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PubMed1989

P300 and probability in children.

The P300 event-related brain potential (ERP) was elicited in three groups of 12 children each, ages 5-9, 10-14, and 15-19 years. A simple auditory task was employed in which subjects indicated with a finger movement when a randomly occurring target tone (high pitch) was presented in a series of standard (low pitch) tones. The probability of the target tone was varied across conditions at 0.10, 0.30, or 0.50 to determine if P300 amplitude would respond similarly across age groups. Immediate memory capacity was measured with forward and reverse digit spans. P300 amplitude increased with decreases in target stimulus probability for each age group and also tended to become larger with age. P300 latency decreased in the same fashion across probability levels as age increased. Digit span demonstrated the usual increase with age. The results suggest that cognitive development is indexed by decreases in P300 latency, and that P300 amplitude changes from the probability of the target stimulus are similar across age groups. The implications for the theoretical interpretation of the P300 and application of ERPs for evaluating cognitive development are discussed.

Adolescent↗

PubMedDate not supplied

Affinity in paired event probability.

It is shown that a general parametric functional generates the conditional and joint probabilities of event pairs when the order within paired events is irrelevant. The parameters represent affinities or associations between single events. If the marginal probabilities of the single events are known, then these parameters specify a hypersurface on which all the joint probabilities of event pairs must lie. Examples are presented, and applications in probability, ecology, epidemiology, genetics, and distribution theory are offered.

Ecology↗

PubMed1991

Calculation of normal tissue complication probability and dose-volume histogram reduction schemes for tissues with a critical element architecture.

We investigate a model of normal tissue complication probability for tissues that may be represented by a critical element architecture. We derive formulas for complication probability that apply to both a partial volume irradiation and to an arbitrary inhomogeneous dose distribution. The dose-volume isoeffect relationship which is a consequence of a critical element architecture is discussed and compared to the empirical power law relationship. A dose-volume histogram reduction scheme for a "pure" critical element model is derived. In addition, a point-based algorithm which does not require precomputation of a dose-volume histogram is derived. The existing published dose-volume histogram reduction algorithms are analyzed. We show that the existing algorithms, developed empirically without an explicit biophysical model, have a close relationship to the critical element model at low levels of complication probability. However, we also show that they have aspects which are not compatible with a critical element model and we propose a modification to one of them to circumvent its restriction to low complication probabilities.

Algorithms↗

PubMed1990

Probability and inter-stimulus interval effects on the P300 from auditory stimuli.

The relationship between target stimulus probability and inter-stimulus interval (ISI) on the P300 (P3) component of the event-related potential was assessed in two experiments. An auditory discrimination paradigm was employed wherein subjects indicated with a finger tap response the occurrence of a randomly presented 2000 Hz target tone embedded in a series of 1000 Hz tones. Experiment 1 presented stimuli with target probabilities of 0.10, 0.30, and 0.50 at ISIs of 1.5 or 3.0 s and produced P3 amplitudes which decreased with increases in target probability and were smaller at the shorter compared to the longer ISI. Experiment 2 presented stimuli with target probabilities of either 0.20, 0.50, or 0.80 at ISIs of 4.0 and 10.0 s and produced P3 amplitudes which were unaffected by either variable. P3 latency demonstrated relatively few changes in either experiment. When taken together with previous findings, the results suggest that inter-stimulus interval affects P3 amplitude by determining the amount of processing resources available during ERP generation.

Acoustic Stimulation↗

PubMed1983

Inactivation probability of heavy ion-irradiated Bacillus subtilis spores as a function of the radial distance to the particle's [correction of paricle's] trajectory.

