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PubMed1987

Isotropic probability measures in infinite-dimensional spaces.

Every isotropic probability measure on the space R(infinity) of real sequences x = (x(1), x(2),...) is a convex combination of the measure concentrated at 0 and a member of I(0)(R(infinity)), the set of all isotropic probability measures p(infinity) on R(infinity) with p(infinity)({0}) = 0. Each p(infinity) [unk] I(0)(R(infinity)) is completely determined by any one of its finite-dimensional marginal distributions p(n). Each p(n) has a density function f(n) with dp(n)(x(1),..., x(n)) = dx(1)... dx(n)f(n)(x(1) (2) +... + x(n) (2)). Each f(n) is completely monotone in 0 < xi < infinity (hence analytic in the right complex xi half-plane), and pi(n/2)Gamma(n/2)(-1) (0) (infinity)dxi xi(n/2-1)f(n)(xi) = 1. Every f that satisfies these two conditions is f(n) for a unique p(infinity) [unk] I(0)(R(infinity)). Hence the equation pi(xi) (infinity)dzeta f(2)(zeta) = (0) (infinity)dmu (t)e(-txi) defines a bijection between I(0)(R(infinity)) and the set of all probability measures mu on 0 </= t < infinity. If p(infinity) [unk] I(0)(R(infinity)) then p(infinity)({x: Sigma(i=1) (infinity)x(i) (2) < infinity}) = 0, so p(infinity) is not a "softened" or "fuzzy" version of the inequality Sigma(i=1) (infinity)x(i) (2) </= 1. If the prior information in a linear inverse problem consists of this inequality and nothing else, stochastic inversion and Bayesian inference are both unsuitable inversion techniques.

Journal Article↗

PubMed1997

Decreased probability of neurotransmitter release underlies striatal long-term depression and postnatal development of corticostriatal synapses.

Changes in synaptic efficacy are crucial for the development of appropriate neural circuits and brain information storage. We have investigated mechanisms underlying long-term depression (LTD) at glutamatergic synapses in the striatum, a brain region important in motor performance and cognition, and a target for Huntington and Parkinson diseases. Induction of striatal LTD is dependent on postsynaptic depolarization and calcium influx through L-type channels. Surprisingly, LTD maintenance appears to involve a decrease in the probability of neurotransmitter release from presynaptic terminals as evidenced by increases in paired-pulse facilitation and the coefficient of variation of synaptic responses that are tightly associated with LTD expression. Furthermore, both the apparent probability of neurotransmitter release and the magnitude of LTD decrease concomitantly during postnatal development, consistent with the idea that striatal LTD is involved in a developmental decrease in the probability of neurotransmitter release at corticostriatal synapses. The presynaptic changes that underlie striatal LTD may also be important for motor performance and certain forms of learning and memory.

Aging↗

PubMed2006

Probability of an egg cracking during packing can be predicted using a simple non-destructive acoustic test.

1. The aim of this investigation was to test the predictive power of the dynamic stiffness measurement to identify eggs which are most likely to crack under field conditions. 2. A representative sample of eggs (n = 1660) was collected from the front of the cages in a commercial battery unit. Egg weight, % damping and dynamic stiffness (Kdyn) were recorded using an acoustic crack detection device. Intact eggs were marked and replaced in the front of the cages. These eggs were subsequently passed through online collection, grading and packing machinery, along with a volume of unmarked eggs. At the end of packing the acoustic test was repeated on the marked eggs, and these were subsequently categorised as being either intact (0) or cracked (1). 3. A logistic regression of the probability of cracking vs Kdyn revealed that as the Kdyn measurement decreases below 15,000 N/m there is a rapid increase in the probability that an egg will crack during routine handling. 4. Additional variables (visit, egg weight,% damping and position in the house (battery [1 to 7], side [1, 2] and tier [1 to 8]) were also fitted to the model but only egg weight, visit and tier effects significantly improved the model fit. 5. This study confirms that the dynamic stiffness measurement can predict the probability of an egg cracking in the field and with high precision. As this measurement also has a high heritability, it could be incorporated into breeding programmes, where it would offer an excellent method to improve eggshell quality and reduce the incidence of cracked eggs.

