Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Binomial Distribution”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12Linked to original sources
PubMed2003

Does information sharing promote group foraging?

Individuals may join groups for several reasons, one of which is the possibility of sharing information about the quality of a foraging area. Sharing information in a patch-foraging scenario gives each group member an opportunity to make a more accurate estimate of the quality of the patch. In this paper we present a mathematical model in which we study the effect of group size on patch-leaving policy and per capita intake rate. In the model, group members share information equally in a random search for food. Food is distributed in patches according to a negative binomial distribution. A prediction from our model is that, the larger the group, the earlier each group member should leave the current patch. We also find that the benefit from enhanced exchange of information does not exceed the cost of sharing food with group members. The per capita intake rate decreases as the group size increases. Therefore, animals should only form groups when other factors outweigh the costs, which is easiest to achieve when the travelling time is short.

Animal Communication↗
PubMed1977

Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle.

Total capillary length, capillary segment length, and number of anastomoses per capillary were measured in rat gracilis muscle at rest and after 2 min of phasic contraction. Mean values of the foregoing variables at rest (+/-SD) were, respectively, 1,012 micronm +/- 484, 409 micron +/- 274, and 0.83 +/- 1.09. Total capillary lengths are well described by the gamma distribution, number of anastomoses by the negative binomial distribution, and segment length by the Weibull distribution. Contraction has no significant effect on the means or the frequency distributions, indicating that: 1) pressure gradients between adjacent capillaries are small, and 2) intercapillary anastomoses do not improve flow distribution in exercise. Erythrocyte velocities observed in resting muscle (Burton, K. S., and P. C. Johnson. Am J. Physiol. 223: 517-524, 1972) were shown to be adequately characterized by the gamma distribution. From these velocities and the observed distribution of path lengths, we computed an estimated distribution of capillary transit times. Mean transit time was 4.29 s. The median was 2.45 s, and 11% of values exceeded 8 s. The range was 90 ms-43 s. This heterogeneity of transit times should profoundly affect calculations of O2 transport and the shape of indicator dilution curves.

Animals↗
PubMed2005

Variation among faecal egg counts following natural nematode infection in Scottish Blackface lambs.

Faecal egg counts were examined in 2 flocks of naturally infected Scottish Blackface sheep in southern and central Scotland. The distribution of mean counts was right skewed and similar to a gamma distribution. The counts varied with month, with mean counts rising from May to July, then falling but rising again in October, although data within each year did not always show such a clear pattern. There was no significant difference in mean egg count between the 2 farms examined. The distribution of egg count variances was also right skewed and conformed to a gamma distribution. There was a strong relationship between the mean and the variance for each population, implying that variation among populations in variances largely mirrored variation in mean egg counts. Populations with high mean egg counts and variances did not necessarily have more adult nematodes but had a greater number of adult nematodes from species other than Teladorsagia circumcincta, particularly Cooperia spp., Trichostrongylus axei and Trichostrongylus vitrinus. The contribution of different parasite species to the egg count explains the relatively poor and inconsistent fit of the negative binomial distribution to faecal egg counts in lambs.

Albendazole↗
PubMed1992

A search for Parelaphostrongylus andersoni in white-tailed deer from Maine.

Longissimus dorsi muscles from 42 white-tailed deer (Odocoileus virginianus) from Maine (USA) were examined for the Parelaphostrongylus andersoni. No adult nematodes were found. Prevalence based on the Poisson approximation of a binomial distribution could have been between 0 and 9% (95% C.I.). However, based on prevalence documented elsewhere (10 to 18%), it is unlikely that P. andersoni occurs in white-tailed deer in central Maine.

Animals↗
PubMed1990

A bivariate negative binomial model to explain traffic accident migration.

The phenomenon of "regression to the mean" is now widely known in the study of the effectiveness of remedial treatment of traffic accident blackspots. What happens is that the criterion used for selection of sites at which treatment is to be applied gives rise to bias in the estimate of the effectiveness: the conditional expectation of the after frequency is less than the true mean, even if the treatment is totally ineffective. It has been reported in some previous studies that accident "migration" has been observed. This is the phenomenon whereby the accident rate apparently rises at sites that are untreated but that are neighbours to treated sites. If this were a genuine effect, it would have serious implications for the assessment of remedial treatments. This paper aims to explain this migration effect in purely probabilistic terms, without recourse to the concept of physical migration. The model used is a new bivariate negative binomial distribution, incorporating spatial correlation between the true mean site accident rates. As with the regression to mean effect, the migration effect can then be explained in terms of the conditioning implicit in the selection process.