The understanding of the radiobiological action of heavy ions requires the knowledge of the dependence of the inactivation probability on the distance between the particle's trajectory and the biological test organism (the impact parameter). Spores of Bacillus subtilis with a cytoplasmic core of about 0.22 micrometer cross section are suitable test objects for the study of this radial inactivation probability in its microscopic details. The spores are irradiated at low fluences of some 10(6) ions/cm2 with very heavy ions at different specific energies up to 10 MeV per atomic mass unit u while in fixed contact with visual nuclear track detectors. The methods are described by which the biological response of individual cells can be evaluated and the impact parameter be determined with an accuracy typically better than 0.2 micrometer. The results demonstrate that the common characteristics of inactivation, e.g., an effective range of inactivation extending to at least 3 micrometers, a nonmonotonic dependence of the inactivation probabilities on the radial distance, and the fact that the inactivation probability even for direct central hits on the cytoplasmic core is substantially below one, are nearly independent of the particle energy and type. The results are incompatible with the assumption that the radiobiological effectiveness can be attributed to the dose of secondary electrons as currently understood. They also demonstrate that the widely held notion of an "overkill" at low impact parameters does not apply for the spores even with the most densely ionizing ions.

Argon↗

PubMed1980

A general method for biological inference: illustrated by the estimation of gene nucleotide transition probabilities.

The method of maximum entropy inference developed by Jaynes can be a particularly useful method for obtaining unbiased estimates of biological parameters when the experimental knowledge about a system can be explicitly formulated. Base transition probabilities between genes, though central to evolutionary theory and understanding, present a difficult estimation problem because the ancestral genes are not experimentally accessible. The necessary estimates must therefore be made on the basis of experimental knowledge other than a direct frequency count of base replacements (A leads to C, for example) between contemporary genes. It is shown how maximum entropy inference together with the experimentally observed fact of compositional fidelity in a given gene family can be used to obtain meaningful gene base transition probabilities at each of the three nucleotide positions within codons. Both symmetric and asymmetric transition probabilities are considered. Tables of these probabilities are given for each codon position for the alpha-hemoglobin, beta-hemoglobin, myoglobin, cytochrome c, and the parvalbumin group genes. Tabular values of the average amino acid composition of these five protein families and the average nucleotide composition of their coding genes at varied codon loci are given. It is thus no longer necessary to assume in theories of evolutionary divergence equimolar base ratios A:C:G:U::1:1:1:1 or that each base has an equal chance of mutating to and being fixed as any one of the other three bases.

Amino Acids↗

PubMed1987

Optimization of radiation therapy, III: A method of assessing complication probabilities from dose-volume histograms.

To predict the likelihood of success of a therapeutic strategy, one must be able to assess the effects of the treatment upon both diseased and healthy tissues. This paper proposes a method for determining the probability that a healthy organ that receives a non-uniform distribution of X-irradiation, heat, chemotherapy, or other agent will escape complications. Starting with any given dose distribution, a dose-cumulative-volume histogram for the organ is generated. This is then reduced by an interpolation scheme (involving the volume-weighting of complication probabilities) to a slightly different histogram that corresponds to the same overall likelihood of complications, but which contains one less step. The procedure is repeated, one step at a time, until there remains a final, single-step histogram, for which the complication probability can be determined. The formalism makes use of a complication response function C(D, V) which, for the given treatment schedule, represents the probability of complications arising when the fraction V of the organ receives dose D and the rest of the organ gets none. Although the data required to generate this function are sparse at present, it should be possible to obtain the necessary information from in vivo and clinical studies. Volume effects are taken explicitly into account in two ways: the precise shape of the patient's histogram is employed in the calculation, and the complication response function is a function of the volume.

Humans↗

PubMedDate not supplied

Problems in probability of paternity interpretation.

This paper discusses the statistical interpretation of blood group findings in paternity testing. As a consequence of the large number of systems now employed, high probabilities of paternity are usual and evaluation problems arise. The purpose of this investigation was to calculate the paternity probabilities for a sample of legitimate families with a true father compared with those obtained in some cases of non-excluded men chosen randomly from the population as the accused fathers for the same mother-child pairs. The calculations were based on Essen-Möller formula, derived from Bayes' Theorem. The blood group systems taken into account were ABO, Rh, MNSs, Kell-Cellano, P1, Duffy, Lutheran, Kidd, Gc, Hp, Gm, Km, Tf, alpha 1-AT, AcP, PGM1, AK, ADA, EsD, 6-PGDH and GLO-I. Applied together these give an exclusion probability of 97.32%. The results of probability of paternity for some mother-child-father triplets and its comparison with the chance of exclusion for the same mother-child pairs are reported.

