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At least 19 recordsLinked to original sources

PubMed1989

Probability learning and Piagetian probability conceptions in children 5 to 12 years old.

This study focused on the relations between performance on a three-choice probability-learning task and conceptions of probability as outlined by Piaget concerning mixture, normal distribution, random selection, odds estimation, and permutations. The probability-learning task and four Piagetian tasks were administered randomly to 100 male and 100 female, middle SES, average IQ children in three age groups (5 to 6, 8 to 9, and 11 to 12 years old) from different schools. Half the children were from Middle Eastern backgrounds, and half were from European or American backgrounds. As predicted, developmental level of probability thinking was related to performance on the probability-learning task. The more advanced the child's probability thinking, the higher his or her level of maximization and hypothesis formulation and testing and the lower his or her level of systematically patterned responses. The results suggest that the probability-learning and Piagetian tasks assess similar cognitive skills and that performance on the probability-learning task reflects a variety of probability concepts.

Child↗

PubMed1997

Adding a visual linear scale probability to the PIOPED probability of pulmonary embolism.

PURPOSE: Reporting a lung scintigraphy diagnosis as a PIOPED categorical probability of pulmonary embolism offers the clinician a wide range of interpretation. Therefore the purpose of this study was to analyze the impact on lung scintigraphy reporting of adding a visual linear scale (VLS) probability assessment to the ordinary PIOPED categorical probability. MATERIAL AND METHODS: The study material was a re-evaluation of lung scintigrams from a prospective study of 170 patients. All patients had been examined by lung scintigraphy and pulmonary angiography. The scintigrams were re-evaluated by 3 raters, and the probability of pulmonary embolism was estimated by the PIOPED categorization and by a VLS probability. The test was repeated after 6 months. RESULTS: There was no significant difference (p > 0.05) in the area under the ROC curve between the PIOPED categorization and the VLS for any of the 3 raters. Analysis of agreement among raters and for repeatability demonstrated low agreement in the mid-range of probabilities. CONCLUSION: A VLS probability estimate did not significantly improve the overall accuracy of the diagnosis compared to the categorical PIOPED probability assessment alone. From the data of our present study we cannot recommend the addition of a VLS score to the PIOPED categorization.

Angiography↗

PubMedDate not supplied

Qualitative probability versus quantitative probability in clinical diagnosis: a study using a computer simulation.

The use of Bayes' theorem as a diagnostic tool in clinical medicine normally requires an input of exact probability estimates. However, humans tend to think in categories ("likely," "unlikely," etc.) rather than in terms of exact probability. A computer simulation of the presenting features of a case of pelvic infection has been used to compare the effects of quantitative and qualitative probability estimates on the diagnostic accuracy of Bayes' theorem. For the commoner conditions (prior probability greater than or equal to 0.2) the use of a two- or three-category system is virtually equivalent to the use of exact probability. However, uncommon conditions (prior probability less than or equal to 0.03) are completely ignored by the qualitative system. It is concluded that the use of simple categories of probability is acceptable for a Bayesian diagnostic system provided that the target conditions have a relatively high prior probability.

Artificial Intelligence↗

PubMed1994

Risks and probabilities of breast cancer: short-term versus lifetime probabilities.

OBJECTIVE: To calculate age-specific short-term and lifetime probabilities of breast cancer among a cohort of Canadian women. DESIGN: Double decrement life table. SETTING: Alberta. SUBJECTS: Women with first invasive breast cancers registered with the Alberta Cancer Registry between 1985 and 1987. MAIN OUTCOME MEASURES: Lifetime probability of breast cancer from birth and for women at various ages; short-term (up to 10 years) probability of breast cancer for women at various ages. RESULTS: The lifetime probability of breast cancer is 10.17% at birth and peaks at 10.34% at age 25 years, after which it decreases owing to a decline in the number of years over which breast cancer risk will be experienced. However, the probability of manifesting breast cancer in the next year increases steadily from the age of 30 onward, reaching 0.36% at 85 years. The probability of manifesting the disease within the next 10 years peaks at 2.97% at age 70 and decreases thereafter, again owing to declining probabilities of surviving the interval. CONCLUSIONS: Given that the incidence of breast cancer among Albertan women during the study period was similar to the national average, we conclude that currently more than 1 in 10 women in Canada can expect to have breast cancer at some point during their life. However, risk varies considerably over a woman's lifetime, with most risk concentrated after age 49. On the basis of the shorter-term age-specific risks that we present, the clinician can put breast cancer risk into perspective for younger women and heighten awareness among women aged 50 years or more.

