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Results for “Poisson Distribution”

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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↗

PubMed1991

A two-state Markov mixture model for a time series of epileptic seizure counts.

This paper discusses a model for a time series of epileptic seizure counts in which the mean of a Poisson distribution changes according to an underlying two-state Markov chain. The EM algorithm (Dempster, Laird, and Rubin, 1977, Journal of the Royal Statistical Society, Series B 39, 1-38) is used to compute maximum likelihood estimators for the parameters of this two-state mixture model and extensions are made allowing for nonstationarity. The model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple Poisson distribution and Poisson regressions. Some simulation results are also presented to demonstrate the feasibility of this model.

Biometry↗

PubMed1978

Statistical aspects of the treponemal counts in the TPI test.

A method of counting treponemes in randomly selected visual fields is described. It was found that Treponema pallidum is distributed as a Poisson distribution among the visual fields and also among samples drawn from the same suspension. Immobilized treponemes are binomally distributed among the total number of treponemes. Application of the parameters of the Poisson and the binomial distributions should be made in order to determine the dosage of T. pallidum in animal experimentation and to evaluate the outcome of the TPI test. Some statistical aspects of the investigation of treponemal survival are presented.

Probability↗

PubMedDate not supplied

A pseudo-Poisson noise model for simulation of positron emission tomographic projection data.

Although radioactive decay obeys Poisson statistics, because of the corrections that are applied to the projection data prior to reconstruction, the noise in positron emission tomography (PET) projections does not follow a Poisson distribution. Use of Poisson noise when simulating PET projections in order to test the performance of reconstruction and processing techniques is therefore not appropriate. The magnitude of PET projection noise was observed to be as much as 10 to 100 times greater than Poisson noise in some instances. A quadratic function was found to fit the relationship between noise power spectral density and total projection count. The coefficients of the quadratic function were determined for projections of different tracer distributions and types. Using these observations, a method of simulating PET projections was developed based on a pseudo-Poisson noise model. Projections simulated according to this method are good approximations to real projection data and take into account the characteristics of individual PET cameras and particular tracer distributions. Such simulated projections have been valuable in predicting the performance of reconstruction algorithms. This approach can also be applied to single photon emission tomography.

Computer Simulation↗

PubMed1991

[Clustering of suicides under age 20--seasonal trends and the influence of newspaper reports].

The existence of temporal clustering of suicides was analyzed by comparing the distribution of weekly numbers of suicides under age 20 in Japan (1982-1987) with a Poisson distribution. The linkage between newspaper reports about teenage suicides and these clusters of suicides was examined in an ecologic study. The following results were obtained: 1) The distribution of weekly numbers of suicides under age 20 was not consistent with a Poisson distribution. The observed numbers for weeks with clustering was higher than the expected numbers. Therefore it is suspected that teenage suicides was not an independent occurrence but clustered in specific weeks with clustering observed in April and between the 15th and 25th weeks in 1986. 2) The age and sex characteristics of those who committed suicide during the observed clusters every April did not differ from that of suicide victims for the rest of the year. The incidence ratio for suicide between 15th and 25th weeks in 1986 compared to the same period for other years was higher in girls than in boys, and higher in younger teenagers than older teenagers. Analysis by prefecture of suicides which occurred between the 15th and 25th weeks in 1986 showed high incidences for Hokkaido, Tohoku, Chugoku, and Shikoku blocks, and low incidences for the Kanto and Kinki blocks. 3) Twenty news articles reporting teenage suicides with headings much larger than four columns appeared in the Asahi Newspaper in 1982-87. Significant linkage between newspaper reports about teenage suicides and trend of weekly numbers of suicides in 1985 and 1986 was not observed. 4) Weekly numbers of suicides significantly increased following newspaper reports on January 23rd 1985 and on April 8th 1986, describing a suicide caused by battering, and a jumping suicide of a young singer who was popular among teenagers, respectively. However no increase in the number of suicides was observed following other newspaper reports.

Adolescent↗

PubMed1990

Variability in expression of common fragile sites: in search of a new criterion.