Humans↗

PubMed1996

Standard error and sample size determination for estimation of probabilities based on a test variable.

A method of sample size determination for estimation of probabilities based on a test variable is presented. Applications to estimation of sensitivity and specificity of medical tests are the focus of this research, although the methods can be applied to other areas of study such as engineering reliability. Examples are given for determining sample sizes required for the classification of patients with cutaneous lupus erythematosus based on the incidence of several markers. In this example, the test variable is the number of markers present. The methodology employs a weighted average of model-based and non-model-based estimates of the probability with the weights determined by the closeness to or the confidence in the given model. Formulas and charts required for determining sample size are provided for test variables that can be modeled by the binomial, Poisson, or normal distributions, i.e., for the most commonly encountered distributions for counting events (binomial and Poisson) and for measurements (normal). However, the methods given can be applied to any distribution, including multivariate. Especially when relatively small probabilities (the rare events) are being estimated, the techniques provided assistance in safeguarding against undersampling brought on by unwarranted confidence in a test variable distribution and against oversampling required for high accuracy in non-model-based probability estimators.

Epidemiologic Methods↗

PubMed2005

Determination of mutation trend in proteins by means of translation probability between RNA codes and mutated amino acids.

In this study, we estimate the translation probability to amino acid from RNA codon. With the determined 183 translation probabilities and amino-acid composition of eight highly mutated proteins, we construct the theoretical distributions of mutated amino acids in these proteins and then compare them with their actual distributions affected by mutations. Thereafter we trace the pattern of translation probabilities from RNA codons to mutated amino acids of 1053 point missense mutations. Finally, we statistically conclude that the natural mutation trend goes along the theoretical translation probability.

Amino Acid Sequence↗

PubMed2006

The combined effects of delay and probability in discounting.

Human discounting studies have frequently observed hyperbolic discounting of rewards that are delayed or probabilistic. However, no studies have systematically combined delay and probability in a single discounting procedure. Indifference points of hypothetical money rewards that are both delayed and probabilistic were determined. Probabilities were converted into comparable delays according to the h/k constant of proportionality determined by , and discounting rates were calculated. These data provided a very good fit to the hyperbolic model of discounting, suggesting that delay and probability can be combined into a single metric in studies of discounting. The inclusion of a magnitude condition found the Magnitude Effect commonly found in studies of temporal discounting. A temporal resolution of uncertainty condition found no effect. The present paper offers a novel statistical method, within an established framework, for the analysis of data from studies of discounting that combine delay and probability.

Adolescent↗

PubMed2004

A SAS macro for estimating transition probabilities in semiparametric models for recurrent events.

In many clinical studies involving event history analysis, the event of interest is non-fatal and may occur more than once for each subject. Models based on the theory of counting processes have been developed to deal with such data, the recurrences being considered as transitions in a Markovian process. Under this setting, the experimental units can move between states over time, and it is possible to estimate the corresponding transition probabilities employing regression models that incorporate the influence of covariates. Despite of this, most of the softwares are concerned only in the estimation of regression parameters and do not provide transition probabilities estimates. The aim of this paper is to present a SAS macro developed to estimate the transition probabilities, considering three approaches for the regression modeling. The macro is flexible enough to allow the user to select the model to be fit providing, for a given set of covariates, plots of the estimates for the predicted transition probabilities as a function of time.

Brazil↗

PubMed2006

Modelling the probability distribution of the number of DNA double-strand breaks due to sporadic alkylation of nucleotide bases.

