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PubMedDate not supplied

Clinical reasoning and cognitive processes.

Expected utility theory, and the Bayesian probability theory on which it is based, form the normative basis of most work in medical decision analysis. Recent work in the psychology of judgments and decisions indicates that people do not conform to the axioms of this theory and that these deviations occur in clinical reasoning as well as in the psychology laboratory. At issue is what to do now. The authors argue that the important next steps lie at the interface between descriptive, prescriptive, and normative accounts, all of which affect each other. They point to examples in which the simplest application of supposedly normative theory seems inappropriate, and suggest ways in which the tension between normative and descriptive models may be resolved.

Cognition↗
PubMed1983

Stability and coherence of health experts' upper and lower subjective probabilities about dose-response functions.

As part of a method for assessing health risks associated with primary National Ambient Air Quality Standards. T. B. Feagans and W. F. Biller (Research Triangle Park, North Carolina. EPA Office of Air Quality Planning and Standards, May 1981) developed a technique for encoding experts' subjective probabilities regarding dose--response functions. The encoding technique is based on B. O. Koopman's (Bulletin of the American Mathematical Society, 1940, 46, 763-764; Annals of Mathematics, 1940, 41, 269-292) probability theory, which does not require probabilities to be sharp, but rather allows lower and upper probabilities to be associated with an event. Uncertainty about a dose--response function can be expressed either in terms of the response rate expected at a given concentration or, conversely, in terms of the concentration expected to support a given response rate. Feagans and Biller (1981, cited above) derive the relation between the two conditional probabilities, which is easily extended to upper and lower conditional probabilities. These relations were treated as coherence requirements in an experiment utilizing four ozone and four lead experts as subjects, each providing judgments on two separate occasions. Four subjects strongly satisfied the coherence requirements in both conditions. and three more did no in the second session only. The eighth subject also improved in Session 2. Encoded probabilities were highly correlated between the two sessions, but changed from the first to the second in a manner that improved coherence and reflected greater attention to certain parameters of the dose--response function.

Air Pollution↗
PubMed1980

The single supratentorial lesion. An evaluation of preoperative diagnostic tests.

The role of preoperative diagnostic test was evaluated in 210 adult patients with single supratentorial lesions demonstrated by computerized tomography. At craniotomy, 59.5% of these patients proved to have primary brain tumors, 36.2% had metastatic tumors, and 4.3% had non-neoplastic lesions. In 23 (11%) of these patients, a single brain metastasis was the first manifestation of a systemic cancer. The primary site of cancer was identified in 14 patients (10 in the lung, three in the kidney, and one in the colon), and in nine patients the primary site could not be established. Using simple conditional probability theory, we established that the probability of a metastatic lesion in patients without a history of previously treated cancer is about 7%, if their chest x-ray film and intravenous pyelogram (IVP) are negative. Extensive preoperative testing to try to establish a primary site is unrewarding if the chest x-ray film and IVP are negative, since these are the only sites likely to be identified in these patients. In patients with a history of previously treated cancer, thest tests are justified because they have prognostic value in determining treatment.

Adult↗
PubMed2006

Does learning about the mathematics of gambling change gambling behavior?

The present research examined the influence of improved knowledge of odds and mathematical expectation on the gambling behavior of university students. A group of 198 students in an introductory statistics class received instruction on probability theory using examples from gambling. A comparison group of 134 students received generic instruction on probability, and another group of 138 students in classes on unrelated topics received no mathematical instruction. Students receiving the intervention demonstrated superior ability to calculate gambling odds as well as resistance to gambling fallacies 6 months after the intervention. Unexpectedly, this improvement in knowledge and skill was not associated with any decreases in actual gambling behavior. The implication of this research is that enhanced mathematical knowledge on its own may be insufficient to change gambling behavior.

Adult↗
PubMed2001

A probabilistic approach to space-group determination from powder diffraction data.

An algorithm for the determination of the space-group symmetry of a crystal from powder diffraction data, based upon probability theory, is described. Specifically, the relative probabilities of different extinction symbols are assessed within a particular crystal system. In general, only a small number of extinction symbols are relatively highly probable and a single extinction symbol is often significantly more probable than any other. Several examples are presented to illustrate this approach.

Journal Article↗
PubMed1996

Probability density estimation for the interpretation of neural population codes.

1. Electrophysiological recording data from multiple cells in motor cortex and elsewhere often are interpreted using the population vector method pioneered by Georgopoulos and coworkers. This paper proposes an alternative method for interpreting coding across populations of cells that may succeed under circumstances in which the population vector fails. 2. Population codes are analyzed using probability theory to find the complete conditional probability density of a movement parameter given the firing pattern of a set of cells. 3. The conditional probability density when a single cell fires is proportional to the shape of the cell's tuning curve of firing rate in response to different movement parameters. 4. The conditional density when multiple cells fire is proportional to the product of their tuning curves. 5. Movement parameters can be estimated from the conditional density using statistical maximum likelihood or minimum mean-squared error methods. 6. Simulations show that density estimation correctly finds movement directions for nonuniform distributions of preferred directions and noncosine cell tuning curves, whereas the population vector method fails for these cases. 7. Probability methods thus provide a statistically based alternative to the population vector for interpreting electrophysiological recording data from multiple cells.

Cell Count↗
PubMed2004

Decryption of pure-position permutation algorithms.

