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PubMedDate not supplied

Converting a rule-based expert system into a belief network.

The theory of belief networks offers a relatively new approach for dealing with uncertain information in knowledge-based (expert) systems. In contrast with the heuristic techniques for reasoning with uncertainty employed in many rule-based expert systems, the theory of belief networks is mathematically sound, based on techniques from probability theory. It therefore seems attractive to convert existing rule-based expert systems into belief networks. In this article we discuss the design of a belief network reformulation of the diagnostic rule-based expert system HEPAR. For the purpose of this experiment we have studied several typical pieces of medical knowledge represented in the HEPAR system. It turned out that, due to the differences in the type of knowledge represented and in the formalism used to represent uncertainty, much of the medical knowledge required for building the belief network concerned could not be extracted from HEPAR. As a consequence, significant additional knowledge acquisition was required. However, the objects and attributes defined in the HEPAR system, as well as the conditions in production rules mentioning these objects and attributes, were useful for guiding the selection of the statistical variables for building the belief network. The mapping of objects and attributes in HEPAR to statistical variables is discussed in detail.

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↗
PubMedDate not supplied

[Statistical analysis of genome].

The chemical structure of DNA is characterized by sequences of four basic nitrogens occurring in one of two nucleic acid chains and in a complementary fashion in the other. Markov chain is the aspect of probability theory that analyzes discrete states in which transition is a fixed probability not affected by the history of the system. It is shown that DNA is represented in the form of regular Markov chain. Ergodicity property and law of large numbers follow from the statistical analysis of stationary transition probabilities.

Algorithms↗
PubMed1995

Decision analysis: theory and application to medicine.

The formal methodology of clinical decision analysis has its origins in probability theory, statistical inference, game theory, and economics. Its application to the arena of problems in medicine and public policy should have a vast impact on the way medicine is practiced in the twenty-first century and beyond. The clinical decision analyses published in journals are based on particular assumptions; if these assumptions do not hold true, the results must be regarded as suspect. However, if the assumptions do hold true or if they reasonably approximate reality, the analyses and results of decision analyses must be appreciated and understood. Their interpretation may yield improved health for patients, monetary savings, or an explicit understanding of the uncertainties that exist and the tradeoffs that must be considered in decision making in primary care.

Animals↗
PubMed2006

A mathematical framework for probabilistic choice based on information theory and psychophysics.

Risky decision-making (e.g. reward dependency) has been associated with substance abuse, psychopathy and pathological gambling; conversely, marked sensitivity to risk and uncertainty have been observed in anxiety disorder patients. In economic decision theory, probability and uncertainty have been dissociated. Frank Knight defined uncertainty as loss of information on the probability distribution of outcomes for choices (i.e., unpredictability), which is referred to as Knightian uncertainty (also as ambiguity). However, even when the probability distribution of outcomes is known, there are different degrees of predictability. In information theory, this type of degrees of uncertainty/unpredictability has been parametrized by introducing Shannon entropy. In the present paper, we show: (i) a mathematical framework combining Shannon entropy in information theory and Weber's law in psychophysics is capable of parametrizing subject's level of both aversion to probabilistic uncertainty (exaggerated in anxiety disorder patients) and reward dependency (enhanced in drug addicts and pathological gamblers), and (ii) this framework has an analogue in thermodynamics, therefore this can readily be utilized in studies in the nascent fields of neuroeconomics and econophysics as well. Future study directions for elucidating maladaptive personality characteristics in neuropsychiatric patients by using the present framework are discussed.

Anxiety Disorders↗
PubMed2001

[Interpretation of efficacy measures derived from 2 X 2 tables for the evaluation of diagnostic tests and treatment].

BACKGROUND: To describe the efficacy of diagnostic tests and the effect of treatment a number of measures are used, which can be derived from 2 x 2 tables of frequencies. For the comprehension of these measures the knowledge of their properties in the framework of probability theory is necessary. MATERIAL AND METHOD: After an introduction of basic terms such as probability, odds, joint and conditional probability the usual measures sensitivity, specificity, likelihood ratio, positive and negative predictive value, relative risk, odds ratio, relative risk reduction, absolute risk reduction, and number needed to treat are presented and explained. In particular, the importance of disease prevalence and baseline risk for the interpretation of these measures is pointed out by means of examples. CONCLUSION: If the disease prevalence or the baseline risk is not appropriately taken into account, the efficacy of a diagnostic test and the effect of a treatment are overestimated, especially in screening and prevention trials.