Adolescent↗

PubMed2001

Using full probability models to compute probabilities of actual interest to decision makers.

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori, the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a "probabilistic" manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the "similarity region" of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.

Arterial Occlusive Diseases↗

PubMedDate not supplied

Improved estimation of the ranking probabilities in partial orders using random linear extensions by approximation of the mutual ranking probability.

The application of partial order theory and Hasse diagram technique in environmental science is getting increasing attention. One of the latest developments in the field of Hasse diagram technique is the use of random linear extensions to estimate ranking probabilities. In the original algorithm for estimating the ranking probability it is assumed that the order between two incomparable pair of objects can be chosen randomly. However, if the total set of linear extensions is considered there is a specific probability that one object will be larger than another, which can be far from 50%. In this study it is investigated if an approximation of the mutual ranking probability can improve the algorithm. Applying an approximation of the mutual ranking probability the estimation of the ranking probabilities are significantly improved. Using a test set of 39 partial orders with randomly chosen values the relative mean root square difference (MRSD) decrease in average from 7.9% to 2.2% and a maximum relative improvement of 90% can be found. In the most successful case the relative MRSD goes as low as 0.77%.

Journal Article↗

PubMed1991

[Diagnosis of paternity by deduction of the probable genotype of the deceased person from the relatives--in addition to the examination of the Essen-Möller value and diagnosis of paternity based on the probability distribution of log (Y/X)].

1) The present paper deals with the general formulas of paternity probability, applicable to any cases where the putative man and/or the plaintive mother are deceased, using the blood types of various relatives. Two typical examples are described. 2) Bayes's theorem is applied to the calculation of probability of paternity using the Essen-Möller's formula, in which a putative father is to be compared with any one of the men in the general population whose blood types are unidentified. Statistically, those men are supposed to have any one of several blood types, depending on the frequency of occurrence of those types. This means that their blood types include the blood type of the putative father. According to Bayes's theorem, however, probability calculations are valid only when the two types to be compared are mutually exclusive. Consequently, the theorem should not be applied to probability calculations using the Essen-Möller's formula. 3) A new basis of judgement for the diagnosis of paternity is proposed using the probability distribution of the relative frequencies of log (Y/X) for true father and that for non-father.

Blood Group Antigens↗

PubMed1999

Biological probability: cognitive processes of generating probabilities of events in biological systems.

This paper analyses relationships between probabilities of events happening in biological systems (or probabilistic disposition of systems) and cognitive properties of biological entities comprising such systems. Two kinds of cognitive properties are identified as relevant to the current problem: the ability to respond differently against different configurations of the environment (discriminability of cognition), and the ability to make an appropriate response to maintain a particular relation with the environment (selectivity of cognition). A basic framework bridging the two features of living systems, probabilistic disposition and the cognitive properties, is presented towards a general theory explaining the process generating probabilities of biological events. In this framework, a deterministic model of a system of entities is developed, in which objects are described as subjects that cognize events (i.e. entities as cognizers). Cognition is used in a wider sense, including not only biotic but also abiotic, and cognizers are conceptually distinguished from the meta-observer who describes the system externally. Based on this perspective, this paper seeks to explicate how events can occur in an uncertain, probabilistic manner, if observed from a cognizer viewpoint, even under a deterministic system. Each cognizer is identified with both the set of states that are actually taken, and its motion function which maps its state uniquely to a successor state depending on the current states of itself and of the rest of cognizers constituting the system. The model analysis reveals that the cognitive properties, discriminability and selectivity, of a cognizer can contribute to determining the probability of an event encountered by the cognizer itself-in particular, discrimination reducing the uncertainty in events occurrence for the cognizer. Biological implication of this result is discussed focusing on the concept of the probability of survival and reproduction.

Animals↗

PubMed2003

Infection Probability Score (IPS): A method to help assess the probability of infection in critically ill patients.

