Signal detection theory and probability matching apply to vigilance.
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Competing failure risk analysis using evidence theory.
Safety systems are important components of high-consequence systems that are intended to prevent the unintended operation of the system and thus the potentially significant negative consequences that could result from such an operation. This presentation investigates and illustrates formal procedures for assessing the uncertainty in the probability that a safety system will fail to operate as intended in an accident environment. Probability theory and evidence theory are introduced as possible mathematical structures for the representation of the epistemic uncertainty associated with the performance of safety systems, and a representation of this type is illustrated with a hypothetical safety system involving one weak link and one strong link that is exposed to a high temperature fire environment. Topics considered include (1) the nature of diffuse uncertainty information involving a system and its environment, (2) the conversion of diffuse uncertainty information into the mathematical structures associated with probability theory and evidence theory, and (3) the propagation of these uncertainty structures through a model for a safety system to obtain representations in the context of probability theory and evidence theory of the uncertainty in the probability that the safety system will fail to operate as intended. The results suggest that evidence theory provides a potentially valuable representational tool for the display of the implications of significant epistemic uncertainty in inputs to complex analyses.
Journal Article↗
Medical concepts related to individual risk are better explained with "plausibility" rather than "probability".
BACKGROUND: The concept of risk has pervaded medical literature in the last decades and has become a familiar topic, and the concept of probability, linked to binary logic approach, is commonly applied in epidemiology and clinical medicine. The application of probability theory to groups of individuals is quite straightforward but can pose communication challenges at individual level. Few articles by the way have tried to focus the concept of "risk" at the individual subject level rather than at population level. DISCUSSION: The author has reviewed the conceptual framework which has led to the use of probability theory in the medical field in a time when the principal causes of death were represented by acute disease often of infective origin. In the present scenario, in which chronic degenerative disease dominate and there are smooth transitions between health and disease the use of fuzzy logic rather than binary logic would be more appropriate. The use of fuzzy logic in which more than two possible truth-value assignments are allowed overcomes the trap of probability theory when dealing with uncertain outcomes, thereby making the meaning of a certain prognostic statement easier to understand by the patient. SUMMARY: At individual subject level the recourse to the term plausibility, related to fuzzy logic, would help the physician to communicate to the patient more efficiently in comparison with the term probability, related to binary logic. This would represent an evident advantage for the transfer of medical evidences to individual subjects.
Chronic Disease↗
Constructing reproductive histories by linking vital records.
Certificates of 1,449,287 live births and fetal deaths filed in Georgia from 1980 through 1992 were linked to create chronologies that, excluding induced abortions and ectopic pregnancies, constituted the reproductive experience of individual women. The authors initially used a deterministic method (whereby linking rules were not based on probability theory) to link as many records as possible, knowing that some of the linkages would be incorrect. They subsequently used a probabilistic method (whereby evaluation of linkages was developed from probability theory) to evaluate each linkage, and they broke those that were judged to be incorrect. Of the 1.4 million records, 38% did not link to another record. From the remaining records, 369,686 chains of two or more events were constructed. The longest chain included 12 events. Of the chains, 69% included two events; 22% included three events. Longer chains tended to have lower scores for probable validity. The probability-based evaluation of chains affected 3.0% of the records that had been in chains at the end of the deterministic linkage. A greater percentage of records in longer chains were affected by the evaluation. Unfortunately, the small subset of records that were the most difficult to link tended to overrepresent groups with the greatest risk of adverse pregnancy outcomes. Researchers contemplating a similar linkage can anticipate that, for the majority of records, linkage can be accomplished with a relatively straightforward, deterministic approach.
Adolescent↗
Bayesian contour integration.
The process by which the human visual system parses an image into contours, surfaces, and objects--perceptual grouping--has proven difficult to capture in a rigorous and general theory. A natural candidate for such a theory is Bayesian probability theory, which provides optimal interpretations of data under conditions of uncertainty. But the fit of Bayesian theory to human grouping judgments has never been tested, in part because methods for expressing grouping hypotheses probabilistically have not been available. This paper presents such methods for the case of contour integration--that is, the aggregation of a sequence of visual items into a "virtual curve." Two experiments are reported in which human subjects were asked to group ambiguous configurations of dots (in Experiment 1, a sequence of five dots could be judged to contain a "corner" or not; in Experiment 2, an arrangement of six dots could be judged to fall into two disjoint contours or one smooth contour). The Bayesian theory accounts extremely well for subjects' judgments, explaining more than 75% of the variance in both tasks. The theory thus provides a far more quantitatively precise account of human contour integration than has been previously possible, allowing a very precise calculation of the subjective goodness of a virtual chain of dots. Because Bayesian theory is inferentially optimal, this finding suggests a "rational justification," and hence possibly an evolutionary rationale, for some of the rules of perceptual grouping.
