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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↗
PubMed2003

[Diagnostic reasoning in neurology. An analysis of the more frequent errors].

Diagnostic reasoning is a cognitive proccess that has various performance and results. There are several kinds of clinical reasoning, such as model or pattern recognizing, causal or physiopathologic reasoning, deterministic, exhaustive, and hypotetic-deductive ones. Each form of reasoning may be relevant in certain clinical context, and all of the forms are also complementary. The logical consequence of diagnostic reasoning, like every cognitive proccess, is a clinical error. It is necessary that the neurologist knows the principles of diagnostic reasoning and the more frequent errors and biases. These can be summarized as: errors associated with the proccess of taking history and clinical examination, mnesic and semantic components of clinical reasoning, failure of hipotetic- deductive reasoning, and inadequate use of probability theory in Medicine.

Diagnostic Errors↗
PubMed1993

Improved frequency resolution in multidimensional constant-time experiments by multidimensional Bayesian analysis.

The resolution of spectral frequencies in NMR data obtained from discrete Fourier transformation (DFT) along D constant-time dimensions can be improved significantly through extrapolation of the D-dimensional free induction decay (FID) by multidimensional Bayesian analysis. Starting from Bayesian probability theory for parameter estimation and model detection of one-dimensional time-domain data [Bretthorst, (1990) J. Magn. Reson., 88, 533-551; 552-570; 571-595], a theory for the D-dimensional case has been developed and implemented in an algorithm called BAMBAM (BAyesian Model Building Algorithm in Multidimensions). BAMBAM finds the most probable sinusoidal model to account for the systematic portion of any D-dimensional stationary FID. According to the parameters estimated by the algorithm, the FID is extrapolated in D dimensions prior to apodization and Fourier transformation. Multidimensional Bayesian analysis allows for the detection of signals not resolved by the DFT alone or even by sequential one-dimensional extrapolation from mirror-image linear prediction prior to the DFT. The procedure has been tested with a theoretical two-dimensional dataset and with four-dimensional HN(CO)CAHA (Kay et al. (1992) J. Magn. Reson., 98, 443-450) data from a small protein (8 kDa) where BAMBAM was applied to the 13C alpha and H alpha constant-time dimensions.

Algorithms↗
PubMedDate not supplied

[Stochastic approach in biochemical research].

The logic foundations of the probabilistic style for thinking and its methodological significance in the modern science are given. Complex, joint, ambiguous systems are the object of biochemical investigations at all organization levels and therefore biochemists often cannot obtain unambiguous results. It is shown that such systems are subjects to the study with the use of propositions of the probability theory which considers "random" events as a result of many-channel determination and is aimed to transform knowledge of these events into events predicted with certain probability. This provides a more profound analysis of a sum of facts and specificity of their theoretical interpretation. It is proved expedient to apply the probabilistic approach to study intramolecular and intermolecular interaction of elements, to characterize enzymes and membranes, to investigate objects comparatively and chemotaxanomically. It is stated that comprehension of "random" as a manifestation of a part of a sum of the possible or one of its variants stimulates the theoretical generalization of facts, elucidation of regularities of functioning, adaptation, development and diversity of every living thing.

Biochemical Phenomena↗
PubMed1990

The conjunction fallacy?

Tversky and Kahneman (1983) showed that when subjects are asked to rate the likelihood of several alternatives, including single and joint events, they often make a "conjunction fallacy." That is, they rate the conjunction of two events as being more likely than one of the constituent events. This, they claim, is a fallacy, since the conjunction of two events can never be more probable than either of the component events. In addition, they found that prior training in probability theory does not decrease the likelihood of making this fallacy. We argue that in some contexts, an alternative that contains the conjunction of two events can be more probable than an alternative that contains only one of the conjunction's constituent events. We carried out four experiments in which we manipulated this context. The frequency of making a conjunction fallacy was affected by the manipulation of context. Furthermore, when the context was clearly specified, prior training in statistics influenced the ratings.

Decision Making↗
PubMed1999

Similarity between hypotheses and evidence.

We explore two novel consequences of similarity-based likelihood judgment. In Section I, we distinguish between the evidence on which judgments are based and the hypotheses that serve as the objects of judgment. The location of a feature, whether in the evidence or the hypotheses, influences the perceived similarity between evidence and hypotheses and consequently yields judgments that are inconsistent with the requirements of probability theory. In Section II, we examine judgment of disjunctive hypotheses. For certain types of disjunctions, the assessment of similarity produces consistent nonmonotonicities: the support of a disjunction is smaller than that of one of its components. Finally, we discuss the implications of our findings in terms of support theory and the principle of context independence.

Female↗
PubMed1989

Positive-hole correction of multiple-jet impactors for collecting viable microorganisms.