Accidents, Traffic↗
PubMed1992

[The definition of the forms of the epidemic process in intestinal infections].

A method for the identification of the forms of the epidemic process in dysentery (annual, seasonal and outbreak forms) has been worked out. The method is based on the calculation of the upper limits of annual and seasonal morbidity from the data on the period of several years with the use of the formulae of binomial distribution, serving as the mathematical model of alternative random values, such as morbidity. The comparison of actual morbidity for each year of the analyzed period with the upper limits of annual and seasonal morbidity helps identify the form of the epidemic process.

Binomial Distribution↗
PubMed1989

[Optimum number of mixed peripheral blood samples by membrane filtration technique for mass blood survey of filariasis].

The membrane filtration technique has been used widely in the evaluation of effect of control and survey of filariasis. The present study was made to explore an optimum number of mixed peripheral blood samples and a mathematical model of work load for this method in surveying filariasis. By analysing the correlation between the microfilaremia rate and the optimum number of mixed peripheral blood samples and applying the theory of Binomial Distribution or Poisson Distribution, the authors reckoned a table for estimating the number of filariasis cases in villages with different microfilarial rates and different population as well as the optimum number of mixed peripheral blood samples.

Animals↗
PubMedDate not supplied

Making sense of sparse rating data in collaborative filtering via topographic organization of user preference patterns.

We introduce topographic versions of two latent class models (LCM) for collaborative filtering. Latent classes are topologically organized on a square grid. Topographic organization of latent classes makes orientation in rating/preference patterns captured by the latent classes easier and more systematic. The variation in film rating patterns is modelled by multinomial and binomial distributions with varying independence assumptions. In the first stage of topographic LCM construction, self-organizing maps with neural field organized according to the LCM topology are employed. We apply our system to a large collection of user ratings for films. The system can provide useful visualization plots unveiling user preference patterns buried in the data, without loosing potential to be a good recommender model. It appears that multinomial distribution is most adequate if the model is regularized by tight grid topologies. Since we deal with probabilistic models of the data, we can readily use tools from probability and information theories to interpret and visualize information extracted by our system.

Behavior↗
PubMed1987

On the theory of partially inbreeding finite populations. I. Partial selfing.

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities beta and 1 - beta of reproduction by selfing and by random mating. It is assumed that beta much greater than N-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between-lines variance of the fraction of copies of a locus that are identical in two random separate individuals in an equilibrium population are obtained under the assumption that there is an infinite number of possible alleles. It is found that the theory for random mating populations holds if the effective population number is Ne = N'/(1 + FIS), where FIS is the inbreeding coefficient at equilibrium when N is infinite and N' is the reciprocal of the probability that two gametes contributing to random separate adults come from the same parent. When there is a binomial distribution of successful gametes emanating from each adult, N' = N. An approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is found to be 2(N'/N)(FISS1 + (1 - FIS)S2), where S1 and S2 are the selective advantages of AA and AA in comparison with AA. In the last section it is shown that if there is partial full sib mating and binomial offspring distributions Ne = N/(1 + 3FIS).

Alleles↗
PubMed1993

Fixing the number of events in large comparative trials with low event rates: a binomial approach.

In designing large clinical trials where the event rates are low, capabilities can be improved if one fixes the number of events rather than the number of patients. The dependent variable, the number of events in the treatment group, has essentially an unconditional binomial distribution. Simple tables giving the minimum detectable difference are provided for common type I error values and power. Implications for sequential monitoring are also presented. The methods can be applied to large randomized, stratified trials utilizing censored survival data, planned under proportional hazards and equal target population competing losses, provided that event rates are low.

Binomial Distribution↗
PubMed2000

A priori estimation of accuracy and of the number of wells to be employed in limiting dilution assays.

The use of limiting dilution assay (LDA) for assessing the frequency of responders in a cell population is a method extensively used by immunologists. A series of studies addressing the statistical method of choice in an LDA have been published. However, none of these studies has addressed the point of how many wells should be employed in a given assay. The objective of this study was to demonstrate how a researcher can predict the number of wells that should be employed in order to obtain results with a given accuracy, and, therefore, to help in choosing a better experimental design to fulfill one's expectations. We present the rationale underlying the expected relative error computation based on simple binomial distributions. A series of simulated in machina experiments were performed to test the validity of the a priori computation of expected errors, thus confirming the predictions. The step-by-step procedure of the relative error estimation is given. We also discuss the constraints under which an LDA must be performed.