Adult↗
A pattern recognition account of decision making.
In the domain of pattern recognition, experiments have shown that perceivers integrate multiple sources of information in an optimal manner. In contrast, other research has been interpreted to mean that decision making is nonoptimal. As an example, Tversky and Kahneman (1983) have shown that subjects commit a conjunction fallacy because they judge it more likely that a fictitious person named Linda is a bank teller and a feminist than just a bank teller. This judgment supposedly violates probability theory, because the probability of two events can never be greater than the probability of either event alone. The present research tests the hypothesis that subjects interpret this judgment task as a pattern recognition task. If this hypothesis is correct, subjects' judgments should be described accurately by the fuzzy logical model of perception (FLMP)--a successful model of pattern recognition. In the first experiment, the Linda task was extended to an expanded factorial design with five vocations and five avocations. The probability ratings were described well by the FLMP and described poorly by a simple probability model. The second experiment included (1) two fictitious people, Linda and Joan, as response alternatives and (2) both ratings and categorization judgments. Although the ratings were accurately described by both the FLMP and an averaging of the sources of information, the categorization judgments were described better by the FLMP. These results reveal important similarities in recognizing patterns and in decision making. Given that the FLMP is an optimal method for combining multiple sources of information, the probability judgments appear to be optimal in the same manner as pattern-recognition judgments.
Adult↗
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↗
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↗
Spatial distribution of twitch and tonic fibres in a snake muscle one myofibre thick.
The spatial distribution of twitch and tonic fibres in a snake muscle one myofibre thick (ventral costocutaneous) has been investigated. It was found that small groups of like fibres were favoured at the expense of larger groups when compared with sequences generated by a computer in which fibres were distributed randomly. The number of times that like fibres occurred next to one another was used as another measure of their spatial distribution. The number of adjacencies of like fibres was less than the expected number of adjacencies determined both by random sequences and by probability theory. The expected number of adjacencies determined by means of random sequences and a priori probability theory were almost identical. This dispersion of like fibres may reflect processes that occur during muscle development and may have functional implications.
Animals↗
The time-rescaling theorem and its application to neural spike train data analysis.
Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments. We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.
Action Potentials↗
Measurement of uncertainty and discrimination limit in purity tests of drug quality.
Because of baseline fluctuation in an instrumental analysis, a purity test can overlook an illegitimate drug which contains an undesirable substance in more amount than a prescribed reference value. This paper proposes a probability theory to predict the lowest (average) signal, E[Y2], of the substance which can be discriminated from the (average) reference signal, E[Y1], with a high probability (here, 95%) in liquid chromatography (LC). The difference between the lowest signal and reference signal, E[Y2]-E[Y1] (> 0), is referred to here as a discrimination limit. The repetition of experiments to estimate the standard deviation of measurements is unnecessary for the probability theory, but a mathematical treatment of instrumental baselines (Fourier transform, etc.) is essential. The Monte Carlo simulation is carried out in which the reference signal and predicted signal for the discrimination limit are overlaid randomly 5000 times on real LC baselines. The result is satisfactory: the observed probability for the right answer is 94.3 or 94.8%; the theoretical one is 95%. The normality of the measurement distribution is examined for LC and capillary electrophoresis to verify the fundamental assumption of the proposed theory.
Chromatography, Liquid↗
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↗
Evaluation of the reaction kinetics of CORTOSS, a thermoset cortical bone void filler.
The primary objective of this research is to evaluate the reaction kinetics of CORTOSS(TM), a thermoset, Bis-GMA (2,2-bis[4-(2-hydroxymethacryloxypropyl) phenyl]propane) composite system as a function of time, material storage temperature and the temperature of the surrounding environment (site temperature). This study utilizes probability theory to predict the percentage of bifunctional monomers with 0,1 and 2 functional groups that have been reacted. This is a strong indicator of the potential for leaching unreacted components. A differential scanning calorimeter (DSC) was used to measure the isothermal enthalpy at varying site temperatures. After isothermal monitoring, the samples were dynamically heated from the respective isothermal temperature to 175 degrees C at 15 degrees C/min to measure the residual enthalpy from the unreacted functional groups. The experimental results indicate that the degree of conversion for this bifunctional system ranged from 76% to 86%. Applying probability theory it has been determined that approximately 95% of the bifunctional monomers are present with at least one double bond reacted and up to 5% of monomers remain unreacted. This is consistent with theoretical values postulated for various diffusion controlled thermoset systems (Macromolecules 32 (1999) 3913). Overall, curing under physiological conditions yielded a faster reaction rate and a significantly higher degree of conversion as compared to the lower site temperature conditions.