Metabolites and certain chemical agents (for example methyl methanesulfonate) can induce nucleotide bases on chromosomal strands to become alkylated. These alkylated sites have the potential to become single-strand chromosomal breaks, a form of DNA damage, if they are exposed to a sufficient temperature in vitro. It has been proposed that a single-strand break (SSB) sufficiently close to another SSB on the opposite chromosomal strand will form a double-strand break (DSB). DNA repair mechanisms are less able to repair DSBs compared to SSBs. Because of the complex three-dimensional structure of DNA, some chromosomal regions are more susceptible to alkylation than others. A question of interest is therefore whether these alkylated bases are randomly distributed or tend to be clustered. Pulsed-field gel electrophoresis allows the number of DNA fragments (and hence the number of DSBs) to be observed directly. The randomness of alkylation events can therefore be tested using the standard statistical hypothesis-testing framework. Under the null hypothesis, that the SSBs are randomly distributed on each of the strands, we can calculate the probability of observing a number of DSBs at least as large as that observed and hence the associated p-value. Previously, the probability distribution of the number of DSBs has been determined by Monte Carlo simulations; when considering the whole genome this can be very time consuming. In this paper, we theoretically derive an approximation to the distribution enabling appropriate probabilities to be calculated quickly. Based on previous findings we assume that the number of breaks on each strand is small compared to the number of nucleotide bases. We show that our method can give the correct probability distribution when alkylation events are relatively rare, discuss how rare these events have to be and suggest potential extensions to the model when a greater proportion of bases are alkylated.

Alkylation↗

PubMed2003

Exploring the effect of marked normal structure volume on normal tissue complication probability.

Radiation therapy dosimetry software now frequently incorporates biological predictions of the probability of normal tissue complications. This study investigates whether the length of normal structure outlined affects a normal tissue complication probability (NTCP) for that structure. It also researches the effect of any change in the dose parameter used to produce a 50% probability of a complication (the TD50) on the calculated NTCP, as this is related to the clinical observations. An NTCP was calculated for rectum and bladder on a sample of prostate cases receiving external beam radiation therapy. The length of the organs at risk was varied and the NTCP recalculated for each different length using the same treatment plan. Large variations of up to 80% in NTCP for different delineated lengths of organ for a given TD50 were observed. Changing the TD50 dose altered the calculated NTCP and the relative size of the variation in the values. This parameter will need further investigation; a standardized delineated length of 2 cm beyond the beam edge for normal structures is recommended. Interpatient and interinstitution plan comparison using dose volume histograms and/or normal tissue complication probabilities will be compromised until such standardization occurs.

Humans↗

PubMed2004

Automatic segmentation of different-sized white matter lesions by voxel probability estimation.

A new method for fully automated segmentation of white matter lesions (WMLs) on cranial MR imaging is presented. The algorithm uses five types of regular MRI-scans. It is based on a K-Nearest Neighbor (KNN) classification technique, which builds a feature space from voxel intensity features and spatial information. The technique generates images representing the probability per voxel being part of a WML. By application of thresholds on these probability maps binary segmentations can be produced. ROC-curves show that the segmentations achieve a high sensitivity and specificity. Three similarity measures, the similarity index (SI), the overlap fraction (OF) and the extra fraction (EF), are calculated for evaluation of the results and determination of the optimal threshold on the probability map. Investigation of the relation between the total lesion volume and the similarity measures shows that the method performs well for lesions larger than 2 cc. The maximum SI per patient is correlated to the total WML volume. No significant relation between the lesion volume and the optimal threshold has been observed. The probabilistic equivalents of the SI, OF en EF (PSI, POF and PEF) allow direct evaluation of the probability maps, which provides a strong tool for comparison of different classification results. A significant correlation between the lesion volume and the PSI and the PEF has been noticed. This method for automated WML segmentation is applicable to lesions of different sizes and shapes, and reaches an accuracy that is comparable to existing methods for multiple sclerosis lesion segmentation. Furthermore, it is suitable for detection of WMLs in large and longitudinal population studies.

Aged↗

PubMed2006

Queuing theory under competitive social foraging may explain a mathematical equivalence of delay and probability in impulsive decision-making.