Fragile sites are nonrandom, heritable sites on chromosomes that can be induced to form gaps, breaks, and rearrangements under specific conditions. There is currently no established criterion to define a common fragile site. We applied seven published criteria to our data from three groups of subjects: (1) three pairs of like-sexed twins, (2) four unaffected von Hippel-Lindau (VHL) family members, and (3) six patients affected with VHL disease. Substantial differences were present in the numbers of sites considered positive by these criteria. While some of this variability can be attributed to technical factors, our data illustrate the problems in comparing results from different studies to assess the significance of fragile sites. A recently published criterion is based upon the Poisson distribution. We found this criterion to be flawed in its presentation, and furthermore, the Poisson distribution did not provide an adequate approximation to our data. We propose here an alternative approach based upon the negative binomial distribution.

Binomial Distribution↗

PubMed1992

The origin of His+ revertants of Salmonella typhimurium obtained on selective medium.

The spontaneous reversion to His+ of the Salmonella typhimurium alleles hisD3052 and hisG46 was investigated. In fluctuation tests, the expected "jackpot" distribution of His+ revertants was not observed. The experimental distributions were close to Poisson distribution. The redistribution test showed no significant differences in the His+ colony counts between spread and unspread plates. An attempt at indirect selection of His+ revertants in fluid medium failed. It was also shown that the mean number of His+ reversion events and the mean number of revertants per plate were similar. At the same time, kanamycin-resistant mutants had jackpot distribution. Selection for His+ revertants (histidine starvation) did not increase mutation to Kanr.

Alleles↗

PubMed1992

Theoretical epidemiology on bovine ephemeral fever outbreaks in Tanegashima Island, Kagoshima Prefecture of Japan in 1988.

From the end of September to November 1988, a compact scale of bovine ephemeral fever (BEF) outbreaks occurred suddenly in Tanegashima island of Kagoshima Prefecture, southern part of Kyusyu island of Japan. The BEF outbreak pattern showed epidemical characteristics as follows; (1) outbreak spread from few foci to zone during one month, and (2) the disease might be transmitted in farms with a fixed probability of adequate contact. By using the above aspects, we attempted to analyze the disease theoretically with the application of Poisson distribution and Reed-Frost model. The BEF incidence in farms was in well accord with the Poisson distribution. As the very rare event occurred in unit time or in unit area in this epidemic, the cattle population at risk were equivalently susceptible to BEF virus in this island, due to the influence of no vaccination to BEF control before the first outbreak. Similarly, the epidemic curve of the Reed-Frost model was proved to fit well the incidence observed in a farm, and the probability of adequate contact was induced as p = 0.226. If the cattle population is less than 5 in this farm, the outbreak would not occur in the first instance.

Animals↗

PubMed1992

Effects of partial inbreeding on fixation rates and variation of mutant genes.

Diffusion methods were used to investigate the fixation probability, average time until fixation and extinction, and cumulative heterozygosity and genetic variance for single mutant genes in finite populations with partial inbreeding. The critical parameters in the approximation are the coefficient of inbreeding due to nonrandom mating (F) and the effective population size (Ne), which also depends on F and the variance of family size. For large Ns, the fixation probability (u) is u = 2(Ne/N)s (F + h - Fh), where N is the population census, s is the coefficient of selection of the mutant homozygote and h is the coefficient of dominance. For Poisson family size (independent Poisson distributions of selfed and nonselfed offspring with partial selfing, and independent Poisson distributions of male and female numbers with partial sib mating), Ne = N/(1 + F), and the time until fixation is approximately equal to Ne/N times the time to fixation with random mating, but this relation does not hold, however, for other distributions of family size. The cumulative nonadditive variance until fixation or loss for dominant genes is reduced with increasing F while for recessive genes it is increased with intermediate values of F. The average time until extinction of deleterious mutations is reduced by increasing F. This reduction, when expressed as a proportion, is approximately independent of the initial gene frequency as well as the selective disadvantage if this is large.

Animals↗

PubMed1992

Bronchoalveolar lavage cellularity. The distribution in normal volunteers.

