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PubMed1992

A theoretical basis for conditional probability analyses of neural discharge activity.

A theory has been developed which allows the estimation of the probability density of a discharge, given that an arbitrary condition is fulfilled. It is shown that the common methods for the evaluation of a post-stimulus time (PST) histogram and a hazard function can be considered as special applications of this theory. Whereas the usual hazard function shows how the probability of a discharge depends on the time elapsed since the last discharge, generalized hazard functions proposed in the present paper allow to reveal also the influence of the last but one discharge, the last but two discharge, and so on. In contrast to the usual method for the estimation of a hazard function, the applicability of the procedures proposed here is not restricted to stationary discharge activity. Some elementary applications are illustrated by analysing simulated discharge activity mimicing the response of a single auditory-nerve fiber to a high-intensity tone burst.

Action Potentials↗

PubMed1981

Probability of neuronal spike initiation as a curve-crossing problem for Gaussian stochastic processes.

Probability of neuronal spike initiation was considered within the framework of a simple stochastic model. The time of spike occurrence was defined as the first time of crossing of a stochastic process and a determined time function. This problem has been investigated in the case of a stationary Gaussian stochastic process and a linear time function. An integral equation obtained for the probability density function of the first time crossing was numerically solved by means of computer calculations. The model was applied to the analysis of temporal pattern of spike activity evoked in the cat spinal motoneurones by depolarizing current injected through the recording microelectrode.

Animals↗

PubMed1985

On the probability of the emergence of a protein with a particular function.

Proteins with nearly the same structure and function (homologous proteins) are found in increasing numbers in phylogenetically different, even very distant taxa (e.g. hemoglobins in vertebrates, in some invertebrates, and even in certain plants). In discussing the origin of those proteins biologists hardly at all consider convergent evolution because the origin of proteins is held to be a random process, at least ultimately, since selection can work only what the random process delivers as having a minimum adaptive value. The repetition of a random process with the same result is considered to be extremely unlikely. The supposed (un)likelihood, however, is almost never determined quantitatively. This paper attempts such a quantitative determination. It appears that the probability for the random origin of a definite protein is greater than what one would expect in view of the enormous number of equally possible nucleotide sequences in the corresponding gene since what is equally possible is not always equally likely. The probability, however, of the convergent evolution of two proteins with approximately the same structure and function is too low to be plausible, even when all possible circumstances are present which seem to heighten the likelihood of such a convergence. If this is so, then the plausibility of a random evolution of two or more different but functionally related proteins seems hardly greater.

Amino Acid Sequence↗

PubMed1992

Asymptotic rates of growth of the extinction probability of a mutant gene.

We prove that a result of Haldane (1927) that relates the asymptotic behaviour of the extinction probability of a slightly supercritical Poisson branching process to the mean number of offspring is true for a general Bienaymé-Galton-Watson branching process, provided that the second derivatives of the probability-generating functions converge uniformly to a non-zero limit. We show also by examples that such a result is true more widely than our proof suggests and exhibit some counter-examples.

Gene Frequency↗

PubMed1994

Significance probability mapping: the final touch in t-statistic mapping.

Significance Probability Mapping (SPM), based on Student's t-statistic, is widely used for comparing mean brain topography maps of two groups. The map resulting from this process represents the distribution of t-values over the entire scalp. However, t-values by themselves cannot reveal whether or not group differences are significant. Significance levels associated with a few t-values are therefore commonly indicated on map legends to give the reader an idea of the significance levels of t-values. Nevertheless, a precise significance level topography cannot be achieved with these few significance values. We introduce a new kind of map which directly displays significance level topography in order to relieve the reader from converting multiple t-values to their corresponding significance probabilities, and to obtain a good quantification and a better localization of regions with significant differences between groups. As an illustration of this type of map, we present a comparison of EEG activity in Alzheimer's patients and age-matched control subjects for both wakefulness and REM sleep.

Aged↗

PubMed1995

Assessing probability of paternity and the product rule in DNA systems.