OBJECTIVE: To develop a simple score to help assess the presence or absence of infection in critically ill patients using routinely available variables. DESIGN: Observational study of a prospective cohort of patients divided into a developmental set (n = 353) and a validation set (n = 140). SETTING: Department of intensive care at an academic tertiary care center. PATIENTS: Four hundred and ninety-three adult patients admitted to the intensive care unit for > or =24 hrs. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: The presence of infection was defined using the Centers for Disease Control definitions. Body temperature, heart rate, respiratory rate, white blood cell count, and C-reactive protein concentrations were measured, and the Sequential Organ Failure Assessment score was calculated throughout the intensive care unit stay. Infection was documented in 92 of the 353 patients (26%) in the developmental set and in 41 of the 140 patients (29%) in the validation set. Univariate logistic regression was used to select significant predictors for infection. Each continuous predictor was transformed in a categorical variable using a robust locally weighted least square regression between infection and the continuous variable of interest. When more than two categories were created, the variable was separated into iso-weighted dummy variables. A multiple logistic regression model predicting infection was calculated with all the variables coded 1 or 0 allowing for relative scoring of the different predictors. The resulting Infection Probability Score consisted of six different variables and ranged from 0 to 26 points (0-2 for temperature, 0-12 for heart rate, 0-1 for respiratory rate, 0-3 for white blood cell count, 0-6 for C-reactive protein, 0-2 for Sequential Organ Failure Assessment score). The best predictors for infection were heart rate and C-reactive protein, whereas respiratory rate was found to have the poorest predictive value. The cutoff value for the Infection Probability Score was 14 points, with a positive predictive value of 53.6% and a negative predictive value of 89.5%. Model performance was very good (Hosmer-Lemeshow statistic, p =.918), and the areas under receiver operating characteristic curves were 0.820 for the developmental set and 0.873 for the validation set. CONCLUSIONS: The Infection Probability Score is a simple score that can help assess the probability of infection in critically ill patients. The variables used are simple, routinely available, and familiar to clinicians. Patients with a score <14 points have only a 10% risk of infection.

Adult↗

PubMed1990

Is probability sampling always better? A comparison of results from a quota and a probability sample survey.

Two surveys in the same defined population in Sydney's western suburbs in 1986 and 1987 provided the opportunity to compare results obtained from a quota and a probability sample survey. These surveys were designed to provide information for the planning of local health promotion programs. The quota sample survey was conducted in shopping centres and used quota sampling to select 1727 respondents. In the second survey, area probability sampling was used to select 484 respondents. This survey had a response rate of 65 per cent. There were 15 questions common to both surveys; results of only three differed significantly (p less than 0.05) between surveys. None of these differences was important from a public health perspective. The agreement between the results of these two surveys probably reflects the fact that the same selection bias has operated in both. Unless a very high response rate can be achieved, quota sample surveys with age and sex quota controls may be an acceptable alternative to probability sample surveys for gathering local data relevant to the development of health programs.

Adult↗

PubMed2001

The probability-outcome correspondence principle: a dispositional view of the interpretation of probability statements.

This article presents a framework for lay people's internal representations of probabilities, which supposedly reflect the strength of underlying dispositions, or propensities, associated with the predicted event. From this framework, we derive the probability-outcome correspondence principle, which asserts that strong dispositions should lead to (1) strong (forceful) and (2) immediate outcomes and, hence, be characterized by high probabilities. In contrast, weak dispositions lead to (1) weak (fragile) and (2) delayed outcomes and are thus associated with low probabilities. We describe six experiments designed to test the correspondence principle. In the final discussion, we examine the implications of the proposed framework, from both a normative and a descriptive viewpoint.

Adult↗

PubMed1988

[Probability of the occurrence of radiation complications in tissues as a function of the probability of the death of their constituent cells].

The author considers some theoretical aspects of the problem of development of mathematical models to describe probabilities of the absence of radiation complications in tissues as function of the probability of a cell to survive. Since the number of tissue cells in great, a mathematical model based on an assumption of the existence of the maximum number of cells associated with development of radiation complication, leads to a sharp change in dependence of probability of radiation complications in tissues as dose function, which becomes steadier and more adequate to actual functions if one assumes the existence of reparable and irreparable spacious structures which form cells survived after irradiation and characterize cell tissue organization.

Cell Survival↗

PubMed2003

A method to combine non-probability sample data with probability sample data in estimating spatial means of environmental variables.