Multiple-jet impactors, typically with 200 or 400 holes, are used widely for collecting aerosols of living bacteria and fungi. In this type of impactor, the air jets impinge directly onto nutrient agar in a petri dish which is incubated after sampling until collected cells multiply into colonies. The observed number of colonies can be adjusted for the probability that more than one viable particle was collected through a sampling hole and merged with other microorganisms at an impaction site to produce a single colony. A "positive-hole" correction table has been published for a 400-hole impactor, but none has been produced previously for the 200-hole impactor. The expected number of sampled particles required to fill each of 1 through 200 and 1 through 400 impaction sites and the standard deviations of these values were calculated from probability theory. The results were compared with a Monte Carlo simulation. By using correction tables (which include the standard deviation of an expected value) an investigator can report the most probable viable particle count and a 95% confidence interval (mean +/- 2 standard deviations). The range of collected particles that could have produced an observed number of colonies increases as the number of collected particles increases, and investigators should acknowledge the uncertainty associated with adjusted counts. It is advisable to use an impactor with the greatest practical number of sampling holes because this decreases the likelihood that multiple particles are deposited at the impaction sites.(ABSTRACT TRUNCATED AT 250 WORDS)

Air Microbiology↗
PubMed2000

An in-field screen for early detection and monitoring of insect resistance to Bacillus thuringiensis in transgenic crops.

We present a field-based approach to detect and monitor insects with resistance to insecticidal toxins produced by transgenic plants. Our objective is to estimate the phenotypic frequency of resistance in a population by relating the densities of insects on genetically transformed plants to densities on nontransformed plants. We focus on European corn borer, Ostrinia nubilalis (Hübner), in sweet corn, Zea mays L., expressing Cry1Ab from Bacillus thuringiensis subsp. kurstaki Berliner to illustrate principles underlying the method. The probability of detecting one or more rare, resistant larvae depends on sample size, the density of larvae on nontransformed plants, and an assumed frequency of resistant phenotypes in a given population. Probability of detection increases with increases in sample size, background density, or the frequency of resistant individuals. Following binomial probability theory, if a frequency of 10(-4) is expected, 10(3)-10(4) samples must be collected from a B. thuringiensis (Bt) crop to have at least a 95% probability of locating one or more resistant larvae. In-field screens using transgenic crops have several advantages over traditional laboratory-based methods, including exposure to a large number of feral insects, discrimination of resistant individuals based on Bt dosages expressed in the field, incorporation of natural and Bt-induced mortality factors, simultaneous monitoring for more than one insect species, and ease of use. The approach is amenable to field survey crews working in research, extension, and within the seed corn industry. Estimates of the phenotypic frequency of resistance from the in-field screen can be useful for estimating initial frequency of resistant alleles. Bayesian statistical methods are outlined to estimate phenotype frequencies, allele frequencies, and associated confidence intervals from field data. Results of the approach are discussed relative to existing complementary methods currently available for O. nubilalis and corn earworm, Helicoverpa zea (Boddie).

Animals↗
PubMed2000

Probability judgment in three-category classification learning.

People give subadditive probability judgments--in violation of probability theory--when asked to assess each in a set of 3 or more mutually exclusive hypotheses, as indicated by their sum exceeding 1. Three potential evidential influences on subadditivity--cue conflict, cue frequency, and cue redundancy--are distinguished and tested in 5 experiments using a classification-learning task. Results indicate that (a) judgments of probability and of frequency are systematically subadditive even when the judgments are based on cues learned within the experimental context, (b) cue conflict has a reliable influence on the degree of subadditivity, and (c) judgments in this context are well described by a linear-discounting model within the framework of support theory.

Concept Formation↗
PubMed1994

A reappraisal of the controversy of Dax and Broca.

Paul Broca is unanimously recognized as the founder of neuropsychology. Helis development of the scientific method to map mental functions onto brain topographpy has been enormously influential. Nevertheless, Dax's paper on the left hemisphere dominance for speech was written and published before Broca explicitely proposed the same theory. Probably, Broca was aware of the paper prior to 1865, but he never acknowledged Dax's original theoretical contribution. On the contrary, he always claimed to be the first to espouse the theory of left hemisphere dominance for language and never quoted Marc Dax (Broca, 1877 p 536), 'I do not like dealing with the questions of priority concerning myself. That is the reason why I did not mention the name of Dax in my paper'. In our opinion, the weight of evidence reported here suggests that the theory of the left hemisphere dominance for speech must be attributed equally to Dax and Broca, and henceforth should be called 'the theory of Dax-Broca'.

France↗
PubMed2001

A brief history of numbers and statistics with cytometric applications.

A brief history of numbers and statistics traces the development of numbers from prehistory to completion of our current system of numeration with the introduction of the decimal fraction by Viete, Stevin, Burgi, and Galileo at the turn of the 16th century. This was followed by the development of what we now know as probability theory by Pascal, Fermat, and Huygens in the mid-17th century which arose in connection with questions in gambling with dice and can be regarded as the origin of statistics. The three main probability distributions on which statistics depend were introduced and/or formalized between the mid-17th and early 19th centuries: the binomial distribution by Pascal; the normal distribution by de Moivre, Gauss, and Laplace, and the Poisson distribution by Poisson. The formal discipline of statistics commenced with the works of Pearson, Yule, and Gosset at the turn of the 19th century when the first statistical tests were introduced. Elementary descriptions of the statistical tests most likely to be used in conjunction with cytometric data are given and it is shown how these can be applied to the analysis of difficult immunofluorescence distributions when there is overlap between the labeled and unlabeled cell populations.