Clinical Trials as Topic↗
PubMed2000

Brain mechanisms of selective learning: event-related potentials provide evidence for error-driven learning in humans.

Selective learning has been observed in Pavlovian conditioning in animals and in judgements of event contingencies in humans. This analogy led to the suggestion that the formation of associations underlies both types of learning. An alternative theory proposes that both tasks involve the computation of event contingencies as prescribed by probability theory. Error-driven models of learning incorporate trial-by-trial error-correction mechanisms during training whereas probabilistic models view learning merely as the storage of frequency information for later use during judgement of event contingencies. Competitive interaction between cues was observed in a contingency judgement task. Event-related brain potentials (ERPs) provided evidence for brain events related to the discrepancy between actual and expected outcomes during training thus supporting error-driven accounts of selective learning.

Adult↗
PubMed1985

Introduction to hypotheses testing.

The statistical concepts discussed in this review are intended as a basis to understanding concepts that will be presented in PHYSICAL THERAPY during the coming months. The basis for hypotheses testing is probability theory. When a null hypothesis is either accepted or rejected, researchers are stating the probability that a specific treatment will be more or equally effective in a specific population under stated conditions. This ability to predict, based on appropriate application and interpretation of statistical tests, ultimately improves patient care.

Humans↗
PubMed1993

Transport injuries in small coal mines: an exploratory analysis.

Mine Safety and Health Administration (MSHA) surveillance data were analyzed to elucidate mine characteristics or injury characteristics that distinguished mines with high rates of transport-related injuries from mines with lower transport injury rates. The results showed that most high-rate mines are small, high-rate mines have a disproportionate number of injuries involving young and less experienced workers, and injuries in high-rate mines are proportionally more severe. Further analyses of the MSHA injury data showed that smaller mines have a greater share of fatal and permanently disabling injuries, whereas larger mines have a greater share of injuries involving no lost time. Based on these results, we explored two explanations for the small mine injury risk: (1) a suggestion that differences in injury reporting between large and small mines may contribute to an apparent small mine injury risk, and (2) identification of factors contributing to a true difference in transport-related injury risk between small and large mines. Whereas it was true that most high injury rate mines were small, most small mines were actually zero-rate, having reported employment but no injuries to MSHA. An analysis employing binomial probability theory showed that a substantial proportion of small mines reported zero injuries when it was statistically probable that injuries would have occurred. This indicated that small mines may underreport injuries relative to larger mines. The possibility that reporting bias affected the associations found in this study was explored by eliminating the least severe injuries from the data set and evaluating changes in associations. This "adjustment" for reporting bias did not change previously observed relationships. Finally, MSHA injury data were analyzed in concert with mining population data collected by the Bureau of Mines. With such denominator information, the results indicated a disproportionately high risk of injury among workers in their first year at a mine and indicated that higher injury risk in small mines might be explained by the fact that workers at small mines have substantially less experience than workers at large mines. An effect of age was not found in these analyses. These results suggest the potential importance of targeted training programs for newly hired miners. Results also point to the need to explore specific factors contributing to the small mine injury risk, and to the necessity for complete and accurate reporting of injury data.

Accidents, Occupational↗
PubMed2002

On the extinction of radiation by a homogeneous but spatially correlated random medium: comment.

Some extinction laws for radiation transmitted through inhomogeneous random media were discussed by Kostinski [J. Opt. Soc. Am. A 18, 1929 (2001)] by means of a complicated use of concepts of statistical theory of fluids. We show that these extinction laws are readily obtained in terms of classical probability theory. The validity of exponential extinction laws for large observation distances (as compared with the size of inhomogeneities of a medium) is proven and emphasized. It is shown that Kostinski's results turn out to be applicable to small observation distances only, for which the concept of extinction law is hardly applicable.

Comment↗
PubMed2001

A possible loophole in the theorem of Bell.