Intertemporal and probabilistic decision-making has been studied in psychiatry, ecology, and neuroeconomics. Because drug addicts and psycopaths often make risky decisions (e.g., drug misuse and aggression), investigation into types of impulsivity in intertemporal and probabilistic choices (delay and probability discounting) are important for psychiatric treatments. Studies in behavioral ecology proposed that delay and probability discounting are mediated by the same psychological process, because a decrease in probability of winning corresponds to an increase in delay until winning. According to this view, odds-against winning (=1/p-1) in probabilistic choice corresponds to delay in intertemporal choice. This hypothesis predicts that preference of gambling (low degree of probability discounting) may be associated with patience, rather than impulsivity or impatience, in intertemporal choice (low degree of delay discounting). However, recent empirical evidence in psychiatric research employing pathological gamblers indicates that pathological gamblers are impulsive in intertemporal choice (high degrees of delay discounting). However, a hyperbolic discounting function (usually adopted to explain intertemporal choice) with odds-against (instead of delay) explain experimental data in probabilistic choice dramatically well. Therefore, an alternative explanation is required for the hypothetical equivalence of odds-against to delay. We propose that queuing theory (often adopted for analyzing computer network traffic) under a competitive social foraging condition may explain the equivalence. Our hypothesis may help understand impulsivity of psychiatrics in social behavior (e.g., aggression and antisocial behavior) in addition to non-social impulsivity in reward-seeking (e.g., substance misuse).

Behavior, Addictive↗

PubMed2006

Sexual swellings in wild white-handed gibbon females (Hylobates lar) indicate the probability of ovulation.

Conspicuous sexual swellings in the females of some primate species have been a focus of scientific interest since Darwin first wrote about them in 1871. To understand these visual signals, research focused on exaggerated sexual swellings of Old World primates. However, some primate species develop much smaller sexual swellings and it is as yet unclear if these smaller swellings can serve similar functions as those proposed for exaggerated swellings, i.e. advertising fertility to attract mates. We studied the temporal patterns of sexual swellings, timing of ovulation and female reproductive status in wild white-handed gibbons (Hylobates lar) at Khao Yai National Park, Thailand, where this species has a variable social organization. We established fecal progestogen profiles in fifteen cycles of eight cycling females and, to detect swellings outside the menstrual cycle, five pregnant and six lactating females. In 80% of menstrual cycles, ovulation and maximum swelling phase (duration: Ø 9.3 days; 42.8% of cycle length), overlapped tightly. The probability of ovulation peaked on day 3 of the maximum swelling period. Nevertheless, the temporal relationship between maximum swelling and probability of ovulation varied from day -1 to day 13 of the swelling period and three times ovulations fell outside the maximum swelling phase. The different swellings phases occurred in similar proportions in cycling and pregnant, but not lactating females, which were rarely swollen. Despite their smaller size, gibbons' sexual swellings probably serve functions similar to those suggested for exaggerated swellings by the graded-signal hypothesis, which predicts that sexual swellings indicate the probability of ovulation, without allowing males to pinpoint its exact time.

Analysis of Variance↗

PubMed2000

Probability ratings in claustrophobic patients and normal controls.

Forty-nine DSM-IV diagnosed claustrophobics and 49 sex- and age-matched community controls, without any current or past psychiatric disorder, were asked to estimate the probability that three types if events would occur if they were in the described situations. The events were claustrophobic, generally negative, and positive in nature. The results showed that claustrophobics significantly overestimated the probability of events they specifically feared, i.e. the claustrophobic events, while there was no difference between the groups regarding generally negative events and positive events. This finding remained when the higher scores for claustrophobics on the Claustrophobia scale and the Anxiety Sensitivity Index were covaried out. The conclusion that can be drawn is that claustrophobics' probability ratings are characterized by distortions that are specifically connected to anxiety-arousing events and not negative events in general. The hypothesis is proposed that this may be explained by an exaggerated use of simplified rules-of-thumb for probability estimations that build on availability in memory, simulation, and representativity.

Adult↗