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Distances between identical symbols in information strings (biological, language, computer programs (*.exe files) are described with a different precision with four distributions: exponential, Weibull, log-normal and negative binomial. The correlations are sometimes highly significant.
The authors used allozymes encoded by nuclear genes and restriction enzyme analysis of mitochondrial DNA (mtDNA) to study secondary contact between westslope (Salmo clarki lewisi) and Yellowstone cutthroat trout (Salmo clarki bouvieri) in Forest Lake, Montana. Eleven diagnostic allozyme loci identified this as a random-mating hybrid swarm. No parental, first-generation hybrid or backcross genotypes were detected in the sample (N = 33), and genotype distributions at all the variable loci conform to binomial expectations. There is little linkage disequilibrium between the diagnostic loci, indicating that the nuclear genomes of the two subspecies are largely randomly associated. The allozymes and mtDNA give identical estimates of the proportional genetic contribution of each subspecies. Thus, males and females from both subspecies have contributed equally to this hybrid swarm. Although these subspecies have accumulated substantial genetic divergence between their nuclear (Nei's D = 0.34) and mitochondrial (2% sequence divergence) genomes, this has not resulted in a genetic barrier to exchange between them.
The effect of ethanol on the structure of DNA confined to mica in the presence of Mg2+was examined by varying the ethanol concentration and imaging the DNA by atomic force microscopy. Contour length measurements of the DNA show a transition from all-B-form at 0% ethanol to all-A-form at >25% ethanol. At intermediate ethanol concentrations, contour lengths suggest that individual molecules of air-dried DNA are trapped with mixed compositions of A-form and B-form. The relative composition depends on the ethanol concentration. Fitting the length distributions at intermediate ethanol concentrations to a simple binomial model results in an upper bound estimate for the A-form and B-form domains of approximately 54 bp in the individual molecules. In addition to length changes, the apparent persistence length of DNA decreases with increasing ethanol concentration. At high concentrations of ethanol (>20%), DNA formed several higher order structures, including flower shaped condensates and toroids.
1. A statistical analysis has been made of the transmitter release at the hair cell afferent fibre synapse in the sacculus of the goldfish, using the amplitude of the excitatory post-synaptic potentials (e.p.s.p.s) in response to stimulus tone as a measure of the transmitter release under application of tetrodotoxin. 2. Application of binomial statistics allowed a direct calculation of the mean probability of release (p) and the readily available store (n), and the X2-test showed that the binomial predictions fitted fairly well with the observed distribution of the responses. 3. Adaptive rundown of e.p.s.p.s during sound stimulation, i.e. the successive rundown in the size of the mean quantal content (m), was found to be associated with a reduction in the size of parameter n, but not of p. 4. A marked negative correlation was demonstrated between the amplitude of two consecutive e.p.s.p.s, supporting the depletion hypothesis of the adaptive rundown of e.p.s.p.s. 5. The increase in the e.p.s.p. amplitude and the increase in the mean quantal content, m, brought about by an increase in the tone intensity were found mostly explicable in terms of an increase in the statistical parameter n. The probability parameter p was found largely in invariable, although in certain instances the increase in m was also accompanied by a slight increase in the parameter p.
Seasonal population dynamics of the digenean Phyllodistomum pawlovskii in the urinary bladder of the bullhead catfish, Pseudobagrus fulvidraco, were investigated in Liangzi Lake in the flood plain of the Yangtze River in China from February 2001 to July 2002. The overall prevalence of the parasite was high, 41.5% (n = 1,476), while the mean abundance was relatively low, 1.24 +/- 2.11. The parasite exhibited evident seasonality in changes of prevalence and abundance. In brief, prevalence and abundance were very low in midwinter (January), but increased and remained relatively high in other seasons and months. The distribution pattern of this parasite in the fish was overdispersed, with a variance to mean ratio > 1, but its frequency distribution could not be described by the negative binomial model. There were positive correlations between the number of the parasites per fish and the age and length of the fish; a peaked age-parasite abundance curve was not detected in the parasite-host association. It is suggested that the parasite P. pawlovskii has little effect on the population structure of the bullhead catfish.
Properties of procedures for interval estimation of the maximum tolerable dose (MTD) in a Phase I clinical trial are examined, using a two-stage stochastic sampling scheme (Storer, 1989) as a paradigm for development. Although the likelihood function for the data arising from such a scheme is identical to one arising under a conditional binomial sampling assumption, intervals based on the exact distribution of the usual large-sample statistics under this assumption do not offer improvement over unadjusted intervals. However, consideration of the distribution of these statistics based on the true stochastic sampling scheme can lead to the construction of intervals with correct coverage probabilities that do not depend on the true values of the model parameters. Membership in the confidence set can be evaluated by Monte Carlo simulation at a restricted maximum likelihood estimate of the nuisance slope parameter, despite upward bias in its estimation from the up-and-down sampling scheme. The lack of information in the small-sample setting is reflected in a large proportion of confidence intervals that include infinite values for the MTD, especially when the dose-response curve is shallow. Intervals based on a likelihood ratio criterion perform best in this regard.
