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 145 records · Page 8Linked to original sources

Cost variances in health care: when should managers investigate?

When costs must be controlled, variance analysis can be a useful tool to implement that control. Variance analysis compares a standard of performance against actual results and investigates those differences that are felt to be the result of inefficient performance. The question becomes, which variances should be investigated? Using a decision model based on probability theory, variances can be identified that are statistically significant and require further investigation.

Analysis of Variance↗

Bayesian networks and probabilistic reasoning about scientific evidence when there is a lack of data.

Bayesian networks (BNs) are a kind of graphical model that formally combines elements of graph and probability theory. BNs are a mathematically and statistically rigorous technique allowing their user to define a pictorial representation of assumed dependencies and influences among a set of variables deemed to be relevant for a particular inferential problem. The formalism allows one to process newly acquired evidence according to the rules of probability calculus. Applications of BNs have been reported in various forensic disciplines. However, there seems to be some reluctance to consider BNs as a more general framework for representing and evaluating sources of uncertainties associated with scientific evidence. Notably, BNs are widely thought of as an essentially numerical method, requiring "exact" numbers with a high "accuracy". The present paper aims to draw the reader's attention to the point that the availability of hard numerical data is not a necessary requirement for using BNs in forensic science. An abstraction of quantitative BNs, known as qualitative probabilistic networks (QPNs), and sensitivity analyses are presented and their potential applications discussed. As a main difference to their quantitative counterpart, QPNs contain qualitative probabilistic relationships instead of numerical relations. Sensitivity analyses consist of varying the probabilities assigned to one or more variables and evaluating the effect on one or more other variables of interest. Both QPNs and sensitivity analyses appear to be useful concepts that permit one to work in contexts with acute lack of numerical data and where reasoning consistent with the laws of probability should nevertheless be performed.

Journal Article↗

[Correlate non-Gaussian measurement].

A general approach for measuring correlation in non-normal populations is presented. Two ways of tackling the problem are considered. The first relies on an explicit parametric model and some non-elementary notions from probability theory. The second, which relies on a wide class of bivariate laws of which the bivariate normal one is a special case, is very simple to put into practice.

Epidemiologic Methods↗

Organisms, organizations and interactions: an information theory approach to biocultural evolution.

The language metaphor of theoretical biology, proposed by Waddington in 1972, provides a basis for the formal examination of how different self-reproducing structures interact in an extended evolutionary context. Such interactions have become central objects of study in fields ranging from human evolution-genes and culture-to economics-firms, markets and technology. Here we use the Shannon-McMillan Theorem, one of the fundamental asymptotic relations of probability theory, to study the 'weakest' and hence most universal, forms of interaction between generalized languages. We propose that the co-evolving gene-culture structure that permits human ultra-sociality emerged in a singular coagulation of genetic and cultural 'languages', in the general sense of the word. Human populations have since hosted series of culture-only speciations and coagulations, events that, in this formulation, do not become mired in the 'meme' concept.

Biological Evolution↗

Cells responsible for tumor surveillance in man: effects of radiotherapy, chemotherapy, and biologic response modifiers.

Currently, the most probable theory of tumor surveillance is neither the existence of any tumor-specific, antigen-dependent, T-cell-mediated cytotoxic effect that could eliminate spontaneous tumors in man and that could be used for some kind of vaccination against tumors, nor the complete absence of any surveillance or defense systems against tumors. What is probable is the cooperation of a number of antigen-independent, relatively weakly cytotoxic or possibly only cytostatic humoral and cellular effects, including nutritional immunity, tumor necrosis factor, certain cytokines, and the cytotoxic effects mediated by macrophages, NK cells, NK-like cells, and certain stimulated T-cells. One question remaining to be solved is why these antigen-independent effects do not attack normal cells. A number of plausible hypotheses are discussed. The hypothetical surveillance system is modulated both by traditional cancer treatment and by attempts at immunomodulation. Radiotherapy reduced the T-helper cell function for almost a decade, but not those of macrophages or NK cells. T-cell changes have no prognostic implication, supporting, perhaps, the suggestion of a major role for macrophages and NK cells. Cyclic adjuvant chemotherapy reduces the peripheral lymphocyte population and several lymphocyte functions but not NK activity. Most of the parameters were normalized some years following treatment, but NK activity remained elevated and Th/Ts cell ratio was still decreased. This might possibly be taken to support the surveillance role of NK cells. Bestatin increases the frequency of lymphocytes forming rosettes with sheep red blood cells (but not their mitogenic responses), enhances NK activity, and augments the phagocytic capacity of granulocytes and monocytes (but not their cytotoxic activity). Improved survival with Bestatin treatment following chemotherapy has been observed in patients with melanoma Stages 1b and II and in patients with acute nonlymphatic leukemia, where BCG also seems active, although possibly only in patient groups with less than 49% complete remissions.