Acoustics↗

PubMed1999

Relation between spinal load factors and the high-risk probability of occupational low-back disorder.

Spinal compression is traditionally assumed the principal biomechanical mechanism associated with occupationally related low-back disorders (LBD). However, there is little conclusive evidence demonstrating that compression is related to occupational LBD. The objective of this research was to examine whether axial compression in the lumbar spine can predict the probability that a lifting task should be classified as high risk for LBD. Furthermore, the improvement in predictive ability was examined when analyses include 3-D, dynamic biomechanical factors. Ten experienced warehouse workers transferred 12 pallet loads of boxes in a simulation of warehouse working conditions. Biomechanical estimates of 2-D static and 3-D dynamic spinal compression, shear loads and tissue strains were achieved from the subjects during each lifting exertion. Each lift was also assessed for probability of high LBD risk classification. Regression analyses were performed to examine the relationship between biomechanical and epidemiological factors. Results indicate 2-D static estimates of spinal compression describe approximately 13% of the probability of high LBD risk variability. Dynamic estimates of spinal compression describe > 44% of the variability. A multifactor regression model including 3-D spinal loads and tissue strains further improved the predictive ability, but the improvement was not statistically significant. This research demonstrates the biomechanical source of low-back pain is dynamic, multifaceted and multidimensional. Significant improvements in ergonomics assessments can be achieved by examining interactions of dynamic biomechanical factors. Unfortunately, this improved predictive ability is generated at the high cost of computational complexity. However, less realistic biomechanical representations may ignore the injury mechanisms associated with the greater number of workplace injuries. Thus, improved understanding of the dynamic biomechanical interactions influencing the tolerance and injury mechanisms of the spine may permit more accurate assessments of workplace injury factors associated with LBD and reduced incidence of occupationally related low-back pain.

Adult↗

PubMed1978

Interactions of Manifest Anxiety score with anagram letter transition probability and Thorndike-Lorge frequency of solution word.

In an experiment designed for further exploration of the effects of manifest anxiety upon anagram problem solving, two levels each of manifest anxiety score, letter transition probability of anagram, and Thorndike-Lorge frequency of solution word were factorially combined (N = 40 male and 40 female freshmen and sophomores). While corroborating the previous findings that anagram solving rate is positively related to solution word frequency and negatively related to anagram letter transition probability, the results have demonstrated a significant interaction of solution word frequency, though not of anagram letter transition probability, with manifest anxiety score. This interaction, as shown in the facilitative effect of manifest anxiety with anagrams derived from high-frequency words and the inhibitory effect with anagrams derived from low-frequency words, is consistent with Taylor's interpretation that manifest anxiety, as an emotionally based drive, multiplicatively interacts with habit strength.

Adult↗

PubMed1999

Vibrotactile temporal summation: probability summation or neural integration?

Temporal summation, a decrease in the detection threshold that occurs when either the duration of a stimulus or the number of stimuli in a sequence is increased, has been attributed to the operations of either the mechanism of neural integration or of probability summation. Our experiments indicate that under certain conditions, both mechanisms may operate, but that the process of neural integration is an exclusive characteristic of the Pacinian (P) channel. The P channel was isolated by applying 250 Hz stimuli through a 1.5 cm2 contactor to the thenar eminence of the hand and the NPII channel was isolated by applying the stimuli through a 0.01 cm2 contactor. The finding that the slopes of the psychometric functions were the same within both channels indicated that probability summation could not account for temporal summation for stimulus durations less than 1 s. The finding that the threshold for the detection of multiple-pulse stimuli increased as the interpulse interval increased indicated that, for time intervals less than 800 ms, temporal summation results from neural integration. But for interstimulus intervals greater than 800 ms, probability summation accounts for temporal summation.

Adolescent↗

PubMed1988

Unexplained lymphadenopathy in family practice. An evaluation of the probability of malignant causes and the effectiveness of physicians' workup.