In estimating spatial means of environmental variables of a region from data collected by convenience or purposive sampling, validity of the results can be ensured by collecting additional data through probability sampling. The precision of the pi estimator that uses the probability sample can be increased by interpolating the values at the nonprobability sample points to the probability sample points, and using these interpolated values as an auxiliary variable in the difference or regression estimator. These estimators are (approximately) unbiased, even when the nonprobability sample is severely biased such as in preferential samples. The gain in precision compared to the pi estimator in combination with Simple Random Sampling is controlled by the correlation between the target variable and interpolated variable. This correlation is determined by the size (density) and spatial coverage of the nonprobability sample, and the spatial continuity of the target variable. In a case study the average ratio of the variances of the simple regression estimator and pi estimator was 0.68 for preferential samples of size 150 with moderate spatial clustering, and 0.80 for preferential samples of similar size with strong spatial clustering. In the latter case the simple regression estimator was substantially more precise than the simple difference estimator.

Data Collection↗

PubMed1966

Probability of response and probability of reinforcement in a response-defined analogue of an interval schedule.

Variable interval (VI) responding was hypothesized to be a function of differential reinforcement susceptibilities of various unspecified behavior chains that mediate interresponse times (IRTs). To test this hypothesis, probabilities of reinforcement were regulated for the lengths of chains of key pecking responses of pigeons, analogous to the way that VI regulates probabilities of reinforcement for IRTs. This procedure generated a number of VI-like effects, supporting the notion that VI behavior can be construed as a special case of an interaction between the organism's function relating reinforcement susceptibilities to chain length and the experimenter's function relating probabilities of reinforcement to chain length.

Animals↗

PubMed1990

Analysis of the probability distribution of small random samples by nonlinear fitting of integrated probabilities.

Small random samples of biochemical and biological data are often representative of complex distribution functions and are difficult to analyze in detail by conventional means. The common approaches reduce the data to a few representative parameters (such as their moments) or combine the data into a histogram plot. Both approaches reduce the information content of the data. By fitting the empirical cumulative distribution function itself with models of integrated probability distributions, the information content of the raw data can be fully utilized. This approach, distribution analysis by nonlinear fitting of integrated probabilities, allows analysis of normally distributed samples, truncated data sets, and multimodal distributions with a single, powerful data processing procedure.

Data Interpretation, Statistical↗

PubMed1984

Interpretation of laboratory tests using a programmable hand-held calculator: calculation of posterior probability and relative risk on the basis of prior probability and sensitivity, specificity and result of the test.

A program is presented for the Hewlett-Packard HP- 41C programmable hand-held calculator that calculates the posterior probability and relative risk of an event (e.g. a disease) on the basis of prior probability (prevalence) and sensitivity, specificity and result of the test.

Bayes Theorem↗

PubMed1999

The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1; case.

The joint probability distribution function method has been developed in P1; for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F(p1), F(p2)) are found to be useful for phasing purposes, where p1 and p2 are any pair of vectorial indices. A variety of conditional distributions like P(|F(p1)| | |F(p2)|), P(|F(p1)| |F(p2)), P(varphi(p1)| |F(p1)|, F(p2)) are derived, which are able to estimate the modulus and phase of F(p1) given the modulus and/or phase of F(p2). The method has been generalized to handle the joint probability distribution of any set of structure factors, i.e. the distributions P(F(1), F(2),ellipsis, F(n+1)), P(|F(1)| |F(2),ellipsis, F(n+1)) and P(varphi(1)| |F|(1), F(2),ellipsis, F(n+1)) have been obtained. Some practical tests prove the efficiency of the method.

Journal Article↗

PubMed1989

[The role of migration in assessing age-specific event probabilities exemplified by the probability of death].

Estimating probabilities of age-specific events both in demography and in epidemiology (force of mortality, force of morbidity) will contain additional errors if the frequency of the respective events is influenced by net migration and if migration is not taken into consideration when estimating these events. The terms used in including migration into estimating the respective rates are refined terms. The influence of migration on age-specific events is demonstrated by age-specific mortality and the life expectancy computed on the basis of age-specific mortality rates for the GDR in 1984. The results demonstrate that the life expectancy of the population of Berlin will be underestimated by 0.28 years if migration processes are not taken into consideration.

Berlin↗