Adjuvants, Immunologic↗

Construction of a Bayesian network for mammographic diagnosis of breast cancer.

Bayesian networks use the techniques of probability theory to reason under uncertainty, and have become an important formalism for medical decision support systems. We describe the development and validation of a Bayesian network (MammoNet) to assist in mammographic diagnosis of breast cancer. MammoNet integrates five patient-history features, two physical findings, and 15 mammographic features extracted by experienced radiologists to determine the probability of malignancy. We outline the methods and issues in the system's design, implementation, and evaluation. Bayesian networks provide a potentially useful tool for mammographic decision support.

Bayes Theorem↗

Mediotrusive tooth guidance and temporomandibular joint sounds in non-patients and patients.

In 46 non-patients and 46 patients, the authors examined the presence (+) and the absence (-) of laterotrusive (LG) and mediotrusive (MG) tooth guidance, i.e. dynamic dental articulation events in contrast to static dental occlusion events. During a right and left laterotrusion/mediotrusion of the mandible, the number of compound, mutually exclusive and exhaustive tooth guidance events (possibilities) was six. In addition, the presence and the absence of temporomandibular joint (TMJ) sounds, provoked TMJ pains, and the associations between TMJ sounds and tooth guidance events were examined. In non-patients, LG+ and MG+ was relatively infrequent (30%) while LG+ and MG- was relatively frequent (70%). In patients, LG+ and MG+ was relatively frequent (58%) while LG+ and MG- was relatively infrequent (42%). LG- and MG+ was absent in non-patients and rare in patients (3%). Either unilateral or bilateral MG+ was relatively infrequent in non-patients (30%) and relatively frequent in patients (59%). Bilateral MG+ was relatively infrequent in non-patients (20%) and relatively frequent in patients (52%). Either unilateral or bilateral TMJ sounds were relatively infrequent in non-patients (39%) and relatively frequent in patients (74%). Either unilateral or bilateral provoked TMJ pains were absent in non-patients and relatively frequent in patients (72%). The authors found no evidence that TMJ sounds were associated with the ipsilateral absence of so-called balancing contacts (MG-) in non-patients and patients. Finally, no evidence supporting the use of a so-called positive predictive value, and "extension concept' of probability theory was found.

Adult↗

Intelligent machines in the twenty-first century: foundations of inference and inquiry.

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Artificial Intelligence↗

Transitions across a barrier induced by deterministic forcings.

The response of a bistable dynamical system to a deterministic forcing is studied with emphasis on the kinetics of the passage across the barrier separating the two states, and compared to classical Kramers' theory describing the response to a Gaussian white noise forcing. The existence of nontrivial thresholds for the occurrence of transitions is established. Analytic results complemented by numerical simulations are derived for the characteristics of these transitions for periodic and chaotic forcings. The probabilistic properties of the response are finally addressed and some connections are established with the universal stable distributions of probability theory.

Journal Article↗

Expert systems in histopathology. IV. The management of uncertainty.

Expert systems deal with data that are categorical and conceptual, that represent elements of fuzzy sets and that often, by themselves, do not allow an unequivocal decision. The management of uncertainty in expert systems thus becomes a crucial issue. It involves defining measures of uncertainty and procedures for combining accumulating evidence in a manner that properly considers the dependence structure of diagnostic clues. Probability theory offers valuable procedures for uncertainty assessment; however, their practical application in the domain of quantitative histopathology and histopathologic diagnosis can be problematic.

Diagnosis, Computer-Assisted↗

Predicting the response time of an urban ambulance system.

Response time, i.e., the time from dispatch of an ambulance to its arrival at the scene of an emergency, is an important measure of performance in an urban ambulance system. We developed a model that predicts the entire distribution of response time, explicitly accounting for the rate and spatial distribution of demand, variable ambulance velocities, and queueing effects. We tested the model using data sampled from 3,936 ambulance runs in Houston and achieved close agreement between empirical and predicted distributions of response time. Our use of probability theory to predict response times yielded a model that complements those previously reported for planning and evaluating urban ambulance systems.

Ambulances↗

Identification of Euro-Americans, Afro-Americans, and Amerindians from palatal dimensions.

Seven measurements were taken on 414 Euro-American, Afro-American, and Amerindian palates in an attempt to evaluate differences in dental arcade shape among these three groups. Width measurements across the palate at the first incisor, canine, second premolar, and second molar were taken directly on the dental arcade. The distances along the sagittal plane from the front of the palate to the level of these teeth were calculated from measurements taken between the right central incisor and the canine, second premolar and second molar. Discriminant functions computed from the measurements properly classified palates by group 66.0% of the time if sex is unknown. If sex is known to be male, other functions properly classified 65.7% of the sample; for sex known to be female 72.0% correct classification was achieved. Because these percentage are more than twice that expected from probability theory alone, it is concluded that the seven measurements are useful in determining ethnic group.