Binomial Distribution↗
PubMed2001

Sample size tables for exact single-stage phase II designs.

Tables for single-phase II trials based on the exact binomial distribution are presented. These are preferable to those generated using Fleming's design, which are based on the normal approximation and can give rise to anomalous results. For example, if the upper success rate is accepted, the lower success rate, which the trial is designed to reject, may be included in the final confidence interval for the proportion being estimated.

Antiemetics↗
PubMed2000

Negative binomial additive models.

The generalized additive model is extended to handle negative binomial responses. The extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family. The methodology is applied to data involving DNA adduct counts and smoking variables among ex-smokers with lung cancer. A more detailed investigation is made of the parametric relationship between the number of adducts and years since quitting while retaining a smooth relationship between adducts and the other covariates.

Algorithms↗
PubMed1993

Sequential equivalence testing and repeated confidence intervals, with applications to normal and binary responses.

We propose group sequential tests of the equivalence of two treatments based on ideas related to repeated confidence intervals. These tests adapt readily to unpredictable group sizes, to the possibility of continuing even though a boundary has been crossed, and to nonnormal observations. In comparing two binomial distributions, the required sample size depends strongly on the average success probability and an adaptive choice of group size is needed to produce an efficient test meeting specified error probability constraints. A special case is the experiment where interim analyses are performed, not for the purpose of early termination but simply to adjust the sample size so that nominal error rates will be guaranteed, despite the presence of a nuisance parameter.

Binomial Distribution↗
PubMed2004

Incidence of serious adverse events during nocturnal polysomnography.

OBJECTIVES: The purpose of the study was to verify whether minimal concern is warranted in regard to serious adverse effects in the sleep laboratory. DESIGN: A prospective multicenter study PARTICIPANTS: Three scoring teams for 17 sleep laboratories. METHODS: Reports of adverse events occurring during polysomnography or identified upon scoring a study were collected over an 18-month time period. Incidence of mortality and adverse events were evaluated using a binomial distribution based on the Bernoulli process. RESULTS: Of 16,084 studies, the mortality rate during or 2 weeks after an adverse event, as noted, was 0.006%, and the overall rate of adverse events was 0.35%. CONCLUSIONS: Adverse event rates are low; however, procedures for handling medical emergencies or adverse events during or after polysomnography are prudent, and those studies performed for research should include preparedness for the possibility of adverse events.

Adult↗
PubMed2001

An estimation of the size of the water cluster present at the cleavage site of the water splitting enzyme.

In time-dependent measurements of oxygen evolution in tobacco thylakoid membranes we varied the fraction of H(2)(18)O and the temperature and measured water splitting as (18)O(2), (16)O(18)O, and (16)O(2) by mass spectrometry. We show that the approach to the equilibrium of the system after H(2)(18)O addition can be very well understood in terms of the diffusion of water molecules. The equilibrium states of (16)O(2), (16)O(18)O, and (18)O(2) evolution differ from the theoretical binomial distributions, which are expected under the prerequisite of ideal mixing of the water molecules and that of the chemical equivalence of H(2)(18)O and H(2)(16)O for an infinite cluster. The presence of this deviation means that there is a typical size of water clusters having access to cleavage by the water splitting enzyme. We estimated that this cluster contains about 12+/-2 water molecules.

Algorithms↗
PubMed1989

Graphical and statistical approaches to data analysis for in situ hybridization.

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution. The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. From a theoretical perspective, the probabilistic relationship between beta-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1988

The detection and importance of outliers in the in vivo micronucleus assay.

Micronucleus tests are generally analysed statistically for differences between the means of treated and control groups. 'Outliers' may either be rejected or grouped together with data from less responsive animals. In either case, a valuable indicator of a small, more sensitive (responder) population sub-group may then be missed. To alleviate this problem, we have developed an additional strategy, based on historic data, for the detection of any single animal with a significant increase in micronucleated polychromatic erythrocytes in an otherwise insignificant treatment group. Forty-one sets of negative control data (of five male and five female CD-1 mice each) have been analysed. Within each set there were no significant male to female differences and data were consistent with a Poisson distribution. Pooled data from all 41 sets showed slightly hyper-Poisson variation and were adequately described by the negative binomial distribution. The negative binomial probability generating function was used to show that six or more micronuclei per 1000 polychromatic cells from one treated animal would be significant for our laboratory, methodology and strain of mouse, provided that concurrent negative control data conformed with historic values. Changes in methodology desirable for this type of analysis include increasing the number of mice in each test group and possible compensation by a reduction in the number of test groups.

Animals↗