The Trichuris trichiura worm burdens of 23 children living in a Place-of-Safety in Kingston, Jamaica, were assessed by stool collection for more than five days after treatment with mebendazole. This procedure was repeated after a seven-month period of natural re-infection. For both collections the maximum rate of worm expulsion was achieved on the fourth day after starting treatment. The worm population distributions were overdispersed and well described by the negative binomial probability model (k = 0.29) in each case. For any one individual, the number of worms passed on the first expulsion was unrelated, absolutely or relatively, to the number passed on the second. These data suggest that: knowledge of the time dependency of helminth expulsion is essential for the accurate estimation of worm burdens by this method; populations of Trichuris are more highly aggregated than those of Ascaris and may thus be more susceptible to control by selective rather than random chemotherapy; and the inherent predisposition of hosts to infection may be of minor importance in determining the distribution of worms in the population-heavily infected hosts appear no more or less likely to acquire large worm burdens on subsequent exposures.
The spatial distribution of the citrus mealybug, Planococcus citri (Risso) (Homoptera: Pseudococcidae), was studied in citrus groves in northeastern Spain. Constant precision sampling plans were designed for all developmental stages of citrus mealybug under the fruit calyx, for late stages on fruit, and for females on trunks and main branches; more than 66, 286, and 101 data sets, respectively, were collected from nine commercial fields during 1992-1998. Dispersion parameters were determined using Taylor's power law, giving aggregated spatial patterns for citrus mealybug populations in three locations of the tree sampled. A significant relationship between the number of insects per organ and the percentage of occupied organs was established using either Wilson and Room's binomial model or Kono and Sugino's empirical formula. Constant precision (E = 0.25) sampling plans (i.e., enumerative plans) for estimating mean densities were developed using Green's equation and the two binomial models. For making management decisions, enumerative counts may be less labor-intensive than binomial sampling. Therefore, we recommend enumerative sampling plans for the use in an integrated pest management program in citrus. Required sample sizes for the range of population densities near current management thresholds, in the three plant locations calyx, fruit, and trunk were 50, 110-330, and 30, respectively. Binomial sampling, especially the empirical model, required a higher sample size to achieve equivalent levels of precision.
Electrocardiographic rhythm strips were analyzed from three patients who had frequent unifocal extrasystoles. Parasystole was excluded in all three cases. Analysis of the distributions of the numbers (S) of conducted sinus beats between extrasystoles revealed that the distributions conformed to two variants of concealed quadrigeminy (namely, the "S = 4n" and "S = 4n - 2" variants) and to one variant of concealed quintageminy (namely, the "S = 5n - 2" variant). The binomial theorem was used to test the likelihoods that these patterns of distribution of extrasystoles could occur on the basis of chance alone; the probabilities were all extremely small.
Models for estimating the probability of occurrence of a species in the presence of imperfect detection are important in many ecological disciplines. In these "site occupancy" models, the possibility of heterogeneity in detection probabilities among sites must be considered because variation in abundance (and other factors) among sampled sites induces variation in detection probability (p). In this article, I develop occurrence probability models that allow for heterogeneous detection probabilities by considering several common classes of mixture distributions for p. For any mixing distribution, the likelihood has the general form of a zero-inflated binomial mixture for which inference based upon integrated likelihood is straightforward. A recent paper by Link demonstrates that in closed population models used for estimating population size, different classes of mixture distributions are indistinguishable from data, yet can produce very different inferences about population size. I demonstrate that this problem can also arise in models for estimating site occupancy in the presence of heterogeneous detection probabilities. The implications of this are discussed in the context of an application to avian survey data and the development of animal monitoring programs.
Modeling of developmental toxicity studies often requires simple parametric analyses of the dose-response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose-response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta-binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.
We investigated the randomness and uniqueness of human iris patterns by mathematically comparing 2.3 million different pairs of eye images. The phase structure of each iris pattern was extracted by demodulation with quadrature wavelets spanning several scales of analysis. The resulting distribution of phase sequence variation among different eyes was precisely binomial, revealing 244 independent degrees of freedom. This amount of statistical variability corresponds to an entropy (information density) of about 3.2 bits mm(-2) over the iris. It implies that the probability of two different irides agreeing by chance in more than 70% of their phase sequence is about one in 7 billion. We also compared images of genetically identical irides, from the left and right eyes of 324 persons, and from monozygotic twins. Their relative phase sequence variation generated the same statistical distribution as did unrelated eyes. This indicates that apart from overall form and colour, iris patterns are determined epigenetically by random events in the morphogenesis of this tissue. The resulting diversity, and the combinatorial complexity created by so many dimensions of random variation, mean that the failure of a simple test of statistical independence performed on iris patterns can serve as a reliable rapid basis for automatic personal identification.