Bronchoalveolar lavage (BAL) is used to obtain inflammatory cells from the lung. For clinical research, parametric statistics are frequently used to compare cells present in BAL of patients with lung disease with cells present in BAL of normal subjects. To determine if these populations can be compared in this manner we performed BAL on 111 never-smoking, normal volunteers and determined: (1) the mean, median, standard deviation, and range of the cells in BAL; (2) whether the data are normally distributed and satisfy the criteria for use of parametric statistical analysis. The BAL cellularity was expressed as a percentage of total cells, cells per milliliter return, and total cells per lavage. Regardless of the means of expression, no measure of BAL cellularity (total cells, macrophages, lymphocytes, neutrophils, or eosinophils) conformed to the normal (bell-shaped) distribution when tested for goodness of fit with the G statistic (all p < 0.001). The lack of fit to the normal distribution was not substantially altered by either the method of expressing the data (i.e., cells per milliliter, total cells, or percent of cells) or log transformation of the data. The poor fit in all cases resulted from clumping of the data about the mean and large tails. The percent of cells were, therefore, tested for goodness of fit to the Poisson distribution, a distribution of discrete variables. The neutrophil and eosinophil percentages resulted in an excellent fit to the Poisson distribution, but macrophage and lymphocyte percentages did not.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed2026

HiCPotts: An R/Bioconductor package to identify significant interactions in chromosome conformation capture data and model sources of bias.

MOTIVATION: Chromosome Conformation Capture methods, including Hi-C, micro-C or Capture-C, are used to map chromatin interactions genome-wide. Most of the existing computational methods do not account for sources of bias (such as DNA accessibility, GC content or TE content) in the data. RESULTS: We previously developed ZipHiC, a Bayesian method based on the hidden Markov random field (HMRF) model and the Approximate Bayesian Computation (ABC), that uses zero-inflated Poisson distribution to model the noise, signal and false signal of the data and showed that this approach was able to detect bias from DNA accessibility, GC content and TE content in both Hi-C and micro-C data. Here, we present HiCPotts, another Bayesian method based on the HMRF model and the ABC that uses a zero-inflated Negative Binomial distribution instead to model the noise and signal of the data. We systematically show that HiCPotts reduces false positives and increases recovery of true interactions compared to ZipHiC, but also compared to other methods such as FastHiC, Juicer and HiCExplorer. Most importantly, we provide an R/Bioconductor package that allows modelling the noise, signal and false signal using various distributions such as the zero-inflated Negative Binomial (ZINB) and the zero-inflated Poisson distribution (ZIP). AVAILABILITY AND IMPLEMENTATION: https://bioconductor.org/packages/HiCPotts/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Approximate Bayesian Computation↗

PubMed1992

Analysis of body-length distribution of Dirofilaria immitis in the cardio-pulmonary blood vessel of naturally infected dogs in Shiga Prefecture, Japan.

Body-length frequencies of Dirofilaria immitis collected from the cardio-pulmonary blood vessel of the dogs were studied in Shiga Prefecture. Japan, in October 1983 and in January and May 1984. The frequencies were not distributed normally because they included the populations of shorter-bodied worms, probably the growing younger worms, whereas the distributions of the body length of worms collected in July 1983 were proved to fit the single normal distribution. From the results of body-length distribution analysis, the worms collected in different seasons were each composed of 1 to 3 groups with different mean body-lengths, standard deviations and composition rates and successive changes were observed in the distribution patterns. According to the analysis of population structures, the infective season was estimated to range from April or May to October or November in 1983 from the respective ages of shorter-bodied worm groups. The annual rates of first infection and re-infection in 1983 determined by the population of shorter-bodied females collected in January were 48% and 93% respectively and the number of newly infecting females per dog ranged from 1 to 27 with a geometric mean of 8.5. The numbers of newly infecting female worms were distributed following the negative binomial and Poisson distributions in newly infected and already infected dogs respectively.

Animals↗

PubMed1977

Estimates of quantal-release and binomial statistical-release parameters at rat neuromuscular junction.

Quantal-release and binomial statistical-release parameters were examined in the isolated rat diaphragm phrenic nerve preparation. The muscle resting potentials were reduced by cutting the muscle fibers to prevent muscle action potentials and contractions. The cutting technique was modified to allow persistent observation of miniature end-plate potentials (MEPPs) and end-plate potentials (EPPs) with intracellular recording techniques. Direct estimates of quantal release were examined and compared with predicted binomial and Poisson distributions. The results indicate that release is binomial when the nerve is stimulated with low- or high-frequency stimuli. The indirect method of estimating quantal release (variance method), which assumes release is described by a Poisson distribution, seriously overestimates quantal release. The binomial analysis indicates that the statistical store is small (less than 90 quanta) and that most of these quanta are released with each nerve impulse.

Animals↗

PubMed1988

Random oligonucleotide mutagenesis: application to a large protein coding sequence of a major histocompatibility complex class I gene, H-2DP.