Black or African American↗

Hugo de Vries on heredity, 1889-1903. Statistics, Mendelian laws, pangenes, mutations.

The essay describes the development of Hugo de Vries's thinking on heredity from the publication of his Intracellulare Pangenesis in 1889 to the publication of Die Mutations-theorie, Volume 2, in 1903. De Vries's work in the 1890s can be characterized as an attempt to defend his theory of pangenes, especially the fundamental and controversial idea that different characters have different material hereditary carriers. Hybridization experiments served his goal. Recently discovered research notes on hybridization from 1896 suggest that, though he was unaware of Mendel's work, De Vries used the laws of dominance and recessiveness, segregation, and independent assortment to explain the 75:25 ratio in the second generation. He had discovered these laws by applying insights from probability theory to his research. In Die Mutationstheorie De Vries combined central concepts of intracellular pangenesis and his mutation theory by modifying the meanings of important terms and introducing new states of pangenes. In his attempts to describe Mendelian crossings in terms of pangenes and mutations, he became entangled in a number of contradictions. Some of his remarks suggest that he was aware that the Mendelian laws and his own theories of pangenes and mutations could not be made consistent.

Genes, Plant↗

Creatine kinase isoenzymes. Predictive value in the early diagnosis of acute myocardial infarction.

This is a prospective study of the value of the creatine kinase (CK) isoenzyme determination in the early diagnosis of acute myocardial infarction. The presence or absence of the MB isoenzyme was correlated with electrocardiogram and standard enzymes. The frequency of falsely positive and falsely negative results for CK-MB, electrocardiogram and each standard enzyme was calculated and, using the elements of conditional probability theory, their predictive values for the diagnosis of acute myocardial infarction were determined. Results indicate that CK-MB combines the best attributes of the electrocardiogram and standard enzyme tests: detectable MB isoenzyme activity by acrylamide slab electrophoresis has a predictive value for the diagnosis if acute myocardial infarction comparable to that of a positive electrocardiogram; absence of MB isoenzyme activity, in the 24 hour period following the onset of symptoms, excludes the diagnosis of acute myocardial infarction with a probability equivalent to that provided by normal standard enzyme results.

Clinical Enzyme Tests↗

A novel theoretical approach to the analysis of dendritic transients.

A novel theoretical framework for analyzing dendritic transients is introduced. This approach, called the method of moments, is an extension of Rall's cable theory for dendrites. It provides analytic investigation of voltage attenuation, signal delay, and synchronization problems in passive dendritic trees. In this method, the various moments of a transient signal are used to characterize the properties of the transient. The strength of the signal is measured by the time integral of the signal, its characteristic time is determined by its centroid ("center of gravity"), and the width of the signal is determined by a measure similar to the standard deviation in probability theory. Using these signal properties, the method of moments provides theorems, expressions, and efficient algorithms for analyzing the voltage response in arbitrary passive trees. The method yields new insights into spatiotemporal integration, coincidence detection mechanisms, and the properties of local interactions between synaptic inputs in dendritic trees. The method can also be used for matching dendritic neuron models to experimental data and for the analysis of synaptic inputs recorded experimentally.

Algorithms↗

The historical development of the concepts of diagnosis and prognosis and their relationship to probabilistic inference.

The concepts of diagnosis and prognosis are central to the intellectual basis of modern medical practice. These concepts are rooted in philosophical ideas which were introduced by the ancient Greeks. They were also influenced by the growth of scientific understanding following the Renaissance; and the more recent discipline or probability theory. The relative importance of these histological developments are discussed and suggestions are made about the possible nature of future developments.

Bayes Theorem↗

Automated radioautographic grain counting. Correction for grain overlap.

An algorithm is described for the calculation of radioautographic cell grain count from measurements of total cell nuclear area and total grain area. This algorithm provides a statistical correction for grain overlap that is based on the solution to the occupancy problem in probability theory. This method permits the use of automated grain counting over a wide range of grain counts per cell, and extends the useful dynamic range of radioautographic grain counting to well over 200 grains/cell.

Autoradiography↗

Implications of the precautionary principle for primary prevention and research.

The precautionary principle (PP) is an extension of the public health presage that prevention is better than cure. The PP has recently achieved new relevance in regard to serious but uncertain threats to human health and the environment and has now entered national and international legislation. However, frameworks for its unambiguous application in practice are yet to be designed. They will depend on legal and cultural circumstances and are likely to involve pluralities of perspectives and stakeholder participation. The rules for causal reasoning and dose dependence need to be addressed and may be conveniently expressed in accordance with probability theory. Although the PP will allow action before convincing evidence is secured, it is not science averse. However, it provides an occasion to review environmental health research strategies, methodologies, and research-reporting traditions. From this perspective, current research is afflicted by important biases and insufficient focus on major environmental health problems.

Decision Making↗