The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results, these inequalities appear to prove that local hidden parameters cannot exist. This contradiction suggests to many that only instantaneous action at a distance can explain the Einstein, Podolsky, and Rosen type of experiments. We show that, in addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions that contribute to his being able to obtain the desired contradiction. For instance, Bell assumes that the hidden parameters do not depend on time and are governed by a single probability measure independent of the analyzer settings. We argue that the exclusion of time has neither a physical nor a mathematical basis but is based on Bell's translation of the concept of Einstein locality into the language of probability theory. Our additional set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does not permit Bell-type proofs to go forward.

Journal Article↗
PubMed2005

Bayesian inference applied to macromolecular structure determination.

The determination of macromolecular structures from experimental data is an ill-posed inverse problem. Nevertheless, conventional techniques to structure determination attempt an inversion of the data by minimization of a target function. This approach leads to problems if the data are sparse, noisy, heterogeneous, or difficult to describe theoretically. We propose here to view biomolecular structure determination as an inference rather than an inversion problem. Probability theory then offers a consistent formalism to solve any structure determination problem: We use Bayes' theorem to derive a probability distribution for the atomic coordinates and all additional unknowns. This distribution represents the complete information contained in the data and can be analyzed numerically by Markov chain Monte Carlo sampling techniques. We apply our method to data obtained from a nuclear magnetic resonance experiment and discuss the estimation of theory parameters.

Bayes Theorem↗
PubMed2006

Bayesian approach for quantifying the uncertainty of neutron doses derived from spectrometric measurements.

Bayesian methods provide a unified framework for combining information in the presence of uncertainty. All uncertainties that enter into the description of a measurement are modelled using probability distributions, and these are handled according to the rules of probability theory, ensuring that the approach is free of inconsistencies. The final result of the analysis is the full probability distribution for the parameter of interest, and from this distribution an appropriate uncertainty interval can be obtained. Some of the advantages of a Bayesian analysis include a straightforward approach to the problem of dealing with nuisance parameters, the ability to incorporate prior information in a natural way and the flexibility that is necessary for a realistic modelling of the measurement process. As an example, the problem of deriving neutron dose estimates and their uncertainties based on measurements carried out using a Bonner sphere spectrometer is considered.

Bayes Theorem↗
PubMed1984

[The step toward a specific diagnosis. Evaluation of the value of diagnostic methods in the individual case with special attention to probability].

The preliminary diagnosis based on the patient's history and the results of a physical examination, is considered to be the most probable one. In general, however, differential diagnoses with a smaller degree of probability must also be taken into account. This article shows how--making use of simple probability theory--an assessment can be made as to whether an available diagnostic instrument is capable of increasing the probability of a post-test diagnosis vis-a-vis the pre-test probability level. The terms sensitivity and specificity are explained with the aid of clinical examples, and the possibility of increasing the probability of the diagnosis by iteration is discussed.

Bayes Theorem↗
PubMed1999

Social interpersonal dimensions of the psychoses.

This paper looks at the patterns for the creation and social management of insanity and the involvements of those concerned. It describes an interaction model with people in a social reality of everyday living, built up of and defined by 'subjective' definitions of a situation. The psychiatric profession, involved in their conventional medical one-to-one confidential consultations with their patients, fails to be informed about the societal dimensions with two, three or more members as first described by Simmel (1902) (1). The differences are traditional, 'Two is company' and 'Three is a crowd'. If one of the possible two-person relationships in a family develops some emotional change to define itself as 'Two is company', this may alter the emotional balance in the whole family and may lead to 'split minds' (schizo/phrenia) and involving relationships with and between other family members. The arrival of the first baby changes two to three and creates 'Our Family'. 'Two is company: but it is not our family.' 'Three is a crowd' but now, with three possible pairs, who is the odd one to be left out, or to push in or be pushed out? This is proposed as the interpersonal relationships substrate of the manic-(push in) or depressive (pushed out) psychoses in an older family generation. Both propositions are to be developed using probability theory to define the number of members, the corresponding numbers of their possible kinetic interpersonal relationships, their social dynamism probabilities, and potential outcomes involving modern non-linear mathematics. These patients are described as 'not themselves' or 'beside themselves'. Those who are themselves but described as neurotic or psychopathic will also be mentioned.