This study reported here was undertaken to determine the probability of malignancy in patients presenting with unexplained lymphadenopathy in primary care practice and to estimate the effectiveness of current referral patterns by family physicians in relation to malignant disease. Clinical characteristics that may be discriminatory for malignant causes were also investigated. A retrospective analysis was performed of 82 patients who underwent biopsy for unexplained lymphadenopathy from 1982 to 1984; data regarding the incidence of unexplained lymphadenopathy and the referral rate for this problem were obtained from registration projects. A total of 29 malignant lymphadenopathies were identified for a prior probability of 1.1 percent and a posterior (after referral) probability of 11 percent. The ability of the family physician to refer malignant cases within four weeks after initial consultation (sensitivity of referral) was 80 to 90 percent; 91 to 98 percent of benign cases were not referred (specificity of referral). An increased likelihood of malignancy was associated with age over 40 years (4 percent) and supraclavicular lymphadenopathy (50 percent). The incidence of malignancy in patients presenting with unexplained lymphadenopathy to the family physicians is very low (1 to 2 percent). Nevertheless, despite the paucity of validated discriminatory factors, the family physicians perform a reasonably effective selection process toward referral and biopsy.

Adult↗

PubMed2006

Estimating vaccine efficacy from outbreak size household data in the presence of heterogeneous transmission probabilities.

We develop a Bayesian approach for estimating vaccine efficacy for susceptibility (VEs) and infectiousness (VEI) using outbreak size household data. Our method allows for heterogeneity in transmission probabilities due to factors that are related to individuals' characteristics, such as age, in addition to vaccination status. It also allows for between-household heterogeneity in transmission probabilities due to random effects associated with households, such as genetic or environmental effects. Using age as a potential covariate causing heterogeneity in individuals' transmission probabilities in households consisting of adults and children, we present the results of a simulation study designed to evaluate the performance of the proposed estimators of VEs and VE(I). We found that estimates of VE(I) have larger bias and variance compared to those of VEs. We also use the approach to compare two vaccination designs: one vaccinating both adults and children, the other only children. Simulations reveal that the design that vaccinates both adults and children provides better estimates of VEs. There is no obvious difference between the two designs in the performance of the estimates of VE(I). In regard to random effects between households and the scenarios considered, models that do not account for between-households heterogeneity produce fairly robust estimates even when household-level random effects are present.

Adult↗

PubMed2003

Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylogenetics.

Many empirical studies have revealed considerable differences between nonparametric bootstrapping and Bayesian posterior probabilities in terms of the support values for branches, despite claimed predictions about their approximate equivalence. We investigated this problem by simulating data, which were then analyzed by maximum likelihood bootstrapping and Bayesian phylogenetic analysis using identical models and reoptimization of parameter values. We show that Bayesian posterior probabilities are significantly higher than corresponding nonparametric bootstrap frequencies for true clades, but also that erroneous conclusions will be made more often. These errors are strongly accentuated when the models used for analyses are underparameterized. When data are analyzed under the correct model, nonparametric bootstrapping is conservative. Bayesian posterior probabilities are also conservative in this respect, but less so.

Bayes Theorem↗

PubMed2006

Fundamental differences between the methods of maximum likelihood and maximum posterior probability in phylogenetics.

Using a four-taxon example under a simple model of evolution, we show that the methods of maximum likelihood and maximum posterior probability (which is a Bayesian method of inference) may not arrive at the same optimal tree topology. Some patterns that are separately uninformative under the maximum likelihood method are separately informative under the Bayesian method. We also show that this difference has impact on the bootstrap frequencies and the posterior probabilities of topologies, which therefore are not necessarily approximately equal. Efron et al. (Proc. Natl. Acad. Sci. USA 93:13429-13434, 1996) stated that bootstrap frequencies can, under certain circumstances, be interpreted as posterior probabilities. This is true only if one includes a non-informative prior distribution of the possible data patterns, and most often the prior distributions are instead specified in terms of topology and branch lengths. [Bayesian inference; maximum likelihood method; Phylogeny; support.].