The genetic resolution of paternity disputes begins with an intricate detection of inherited traits and finishes with a statistical inference (the probability of paternity, W). Notwithstanding some initial fanfare, statistical inference is a necessary component of DNA-based paternity tests because band patterns may be rare but not yet unique, and even rare events in a vacuum are meaningless. The genetic match must be combined with other evidence for relevancy, thus a Bayesian approach is preferred when computing W. This paper reviews the standard model used to compute W and discusses the model's various properties and assumptions. The standard model is extended to include DNA systems in which alleles are operationally continuous due to measurement error. This extension avoids problems associated with 'matched/non-matched' binned decisions. After outlining the model assumptions for a single DNA system, particular attention is given to the product rule-the procedure of multiplying intermediate probabilities across genetic loci to form a combined W. An empirical alternative to the product rule is also assessed and correlated with standard procedures.

Alleles↗

PubMed1980

Distribution of likelihood ratio in relation to the exclusion probability.

The relation between the exclusion probability (E) and the paternity probability is derived by assuming the distributions of logarithm of paternity likelihood ratio, log(Y/X) for true fathers and unexcluded non-fathers as the normal distributions. Under this assumption the value log(1-E) is equal to the mean of the mean value for true fathers (a) and that for unexcluded non-fathers (b), i.e., log(1-E)=(a+b)/2. This relation holds quite well for the various actual distributions of log(Y/X) of father-child combinations and those of father-mother-child combinations using 14 blood group systems. Therefore, the derived relation is found to be a convenient way to deduce one of the three quantities (E, a, b) from the remaining two quantities in the actual distributions.

Blood Group Antigens↗

PubMed2005

Using half-normal probability plot and regression analysis to differentiate complex traits: differentiating disease response of multigenic resistance and susceptibility in tomatoes to multiple pathogen isolates.

The need for a new analytical approach was encountered in the course of characterizing newly developed tomato lines resistant to late blight. Late blight resistant tomato lines were created in independent breeding programs using the accession Solanum pimpinellifolium L. (formerly Lycopersicon pimpinellifolium (L.) Miller) L3708 as the source of the resistance. However, initial field observation suggested that the late blight resistance in the lines produced by two independent breeding programs differed. Possible causes included a partial transfer of the late blight resistance derived from S. pimpinellifolium L3708 or the possibility of race specificity of this resistance. A crucial issue was determining the most appropriate and robust analytical method to use with data from laboratory analyses of the responses of nine tomato lines against five P. infestans isolates. Prior analysis by standard ANOVA revealed significant differences across tomato lines but could not determine whether the disease responses in the CLN-R lines were different from those of the heterozygous F(1) hybrids, created by crossing susceptible tomatoes with the fixed CU-R lines. A different analytical method was needed. Therefore, sporangia numbers/leaflet and diseased area data were analyzed using a half-normal probability plot and regression analysis. The results of this analysis show its utility for genetic or pathology studies. Considering only populations of the uniform tomato lines, this method confirms the results obtained by using a standard ANOVA, but provides a clearer demonstration of the distributions of the individuals within the populations and how this distribution impacts variance and the difference among the populations. This method also allows a joint analysis of the uniform lines with an additional population that is less uniform, because it is segregating. Such an analysis would be invalid using a standard ANOVA. The results of this joint analysis determined that the additional population was divergent from the fixed CU-R lines, and, against some isolates, against the CLN-R lines as well. Half-normal probability plot analysis method would be applicable more broadly beyond analysis of disease resistance data. It could be useful for data from populations that are not normally distributed, for traits which are affected by epistatic gene action, and could be useful for selection of extremes.

Genotype↗

PubMed2004

Effect of stimulus probability on anti-saccade error rates.

Subjects sometimes fail to suppress a reflexive saccade towards the flashed stimulus in an anti-saccade task. Here, we studied how error rates in the anti-saccade task varied as a function of saccadic probability. Ten subjects performed 200 anti-saccade trials for each of three saccade-direction probability conditions (20%, 50%, and 80%). We found that as the likelihood of a saccade in a given direction increased, the percentage of pro-saccade errors also increased for stimulus presentations in this direction. These results provide support for the hypothesis that errors in the anti-saccade task are the result of an increased level of motor preparation.

Adult↗

PubMed1997

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak.

The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak ('fade-out'). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations.

Communicable Disease Control↗

PubMed2003

Discriminant function for prognostic indexes and probability of death in chronic severe hepatitis B.