Pure position permutation image encryption algorithms, commonly used as image encryption investigated in this work are unfortunately frail under known-text attack. In view of the weakness of pure position permutation algorithm, we put forward an effective decryption algorithm for all pure-position permutation algorithms. First, a summary of the pure position permutation image encryption algorithms is given by introducing the concept of ergodic matrices. Then, by using probability theory and algebraic principles, the decryption probability of pure-position permutation algorithms is verified theoretically; and then, by defining the operation system of fuzzy ergodic matrices, we improve a specific decryption algorithm. Finally, some simulation results are shown.

Algorithms↗
PubMed2001

From computing with numbers to computing with words. From manipulation of measurements to manipulation of perceptions.

Interest in issues relating to consciousness has grown markedly during the last several years. And yet, nobody can claim that consciousness is a well-understood concept that lends itself to precise analysis. It may be argued that, as a concept, consciousness is much too complex to fit into the conceptual structure of existing theories based on Aristotelian logic and probability theory. An approach suggested in this paper links consciousness to perceptions and perceptions to their descriptors in a natural language. In this way, those aspects of consciousness which relate to reasoning and concept formation are linked to what is referred to as the methodology of computing with words (CW). Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language (e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc.). Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples of such tasks are parking a car, driving in heavy traffic, playing golf, riding a bicycle, understanding speech, and summarizing a story. Underlying this remarkable capability is the brain's crucial ability to manipulate perceptions--perceptions of distance, size, weight, color, speed, time, direction, force, number, truth, likelihood, and other characteristics of physical and mental objects. Manipulation of perceptions plays a key role in human recognition, decision and execution processes. As a methodology, computing with words provides a foundation for a computational theory of perceptions: a theory which may have an important bearing on how humans make--and machines might make--perception-based rational decisions in an environment of imprecision, uncertainty, and partial truth. A basic difference between perceptions and measurements is that, in general, measurements are crisp, whereas perceptions are fuzzy. One of the fundamental aims of science has been and continues to be that of progressing from perceptions to measurements. Pursuit of this aim has led to brilliant successes. We have sent men to the moon; we can build computers that are capable of performing billions of computations per second; we have constructed telescopes that can explore the far reaches of the universe; and we can date the age of rocks that are millions of years old. But alongside the brilliant successes stand conspicuous underachievements and outright failures. We cannot build robots that can move with the agility of animals or humans; we cannot automate driving in heavy traffic; we cannot translate from one language to another at the level of a human interpreter; we cannot create programs that can summarize non-trivial stories; our ability to model the behavior of economic systems leaves much to be desired; and we cannot build machines that can compete with children in the performance of a wide variety of physical and cognitive tasks. It may be argued that underlying the underachievements and failures is the unavailability of a methodology for reasoning and computing with perceptions rather than measurements. An outline of such a methodology--referred to as a computational theory of perceptions--is presented in this paper. The computational theory of perceptions (CTP) is based on the methodology of CW. In CTP, words play the role of labels of perceptions, and, more generally, perceptions are expressed as propositions in a natural language. CW-based techniques are employed to translate propositions expressed in a natural language into what is called the Generalized Constraint Language (GCL). In this language, the meaning of a proposition is expressed as a generalized constraint, X isr R, where X is the constrained variable, R is the constraining relation, and isr is a variable copula in which r is an indexing variable whose value defines the way in which R constrains X. Among the basic types of constraints are possibilistic, veristic, probabilistic, random set, Pawlak set, fuzzy graph, and usuality. The wide variety of constraints in GCL makes GCL a much more expressive language than the language of predicate logic. In CW, the initial and terminal data sets, IDS and TDS, are assumed to consist of propositions expressed in a natural language. These propositions are translated, respectively, into antecedent and consequent constraints. Consequent constraints are derived from antecedent constraints through the use of rules of constraint propagation. The principal constraint propagation rule is the generalized extension principle. (ABSTRACT TRUNCATED)

Consciousness↗
PubMed2001

[Maximal entropy principle wavelet denoising].

In the filed of wavelet denoising, an essential problem is how to determine the cutting threshold of wavelet coefficients that divides the coefficients corresponding to signal and noise respectively. The wavelet denoising method discussed here determines this threshold by using the maximal entropy principle (MEP) of information theory. From the basic principle of probability theory, it can be deduced that the detailed wavelet coefficients sequence of an arbitrary distributed random noise sequence satisfies a normal distribution. Based on this conclusion, an optimal threshold is determined using MEP. Such that the coefficients whose absolute values are less than the threshold satisfies a normal probabilistic distribution. This threshold is an optimal value that distinguishes the wavelet coefficients of signal and noise in view of statistics. The simulation analysis using spectral data and the comparison with other methods showed that this method provides a best improvement of signal-to-noise ratio, and its performance is least sensitive to the change of signal-to-noise ratio.

Algorithms↗
PubMed1987

The cardiac ventricular defibrillation threshold: inherent limitations in its application and interpretation.

A quantity termed the "threshold" has been used to describe the results of electrical ventricular defibrillation studies, with the implication of a clear distinction between ineffective and effective shock intensities. Although several definitions of the threshold have been suggested, and various methods have been used to quantify it, no comparison of the accuracies of the various methods could be found in the literature. This article, after presenting a method of applying basic probability theory to an assumed distribution relating probability of successful defibrillation to current amplitude, uses the method to examine several popular algorithms for defibrillation-threshold determination. The results show that where a sharp transition exists from ineffective to effective current amplitudes, most algorithms yield fairly good results. Where that transition is gradual (as it appears to be in all of the published reports examined), the algorithms are shown to be inadequate.

Algorithms↗