Bayes Theorem↗

PubMed2002

Estimating the sensitivity of a genetic test using gene-carrier probability estimates and its application in genetic counselling.

BACKGROUND: The estimation of the sensitivity of a genetic test is of practical importance. If a 'gold standard' (an exact test) is not available, an estimate of the probability of being a gene carrier may be useful for an individual. This information could be based on individual pedigree and family-history data, and a known genetic model for the disease of interest. METHODS: We develop a maximum-likelihood estimate of the sensitivity of a genetic test that may be applied in a situation without a 'gold standard', in which an estimate of the probability of being a gene carrier for an individual is available. RESULTS: A maximum-likelihood estimate for the sensitivity can be obtained through an iterative algorithm. We demonstrate the method using data from a project on familial breast cancer. We further present disease-risk estimates incorporating results from a genetic test with different values of sensitivity, and compare these with disease-risk estimates that are solely based on family-history data. DISCUSSION: We provide a systematic methodology to obtain an estimate of sensitivity of a genetic test when only gene-carrier probability estimates from a genetic model are available. Given a negative result from a genetic test, predictions for lifetime and age-specific disease-risk, accounting for test sensitivity, can then be provided in genetic counselling.

Algorithms↗

PubMed1999

A simulation study of the effects of assignment of prior identity-by-descent probabilities to unselected sib pairs, in covariance-structure modeling of a quantitative-trait locus.

Sib pair-selection strategies, designed to identify the most informative sib pairs in order to detect a quantitative-trait locus (QTL), give rise to a missing-data problem in genetic covariance-structure modeling of QTL effects. After selection, phenotypic data are available for all sibs, but marker data-and, consequently, the identity-by-descent (IBD) probabilities-are available only in selected sib pairs. One possible solution to this missing-data problem is to assign prior IBD probabilities (i.e., expected values) to the unselected sib pairs. The effect of this assignment in genetic covariance-structure modeling is investigated in the present paper. Two maximum-likelihood approaches to estimation are considered, the pi-hat approach and the IBD-mixture approach. In the simulations, sample size, selection criteria, QTL-increaser allele frequency, and gene action are manipulated. The results indicate that the assignment of prior IBD probabilities results in serious estimation bias in the pi-hat approach. Bias is also present in the IBD-mixture approach, although here the bias is generally much smaller. The null distribution of the log-likelihood ratio (i.e., in absence of any QTL effect) does not follow the expected null distribution in the pi-hat approach after selection. In the IBD-mixture approach, the null distribution does agree with expectation.

Alleles↗

PubMed2004

The robustness of Hamilton's rule with inbreeding and dominance: kin selection and fixation probabilities under partial sib mating.

Assessing the validity of Hamilton's rule when there is both inbreeding and dominance remains difficult. In this article, we provide a general method based on the direct fitness formalism to address this question. We then apply it to the question of the evolution of altruism among diploid full sibs and among haplodiploid sisters under inbreeding resulting from partial sib mating. In both cases, we find that the allele coding for altruism always increases in frequency if a condition of the form rb>c holds, where r depends on the rate of sib mating alpha but not on the frequency of the allele, its phenotypic effects, or the dominance of these effects. In both examples, we derive expressions for the probability of fixation of an allele coding for altruism; comparing these expressions with simulation results allows us to test various approximations often made in kin selection models (weak selection, large population size, large fecundity). Increasing alpha increases the probability of fixation of recessive altruistic alleles (h<1/2), while it can increase or decrease the probability of fixation of dominant altruistic alleles (h>1/2).

Altruism↗

PubMed1990

Probability modelling of a surgical probe for tumour detection.

Probability functions for the output counts from a radiation detector probe are needed to implement Bayesian detection strategies or to assess performance of the probe. This paper presents methods for simulating a surgical probe designed for tumour detection to obtain statistical information for modelling probability functions of output data. Statistical models of pharmaceutical uptake in normal organs and tumours were estimated from animal and human data, and these models were combined with a digitised human torso phantom to create a large set of simulated patients. With the simulated patients and with a spatial map of the probe response, computer simulations of intraoperative probe measurements provided a large set of simulated probe data. Probability models derived from these data using maximum-likelihood methods helped to formulate the detection strategy and to evaluate the performance of the surgical probe.