BACKGROUND: We aimed to determine a discriminant function for prognosis in chronic severe hepatitis B (CSHB), by discriminant analysis of prognostic indexes and probability of death. METHODS: In 205 patients with chronic severe hepatitis B (101 patients in the survival group and 104 patients in the death group), we carried out discriminant analysis of serum total bilirubin, prothrombin activity, white blood cells, creatinine, maximum depth of ascites, hepatic encephalopathy, singultus, and digestive tract hemorrhage. RESULTS: The discriminant function was V=0.00043 x total bilirubin (microM) - 0.025 x prothrombin activity (%) + 0.056 x white blood cells (10(9)/l) + 0.00284 x creatinine (microM) + 0.0014 x maximum depth of ascites (mm) + 0.724 x hepatic encephalopathy score + 0.078 x singultus score + 0.457 x digestive tract hemorrhage score - 2.488. The correctness of the function for predicting death in the death group was 92.3%, and that for predicting survival in the survival group was 96.0%. When the V values were -infinity, -4.595, -2.197, -1.386, -0.405, 0.405, 1.386, 2.197, 2.944, 4.595, and infinity, a posterior probabilities of death were 0%, 5%, 10%, 20%, 40%, 60%, 80%, 90%, 95%, 99%, and 100%, respectively. CONCLUSIONS: The discriminant function is an objective, convenient, and practical method to assess the prognosis of chronic severe hepatitis B.

Discriminant Analysis↗

PubMed2005

Sampling of sparse species with probability proportional to prediction.

In this article, a 3P sampling (Probability Proportional to Prediction) approach is presented for surveying sparse species connected to certain types of substrates. The method uses the surveyor's judgement of the probability of finding the species on a substrate as the base for selection of substrates for species inventories. The method is presented together with estimators, variances and variance estimators. The method is first presented for sampling based on all substrates in a study area and then as a subsampling technique in a two-stage design in which plots or strips are selected in a first stage. The presented approach was evaluated as a subsampling technique in a strip survey of calicioid lichen species associated with coarse broadleaf trees. In comparison with a simple random subsampling without replacement, 3P subsampling was in one study area found to be an improvement with 30-55% in terms of standard errors. The improvement was more modest in the other study area, only between 10-16%. The strip survey with 3P subsampling was more cost-efficient than a strip survey without subsampling except in one case. Based on the results in the test, 3P sampling seems to have a potential for sampling sparse species.

Environmental Monitoring↗

PubMed2006

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences.

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the alpha and beta regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.

Algorithms↗

PubMed2006

Assessing the predictive accuracy of hMLH1 and hMSH2 mutation probability models.

Hereditary nonpolyposis colorectal cancer (HNPCC) is characterized by a susceptibility to colorectal and extra-colonic cancers. Several guidelines exist for the identification of families suspected of having HNPCC, however these guidelines lack adequate sensitivity and specificity. In an attempt to improve accuracy for the detection of individuals with HNPCC, the Wijnen pre-test probability model (1998) and Myriad Genetics Laboratory prevalence table (2004) were developed. Here we evaluate the Wijnen model and Myriad table at predicting the presence of a mutation in individuals undergoing genetic testing for HNPCC. Forty-nine patients who had undergone genetic testing for germline mutations in hMLH1 and/or hMSH2 were part of our analysis. Our results revealed that the revised Bethesda guidelines performed with the highest sensitivity for germline mutations (94.4%), however the specificity was low (12.9%). Using a 10.0% mutation probability threshold, the Wijnen model and Myriad table had sensitivities of 55.6 and 60.0%, respectively and specificities of 54.8 and 23.8%, respectively. The Wijnen model and Myriad table were poor predictors of mutation prevalence, which is shown by the areas underneath their corresponding receiver operator characteristic curves (0.616 and 0.400, respectively). The results of this study demonsrate that neither the Wijnen model nor the Myriad table are sensitive or specific enough to be used as the only indication when to offer genetic testing for HNPCC.

Adaptor Proteins, Signal Transducing↗

PubMed1992

Effects of exercise test results on physician perceptions of coronary artery disease probability using a threshold analysis.

