1991

A probabilistic view on steady-state enzyme reactions.

A new theoretical description of steady-state enzyme reactions is proposed. The description is based on the concepts of the probability theory instead of the conventional formalism of chemical kinetics. A general steady-state rate equation is obtained using a probabilistic model of the catalytic act. As a result, the classical problems of enzyme kinetics can be formulated and considered in a different aspect. It is shown that the new theory presents a clearer treatment of some commonly obscure questions, such as the steady-state establishment. The theory also gives additional possibilities in the interpretation of the experimental results of traditional methods and proposes certain new ways in experimental investigations of enzymes.

Animals↗
PubMed1992

Beyond positivism: a metaphysical basis for clinical practice?

Medicine does not have its own unified body of scientific knowledge. Instead, physicians who are oriented to research make sporadic incursions into the basic sciences such as genetics, biochemistry, immunology, epidemiology, physiology, pharmacology and so on. These latter, taken together, comprise biomedicine which is said to have adopted the positivist epistemology or the Cartesian/Newtonian one that regards the scientist as an uninvolved observer of nature. In effect, medical science has come to rest on a theory of knowledge which links meaning to probability and considers prediction as the scientist's chief task. Like its predecessor, the probability theory of meaning rejects metaphysical speculation and remains connected to observations made, directly or indirectly, by means of the five senses. Despite some brilliant successes touching on relatively uncommon disorders, biomedicine cannot explain most day-to-day clinical activity. An understanding of what transpires between patient and doctor, of its diagnostic potential and therapeutic weight requires hermeneutic, or phenomenological, inquiry which brings about changes in both parties to it. Such a science, as ontological speculation has been called, cannot be deciphered by an epistemology couched in the imagery of physics and chemistry.

Metaphysics↗
PubMed1992

[Medical informatics as a complementary method in medical education].

The practice of the decision making at the bed side especially highlights the place to be devoted to medical informatics both at the pre- and post-graduate levels. Still in a relatively recent past, say the 50s-60s, most of the medical educational efforts were delivered when watching and then imitating the medical behaviour of an older physician. The medical educators were aware that besides the formal lessons related to selected chapters of medical textbooks, there were an obvious need for better training in the ability to make sound clinical judgements. If this ability has been considered only as an artful and intuitive process neither subjected to theoretical analysis nor to be captured in a formal quantitative model, now things have changed to such an extent that it becomes broadly shared that a science of medical decision making can be reasonably founded and this threefold: 1) Upon a formulated logic, 2) The probability theory, and 3) A value theory. The first gives the hand to artificial intelligence (AI) technics, the third to medical information data bases dealing either with patients (like in hospital information systems) or with literature like MEDLINE or electronic "cookbooks". Basically the probabilistic theory is based here upon a priori probabilities related to patients informations and data and opens the way to bayesian decision making. After this little summary it is stressed that educational informatics in medicine would appear either very central or very marginal, if not optional.

Computer-Assisted Instruction↗
PubMed1979

Application of case series review results to the evaluation of individual cases in diagnostic radiology.

Probability theory provides a simple method for physicians to use their "intellectual linkages" to their past clinical experience in making current diagnoses. Only a pencil and paper are required for making a few likelihood calculations. To illustrate this method, evaluation was done of a new diagnostic sign (presence of knee ossification centers) for differentiating rubella from cytomegalovirus infection in young infants. Two practical questions can be answered by use of this method for calculating probabilities: (1) How certain can one be about either diagnosis when centers are present or absent? (2) How can other radiologists apply these results to their individual cases?

Cytomegalovirus Infections↗
PubMed1990

Probabilistic belief networks for genetic counseling.

This paper describes a program, GenInfer, which uses belief networks to calculate risks of inheriting genetic disorders. GenInfer is based on Pearl's (J. Pearl, Artif. Intell. 29 (1986) 241-288) algorithm for fusion and propagation in probabilistic belief networks. It is written in Common Lisp. GenInfer can calculate genotypes for any family affected with any single-gene inherited disorder. Besides considering both negative and positive information in the pedigree. GenInfer takes into account additional information about the specific disorder as well as supplementary information for family members. The output consists of genotype probabilities for all family members and estimated genetic risks for prospective children of the consultands. Belief networks provide a way to calculate probabilities for systems of conditionally dependent variables. The impacts of various pieces of information are propagated and fused in such a way that, when equilibrium is reached, each proposition can be assigned a degree of belief consistent with the axioms of probability theory. In Pearl's algorithm, information is communicated through the network by messages sent between nodes. Pearl's basic algorithm cannot directly handle multiple-connected networks, which arise in the genetic counseling domain whenever a family pedigree includes consanguinity or more than one child per couple. GenInfer makes use of two cycle breaking methods, clustering and conditioning, to handle these situations.

Bayes Theorem↗
PubMedDate not supplied

Medical informatics and clinical decision making: the science and the pragmatics.

There are important scientific and pragmatic synergies between the medical decision making field and the emerging discipline of medical informatics. In the 1970s, the field of medicine forced clinically oriented artificial intelligence (AI) researchers to develop ways to manage explicit statements of uncertainty in expert systems. Classic probability theory was considered and discussed, but it tended to be abandoned because of complexities that limited its use. In medical AI systems, uncertainty was handled by a variety of ad hoc models that simulated probabilistic considerations. To illustrate the scientific interactions between the fields, the author describes recent work in his laboratory that has attempted to show that formal normative models based on probability and decision theory can be practically melded with AI methods to deliver effective advisory tools. In addition, the practical needs of decision makers and health policy planners are increasingly necessitating collaborative efforts to develop a computing and communications infrastructure for the decision making and informatics communities. This point is illustrated with an example drawn from outcomes management research.

Artificial Intelligence↗
PubMed1990

Using the patient's history to estimate the probability of coronary artery disease: a comparison of primary care and referral practices.

PURPOSE: According to probability theory, the interpretation of new information should depend on the prior probability of disease. We asked if this principle applies to interpreting the history in patients with chest pain. We compared the prevalence of coronary artery disease (CAD) in patients who had similar histories but who came from populations with different disease prevalence. PATIENTS AND METHODS: We studied two high-disease-prevalence populations (patients referred for coronary arteriography) and two low-disease-prevalence populations (patients from primary care practices). We used clinical characteristics of one arteriography population to develop a logistic rule for estimating the probability of coronary artery narrowing. The number of clinical findings determined the logistic score, which was proportional to the prevalence of CAD. RESULTS: The prevalence of CAD was much lower in the primary care population than in the arteriography population, even when patients with similar logistic scores, and thus similar clinical histories, were compared. CONCLUSION: A clinician must take account of the overall prevalence of disease in the clinical setting when using the patient's history to estimate the probability of disease. Failure to observe this caution may lead to errors in test selection and interpretation.

Adult↗
PubMed1988

Posttest probability calculation by weights. A simple form of Bayes' theorem.

This article reintroduces a different form of Bayes' theorem that allows calculation of posttest probabilities by adding quantities known as "weights." A weight combines information found in both a test's sensitivity and specificity. A single value can describe how a given test result changes the posttest probability of disease. The use of weights and this form of Bayes' theorem should allow more widespread understanding and use of probability theory in clinical practice.

Bayes Theorem↗