Adult↗
PubMed1983

How many blows really make an FEV1, FVC, or PEFR?

We have collected peak expiratory flow rates, one-second forced expiratory volumes, and forced vital capacities in sets of 10 or 20 values at one-minute intervals from 30 normal, 49 asthmatic, and 26 bronchitic subjects. Analysis shows that the derivatives are compatible with a normal distribution of the values in the sets, so that the true value is best represented by the arithmetic mean of all valid attempts. One-third of all subjects showed skewness in one or more indices but these were equally divided between positive and negative directions. There is no sign of the dominant negative skewness that would result if the true value was indeed a maximum, which could be approached or equalled but never exceeded. There is no sign that repetition worsens performance. Seventy-two subjects showed no regression in any index and those of the remainder who deteriorated were balanced by equal numbers in all categories who improved. There is a significant tendency for both the highest and the lowest values to occur in the earlier part of any series. Probability theory suggests that this is a statistical phenomenon. The best estimate of the true value of these indices is probably the mean of as many observations as can be conveniently obtained and the data can be treated statistically as if they were a sample from a normally distributed population.

Adolescent↗
PubMed1999

Statistical limitations in functional neuroimaging. II. Signal detection and statistical inference.

The field of functional neuroimaging (FNI) methodology has developed into a mature but evolving area of knowledge and its applications have been extensive. A general problem in the analysis of FNI data is finding a signal embedded in noise. This is sometimes called signal detection. Signal detection theory focuses in general on issues relating to the optimization of conditions for separating the signal from noise. When methods from probability theory and mathematical statistics are directly applied in this procedure it is also called statistical inference. In this paper we briefly discuss some aspects of signal detection theory relevant to FNI and, in addition, some common approaches to statistical inference used in FNI. Low-pass filtering in relation to functional-anatomical variability and some effects of filtering on signal detection of interest to FNI are discussed. Also, some general aspects of hypothesis testing and statistical inference are discussed. This includes the need for characterizing the signal in data when the null hypothesis is rejected, the problem of multiple comparisons that is central to FNI data analysis, omnibus tests and some issues related to statistical power in the context of FNI. In turn, random field, scale space, non-parametric and Monte Carlo approaches are reviewed, representing the most common approaches to statistical inference used in FNI. Complementary to these issues an overview and discussion of non-inferential descriptive methods, common statistical models and the problem of model selection is given in a companion paper. In general, model selection is an important prelude to subsequent statistical inference. The emphasis in both papers is on the assumptions and inherent limitations of the methods presented. Most of the methods described here generally serve their purposes well when the inherent assumptions and limitations are taken into account. Significant differences in results between different methods are most apparent in extreme parameter ranges, for example at low effective degrees of freedom or at small spatial autocorrelation. In such situations or in situations when assumptions and approximations are seriously violated it is of central importance to choose the most suitable method in order to obtain valid results.

Biometry↗
PubMed2000

Computer-assisted decision analysis in orthopedics: resurfacing the patella in total knee arthroplasty as an example.

The purpose of the present study was to illustrate the use of computer-assisted decision analysis in making decisions in the field of orthopaedic surgery, using the choice between resurfacing and not resurfacing the patella in total knee arthroplasty as an example. We used a decision analysis technique based on probability theory and on Bayesian logic, with the help of an especially developed computer software. The process involves building a decision tree, searching for probabilities and utilities in the literature, folding back the tree to compute the baseline result, and running sensitivity analyses. Our literature search provided 26 useful articles, only 3 of which were randomized controlled trials. In the baseline analysis, both options were rated similarly, with resurfacing the patella faring slightly better. Sensitivity analyses revealed that not resurfacing becomes the procedure of choice if the probability of postoperative anterior knee pain with an unresurfaced patella falls below 14%, or if the probability of having pain with a resurfaced patella rises above 8% or if the utility of patellar implant failure falls below 80% of the utility of a perfect health state. Computer-assisted decision analysis is a promising, evidence-based tool to assist clinical decision making in orthopaedic surgery. However, its validity is limited by the poor quality of data found in the orthopaedic literature, especially the scarcity of randomized controlled trials.

Arthroplasty, Replacement, Knee↗