The incremental diagnostic value of exercise electrocardiographic testing compared with clinical data alone in the diagnosis of coronary artery disease (CAD) was found to be of limited value in a previous study. That study used a computer algorithm for diagnosing disease. Thus, the strict use of the results apply only to computerized disease diagnosis rather than physicians' diagnoses. The aim of the present study was to determine whether exercise test data improve a physician's ability to detect the presence or absence of CAD and 3-vessel or left main CAD, and whether the data effect the decision to perform angiography. The study sample comprised a data base of 312 patients whose clinical data, exercise test results and coronary anatomy were known. Individual cases were presented to 8 cardiologists with and without exercise data. The cardiologists provided estimates of disease probability and were asked whether they would request coronary angiography. Receiver-operating characteristic curves and goodness-of-fit analysis showed better discrimination and calibration of the estimates for the presence of CAD and 3-vessel/left main CAD after exercise test results were known. Individualized probability thresholds for deciding whether to request angiography were determined for each physician. Forty-three percent of patients crossed greater than or equal to 1 threshold, with 64% of the crossings in the correct direction. For estimating the presence of any CAD, 84% of crossings from below to above a threshold were correct, whereas only 36% from above to below were correct. For 3-vessel/left main CAD, 36% of crossings from below to above a threshold were correct, whereas 88% from above to below were correct.(ABSTRACT TRUNCATED AT 250 WORDS)

Coronary Angiography↗

PubMed1990

A bleeding risk index for estimating the probability of major bleeding in hospitalized patients starting anticoagulant therapy.

PURPOSE: To construct and test prospectively a bleeding risk index for estimating the probability of major bleeding in hospitalized patients starting long-term anticoagulant therapy. PATIENTS AND METHODS: In an inception cohort of 617 patients starting long-term anticoagulant therapy in one hospital, data were gathered retrospectively and bleeding was classified using reliable explicit criteria. We constructed a bleeding risk index by identifying and weighting independent predictors of major bleeding using a multivariate proportional-hazards model. The bleeding risk index was tested in 394 other patients prospectively identified in a second hospital. The index was compared to physicians' predictions. RESULTS: Major bleeding developed before discharge in 61 of all 1,011 patients (6%). The bleeding risk index included four independent risk factors for major in-hospital bleeding: the number of specific comorbid conditions; heparin use in patients aged 60 years or older; maximal prothrombin or partial thromboplastin time 2.0 or more times control; liver dysfunction worsening during therapy. In the testing group, the index predicted major bleeding, which occurred in 3% of 235 low-risk patients, 16% of 96 middle-risk patients, and 19% of 63 high-risk patients (p less than 0.001). The bleeding risk index performed as well as physicians' predictions, and integration of the bleeding risk index with physicians' predictions led to a classification system that was more sensitive (p = 0.03) than physicians' predictions alone. In 86% of patients with a high risk of major bleeding, we identified specific ways of improving therapy, e.g., avoiding overanticoagulation and nonsteroidal anti-inflammatory agents. CONCLUSION: The bleeding risk index provides valid estimates of the probability of major bleeding in hospitalized patients starting long-term anticoagulant therapy and complements physicians' predictions. The possibility that bleeding can be prevented in high-risk patients warrants prospective evaluation.

Aged↗

PubMed1987

Proximal segment retraction increases the probability of nerve cell survival after dendrite transection.

Dendrites were transected 100 microns from nerve cell somata. The probability of cell survival increased as a function of the extent of proximal segment retraction. The retraction effect is probably the result of increased resistance to calcium and sodium currents at the lesion. It is speculated that limitation of nerve fiber die-back and neural tissue damage after injury may depend upon the ability of severed neurites to retract.

Animals↗

PubMed1977

A computer program for fitting multimodal probability density functions.

A FORTRAN IV program is described, which may be run interactively with tutorial assistance or in batch and which allows a user to selectively fit any of seven probability density functions (p.d.f.'s) or a combination of the p.d.f.'s to a unimodal or multimodal histogram of empirical data. A "best-fit", uni- or multimodal p.d.f., which may be obtained by a method of nonlinear least squares or a generated p.d.f. may be displayed on a Tektronix 4010 terminal as a continuous curve against the background of a bar, square wave, symbol or point-plot histogram. The following, supportive statistical information is also displayed: (1) Kolmogorov-Smirnov probability of goodness of fit, (2) mean square error, (3) correlation coefficient, and (4) parameter estimates. The resident driver program and six overlayable segments have been implemented on a Digital Equipment Corporation LAB-11 minicomputer (PDP-11/20).

Computers↗