Benzeneacetamides↗
Misrepresenting random sampling? A systematic review of research papers in the Journal of Advanced Nursing.
AIM: This paper discusses the theoretical limitations of the use of random sampling and probability theory in the production of a significance level (or P-value) in nursing research. Potential alternatives, in the form of randomization tests, are proposed. BACKGROUND: Research papers in nursing, medicine and psychology frequently misrepresent their statistical findings, as the P-values reported assume random sampling. In this systematic review of studies published between January 1995 and June 2002 in the Journal of Advanced Nursing, 89 (68%) studies broke this assumption because they used convenience samples or entire populations. As a result, some of the findings may be questionable. DISCUSSION: The key ideas of random sampling and probability theory for statistical testing (for generating a P-value) are outlined. The result of a systematic review of research papers published in the Journal of Advanced Nursing is then presented, showing how frequently random sampling appears to have been misrepresented. Useful alternative techniques that might overcome these limitations are then discussed. REVIEW LIMITATIONS: This review is limited in scope because it is applied to one journal, and so the findings cannot be generalized to other nursing journals or to nursing research in general. However, it is possible that other nursing journals are also publishing research articles based on the misrepresentation of random sampling. The review is also limited because in several of the articles the sampling method was not completely clearly stated, and in this circumstance a judgment has been made as to the sampling method employed, based on the indications given by author(s). CONCLUSION: Quantitative researchers in nursing should be very careful that the statistical techniques they use are appropriate for the design and sampling methods of their studies. If the techniques they employ are not appropriate, they run the risk of misinterpreting findings by using inappropriate, unrepresentative and biased samples.
Data Collection↗
The fuzzy cube and causal efficacy: representation of concomitant mechanisms in stroke.
Twentieth century medical science has embraced nineteenth century Boolean probability theory based upon two-valued Aristotelian logic. With the later addition of bit-based, von Neumann structured computational architectures, an epistemology based on randomness has led to a bivalent epidemiological methodology that dominates medical decision making. In contrast, fuzzy logic, based on twentieth century multi-valued logic, and computational structures that are content addressed and adaptively modified, has advanced a new scientific paradigm for the twenty-first century. Diseases such as stroke involve multiple concomitant causal factors that are difficult to represent using conventional statistical methods. We tested which paradigm best represented this complex multi-causal clinical phenomenon-stroke. We show that the fuzzy logic paradigm better represented clinical complexity in cerebrovascular disease than current probability theory based methodology. We believe this finding is generalizable to all of clinical science since multiple concomitant causal factors are involved in nearly all known pathological processes.
Journal Article↗
Not all (possibly) "random" sequences are created equal.
The need to assess the randomness of a single sequence, especially a finite sequence, is ubiquitous, yet is unaddressed by axiomatic probability theory. Here, we assess randomness via approximate entropy (ApEn), a computable measure of sequential irregularity, applicable to single sequences of both (even very short) finite and infinite length. We indicate the novelty and facility of the multidimensional viewpoint taken by ApEn, in contrast to classical measures. Furthermore and notably, for finite length, finite state sequences, one can identify maximally irregular sequences, and then apply ApEn to quantify the extent to which given sequences differ from maximal irregularity, via a set of deficit (def(m)) functions. The utility of these def(m) functions which we show allows one to considerably refine the notions of probabilistic independence and normality, is featured in several studies, including (i) digits of e, pi, radical2, and radical3, both in base 2 and in base 10, and (ii) sequences given by fractional parts of multiples of irrationals. We prove companion analytic results, which also feature in a discussion of the role and validity of the almost sure properties from axiomatic probability theory insofar as they apply to specified sequences and sets of sequences (in the physical world). We conclude by relating the present results and perspective to both previous and subsequent studies.
Journal Article↗
Newton and the classical theory of probability.
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Demography↗
Early history of the theory of probability.
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Demography↗