Cell Count↗
PubMed1991

On integrating the techniques of direct methods with anomalous dispersion. II. Statistical properties of the two-phase structure invariants.

Results of a statistical study of probabilistic estimates of two-phase structure invariants (TPSI) for Friedel pairs in the case of single-wavelength anomalous scattering are reported. Numerical analysis of the TPSI sign, magnitude and error distributions shows that the concise formula for TPSI by probability theory [Hauptman (1982). Acta Cryst. A38, 632-641; Giacovazzo (1983). Acta Cryst. A39, 585-592] has desirable statistical properties. Computational results for the known structures of cocaine methiodide (N-methylcocaine iodide) and of cytochrome c550 and its PtCl2-4 derivative show that when [E[ values are large most of the signs of the TPSI are correctly determined - for [E[ greater than 1.0, 90% or more of the TPSI signs are positive as predicted - and the errors in the estimated TPSI magnitudes do not exceed approximately 10% for [E[ greater than 1.0 in the small-molecule case or approximately 50% for [E[ greater than 1.5 in the macromolecular case. These results suggest that the theory will be useful for estimating the TPSI for unknown structures.

Models, Chemical↗
PubMed1980

Multi-test screening and the chances of being normal.

Screening programs involve responsibility for appropriate action on abnormal test results. When multiple-test screening batteries are used, a simple probability formula is commonly used to predict the proportion of healthy individuals who will have one or more abnormal test results occur by chance alone. This formula is valid only when the assumptions upon which it rests are met in the population being tested. In many situations the assumptions are not met and the formula overestimates the occurrence of abnormal results in healthy populations. Data for three screening programs involving blood chemistry test batteries on 769 patients document this overestimate and its magnitude. Clinical judgment, not misapplied probability theory, should guide the physician's strategy in evaluating abnormal results of screening tests.

Blood Chemical Analysis↗
PubMedDate not supplied

Adverse events following immunization: assessing probability of causation.

The Monitoring System for Adverse Events Following Immunization of the Centers for Disease Control collects data on events temporally related to immunization. Occasionally, reports are received of neurologic disturbances temporally related to receipt of vaccine. Most of these disturbances are events that regularly occur in the absence of immunization. It is then difficult to determine whether the relationship between the immunization and illness is causal or coincidental. We developed a method to assess causation of serious neurologic events by probability theory. By combining epidemiologic information on disease incidence with specific elements of the patient history, an estimate of the odds of vaccine causation can be derived, based on rational assumptions rather than observer bias. The result is not a diagnosis but an estimate of probability.

Brain Diseases↗
PubMed2004

Need probability effects in animal short-term memory.

Five pigeons performed in a delayed matching-to-sample (DMTS) procedure with five delay durations (0.5, 2.5, 5, 10 and 20 s) mixed within sessions. Contrary to the predictions of need probability theory, discriminability decreased when fewer short than long delays were included in each session. To test whether the decrease in discriminability was due to a decrease in obtained reinforcement at short delays, the number of trials at each delay was held constant and reinforcer probability was increased with increasing delay. This manipulation produced a similar decrease in discriminability as when the frequency of delays was manipulated. It was concluded that the effect of delay frequency on the forgetting function is mediated by the effect of the reinforcer distribution, which influences discriminability by weakening stimulus control.

Animals↗
PubMed1997

Communication about risk--dilemmas for general practitioners. The Department of General Practice Working Group, University of Wales College of Medicine.

Measures of risk frequently contribute to our understanding, prevention, or treatment of disease, but it is important that general practitioners (GPs) explain clinical risks effectively to patients to ensure they are not misunderstood, as risk information can assist in decision-making processes and encourage behavioural change. However, the interpretation of risks by patients and doctors varies. It is argued that problems arise because communication about risk is usually framed in terms of the language of chance or probability. In this paper, we describe how probability theory developed, and suggest that attempts to communicate empirical risk processes in probabilistic language are bound to produce dilemmas. We explore how the theory relates to clinical practice and identify key issues that doctors must address in discussing risk with individual patients.

Communication↗
PubMed1995

Preliminary investigation of a Bayesian network for mammographic diagnosis of breast cancer.

Bayesian networks use the techniques of probability theory to reason under conditions of uncertainty. We investigated the use of Bayesian networks for radiological decision support. A Bayesian network for the interpretation of mammograms (MammoNet) was developed based on five patient-history features, two physical findings, and 15 mammographic features extracted by experienced radiologists. Conditional-probability data, such as sensitivity and specificity, were derived from peer-reviewed journal articles and from expert opinion. In testing with a set of 77 cases from a mammography atlas and a clinical teaching file, MammoNet performed well in distinguishing between benign and malignant lesions, and yielded a value of 0.881 (+/- 0.045) for the area under the receiver operating characteristic curve. We conclude that Bayesian networks provide a potentially useful tool for mammographic decision support.

Bayes Theorem↗