Computer Simulation↗

PubMed2005

The probability of giving birth among women who were born preterm or with impaired fetal growth: a Swedish population-based registry study.

The primary aim of this study was to investigate whether women born prematurely or with impaired fetal growth have a reduced probability of giving birth. Using Swedish population-based registries, the authors identified 148,281 women born in 1973-1975 for follow-up until 2001. Of these women, 4.1% were born preterm and 0.32% very preterm, 0.29% were born with a very low birth weight, and 5.4% were small for gestational age. Outcome measures were the hazard ratios for giving birth during the study period. Adjustments were made for socioeconomic factors. Very-low-birth-weight women displayed a reduced probability of giving birth (hazard ratio = 0.74, 95% confidence interval: 0.60, 0.91), most apparent among women aged 25 or more years. There were also tendencies of reduced hazard ratios of giving birth among women born preterm or very preterm in this age interval. Women born small for gestational age (below -2 standard deviations) seemed to be more likely to have given birth (hazard ratio = 1.09, 95% confidence interval: 1.04, 1.14), but when a more extreme group of small-for-gestational-age women (below -3 standard deviations) was defined, the association was less evident (hazard ratio = 1.04, 95% confidence interval: 0.94, 1.16). The results suggest that very-low-birth-weight women and, possibly, women born preterm or very preterm have a reduced probability of giving birth, while the results regarding small for gestational age are less clear.

Adult↗

PubMed2004

Sample classification from protein mass spectrometry, by 'peak probability contrasts'.

MOTIVATION: Early cancer detection has always been a major research focus in solid tumor oncology. Early tumor detection can theoretically result in lower stage tumors, more treatable diseases and ultimately higher cure rates with less treatment-related morbidities. Protein mass spectrometry is a potentially powerful tool for early cancer detection. We propose a novel method for sample classification from protein mass spectrometry data. When applied to spectra from both diseased and healthy patients, the 'peak probability contrast' technique provides a list of all common peaks among the spectra, their statistical significance and their relative importance in discriminating between the two groups. We illustrate the method on matrix-assisted laser desorption and ionization mass spectrometry data from a study of ovarian cancers. RESULTS: Compared to other statistical approaches for class prediction, the peak probability contrast method performs as well or better than several methods that require the full spectra, rather than just labelled peaks. It is also much more interpretable biologically. The peak probability contrast method is a potentially useful tool for sample classification from protein mass spectrometry data.

Algorithms↗

PubMed2001

Regression modeling of competing crude failure probabilities.

In a randomized trial of tamoxifen therapy for breast cancer, women can experience tumor recurrence or die from competing causes. One goal of analysis is to describe the effect of tamoxifen on the probabilities of recurrence or death from other causes. To this end, we propose a semi-parametric transformation model for the crude failure probabilities of a competing risk, conditional on covariates. The model is developed as an extension of the standard approach to survival data with independent right censoring. Estimation of the regression coefficients is achieved with a rank-based least squares criterion. Simulations show that the procedure works well with practical sample sizes. A separate estimating function is developed for the baseline parameter. Prediction of covariate-adjusted failure probabilities is considered. The methodology is motivated and illustrated with data from the tamoxifen trial.

Journal Article↗

PubMed1998

Halothane increases the open probability of glycine-activated channel current in rat central neurones.

Glycine-activated single-channel currents in rat central neurones were recorded using the outside-out mode of the patch-clamp technique. The unitary conductance of the current was 21 pS. The current evoked by 10 microM glycine had a mean burst duration of 47.8 (2.6) ms and open probability of 0.09 (0.016). Halothane (1 mM) increased the open probability to 0.19 (0.03) without changing either unitary conductance or burst duration. These results suggest that halothane increased the open probability via an increase in the affinity of the receptor for the agonist. Potentiation of the glycine response may reduce excitability of postsynaptic neurones and may contribute to general anaesthesia produced by volatile agents.

Anesthetics, Inhalation↗