We have used random oligonucleotide mutagenesis (or saturation mutagenesis) to create a library of point mutations in the alpha 1 protein domain of a Major Histocompatibility Complex (MHC) molecule. This protein domain is critical for T cell and B cell recognition. We altered the MHC class I H-2DP gene sequence such that synthetic mutant alpha 1 exons (270 bp of coding sequence), which contain mutations identified by sequence analysis, can replace the wild type alpha 1 exon. The synthetic exons were constructed from twelve overlapping oligonucleotides which contained an average of 1.3 random point mutations per intact exon. DNA sequence analysis of mutant alpha 1 exons has shown a point mutant distribution that fits a Poisson distribution, and thus emphasizes the utility of this mutagenesis technique to "scan" a large protein sequence for important mutations. We report our use of saturation mutagenesis to scan an entire exon of the H-2DP gene, a cassette strategy to replace the wild type alpha 1 exon with individual mutant alpha 1 exons, and analysis of mutant molecules expressed on the surface of transfected mouse L cells.

Amino Acid Sequence↗

PubMed1989

Mean and quasideterministic equivalence for linear stochastic dynamics.

In linear, stochastic dynamics it is shown that the quasideterministic population size is equivalent to the mean population size. The quasideterministic dynamics are defined by the conditional infinitesimal mean of the process. The stochastic component of the dynamics includes both Gaussian and Poisson white noise, with amplitude coefficients proportional to the population size. Generalizations are given for nonautonomous coefficients and for distributed Poisson jump amplitudes. A counter example--an exactly integrable nonlinear jump model--shows that the equivalence result does not hold for nonlinear stochastic dynamics.

Linear Models↗

PubMed1992

Routine urine drug screening at the first prenatal visit.

OBJECTIVE: The purpose of this study is to determine whether routine urine drug screening at the first prenatal visit will identify and permit early intervention for those at risk for poor outcome. STUDY DESIGN: Comparisons of maternal and neonatal outcomes between 166 randomly chosen patients with positive and 150 randomly chosen patients with negative drug screens identified by the enzyme multiplied immunoassay test were made by unpaired t test, chi 2 test, probit analysis, and tests of independent Poisson distributions. RESULTS: Forty percent of those identified denied drug use. Antepartum (p less than 0.01) and postpartum (p less than 0.05) complications were increased among drug users. Birth weight (p less than 0.001), gestational age (p less than 0.03), and head circumference (p less than 0.05) were decreased among neonates. CONCLUSION: Because of difficulty in identifying illicit substance--using patients, consideration should be given to the implementation of routine urine drug screening at the first prenatal visit in populations with a high rate of illicit substance use.

Chi-Square Distribution↗

PubMed1977

Precision of analysis for waterborne chrysotile asbestos by transmission electron microscopy.

Detailed examinations of water samples were carried out to determine the precision of analysis for chrysotile asbestos by transmission electron microscopy (TEM). Since the frequency distribution of counts fits a Poisson distribution, several statistical inferences were made, including (1) an estimate of precision, and (2) a model for determining the probability of observing chrysotile as a function of its concentration in water and magnitude of area scanned by TEM.

Asbestos↗

PubMed1977

Microdosimetry and chromosome aberrations: effects of 230 keV neutrons on Vicia faba chromosomes.

Physical energy deposition events have been related to sub-nuclear cytological events (chromosomal changes) in metaphases sequentially accumulated from the latter part of the cell cycle of Vicia faba. 230 keV neutrons produce about 0.4 recoil protons per late interphase nucleus per rad with the majority of protons traveling 1 to 2 microns from their origin, depositing energy at around 90 keV per micron. The frequency of induced abberrations is basically linear with dose, though varying through consecutive cell sampling periods because of differential induced mitotic delay. Distributions of chromosomal aberrations and total cytological events are overdispersed in relation to the Poisson distribution indicating that some proton recoils produce multiple events. When gaps and aberrations within chromosomes and multiple aberrations between chromosomes, are considered as discrete events, distributions follow Poisson expectations. About 40% of proton recoils result in observable cytological change. The highly energetic proton recoils (approximately 90 keV per micron) which can induce multiple events are the ones most likely to produce effects which result in cell death. The sphere of influence of the proton recoils is probably adequately estimated from their range (approximately 1 to 2 micron) since it seems compatible with the spatial proximity of the initial components of the resultant chromosome aberrations.

Chromosome Aberrations↗