The pool adjacent violator algorithm Ayer et al. (1955, The Annals of Mathematical Statistics, 26, 641-647) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972, Statistical Inference under Order Restrictions, Wiley, New York). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of 'ordered' multinomial parameters p(i)= (p(1i),p(2i),.,p(mi)) for 1 <or=i <ro=k, where ordered means that p(j1) <or=p(j2) <or=<or=p(jk) for each j with 1 <or=j <or=m-1. The data consist of k independent observations X(1),., X(k) where X(i) has a multinomial distribution with probability parameter p(i) and known index n(i)\geq 1. By making use of variants of the pool adjacent violator algorithm, we obtain a simple algorithm to compute the maximum likelihood estimator of p(1),., p(k), and demonstrate its convergence. The results are applied to nonparametric maximum likelihood estimation of the sub-distribution functions associated with a survival time random variable with competing risks when only current status data are available (Jewell et al. 2003, Biometrika, 90, 183-197).
PURPOSE: Individual expectations among community-dwelling older adults and their subsequent effect on placement status have recently been considered. Previous studies, however, have been limited by eligibility and exclusion criteria, treating expectations as a continuous measure, omitting potential confounders, and ignoring Race x Gender interactions. DESIGN AND METHODS: We used data on 6,242 Black or White self-respondents who were 70 years old or older when they were enrolled in the survey of Assets and Health Dynamics Among the Oldest Old. We modeled expectations for nursing home placement over the next 5 years, as well as actual placement status, by using multivariable multinomial and binomial logistic regression models. RESULTS: Expectations are not normally distributed: 14% of the participants refused to answer, 51% estimated no chance, 10% indicated a 1% to 50% chance, 21% indicated an 11% to 50% chance and 4% indicated a 51% to 100% chance. Age, gender, education, social supports, and health status were associated with expectations, as well as an interaction effect for Black men. Age, social supports, health status, prior hospital or nursing home use, and expectations were associated with subsequent placement. IMPLICATIONS: Black and White older adults' expectations for nursing home placement rationally reflect their individual risk profiles and are associated with subsequent placement status. The expectations question may facilitate the early identification of high-risk individuals for further evaluation.
Healthy human skeletal muscles are composed of two distinguishable types of fibre, apparently randomly arranged within fascicles (bundles of fibres surrounded by connective tissue). Large groups of fibres of the same type indicate a neurogenic muscle disorder. An objective method for detecting nonrandom arrangements of fibres could improve the diagnosis of such disorders, particularly at an early stage. The number of enclosed fibres (NEF)--fibres surrounded by others of the same type--is considered here as a measure of nonrandomness. The distribution of NEF is shown to be approximately negative binomial for a non-free-sampling model, which is then compared with a free-sampling model studied previously. A modification for a known boundary effect is also investigated. The models are applied to data from m. vastus lateralis obtained post mortem from 24 previously healthy men. Finally, the relationship between size of biopsy and the accuracy of predictions is discussed.
We determine the liquid-state thermodynamics for a model energy landscape corresponding to soft spheres with a mean-field attraction. We consider two approximations, in which the distribution of potential energy minima is either Gaussian or binomial, and for each we calculate the liquid spinodal, binodal, and "effective" glass transition locus. The resulting models provide a unified description of the liquid state across the complete range from low-temperature glassiness to high-temperature instability with respect to the vapor phase.
The prevalence and distribution of Echinococcus granulosus in domestic dogs was examined in three dog populations in the Durazno region of Uruguay. The prevalence was 19.7 per cent in 704 dogs successfully purged with arecoline hydrobromide. Higher prevalences were detected in dogs from the rural area (30.0 per cent) and the village of La Paloma (25.9 per cent) than in the town of Sarandi del Yi (7.9 per cent). The frequency distribution of E granulosus was overdispersed (k, the negative binomial parameter = 0.08), with only a few animals harbouring heavy infections. The results of a questionnaire showed that the prevalence was greatest in male dogs, in dogs that were not kennelled, in dogs that had access to fields and in dogs that were not dosed with praziquantel. Dogs that were given raw sheep offal by their owners were no more likely to be parasitised than other dogs; this may reflect the inaccuracy of the owners' replies, or that the dogs were being infected outside their home.
BACKGROUND: The genetic differences among HIV-1 subtypes may be critical to clinical management and drug resistance surveillance as antiretroviral treatment is expanded to regions of the world where diverse non-subtype-B viruses predominate. METHODS AND FINDINGS: To assess the impact of HIV-1 subtype and antiretroviral treatment on the distribution of mutations in protease and reverse transcriptase, a binomial response model using subtype and treatment as explanatory variables was used to analyze a large compiled dataset of non-subtype-B HIV-1 sequences. Non-subtype-B sequences from 3,686 persons with well characterized antiretroviral treatment histories were analyzed in comparison to subtype B sequences from 4,769 persons. The non-subtype-B sequences included 461 with subtype A, 1,185 with C, 331 with D, 245 with F, 293 with G, 513 with CRF01_AE, and 618 with CRF02_AG. Each of the 55 known subtype B drug-resistance mutations occurred in at least one non-B isolate, and 44 (80%) of these mutations were significantly associated with antiretroviral treatment in at least one non-B subtype. Conversely, of 67 mutations found to be associated with antiretroviral therapy in at least one non-B subtype, 61 were also associated with antiretroviral therapy in subtype B isolates. CONCLUSION: Global surveillance and genotypic assessment of drug resistance should focus primarily on the known subtype B drug-resistance mutations.