Calculation of narrower confidence intervals for tree mortality rates when we know nothing but the location of the death/survival events

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Evolution of marine invertebrate reproductive patterns

A simple model of the evolution of reproductive patterns in marine benthic invertebrates is presented. The aim is to discuss the dichotomous distribution of forms into those which produce a large number of small eggs with planktotrophic development, and those which produce a small number of large eggs with direct or lecithotrophic development. The fecundity of adult individuals is assumed to be inversely proportional to egg size, and the mortality of planktonic larvae is assumed to be density independent and size dependent. The growth of planktonic larvae is assumed to be sigmoid with metamorphosis occurring at a given size. The model concludes that there are at most two evolutionarily stable egg sizes. Depending on larval growth rate and death rate, the metamorphosis size, a smaller egg size, or both may be evolutionarily stable. The predictions of the model are compared to patterns observed in nature. Illustrative data are supplied mainly from prosobranch molluscs.     

Estimation of Clustering Parameters Using Gaussian Process Regression

We propose a method for estimating the clustering parameters in a Neyman-Scott Poisson process using Gaussian process regression. It is assumed that the underlying process has been observed within a number of quadrats, and from this sparse information the distribution is modelled as a Gaussian process. The clustering parameters are then estimated numerically by fitting to the covariance structure of the model. It is shown that the proposed method is resilient to any sampling regime. The method is applied to simulated two-dimensional clustered populations and the results are compared to a related method from the literature.     

Modeling late entry bias in survival analysis

In a failure time analysis, we sometimes observe additional study subjects who enter during the study period. These late entries are treated as left-truncated data in the statistical literature. However, with real data, there is a substantial possibility that the delayed entries may have extremely different hazards compared to the other standard subjects. We focus on a situation in which such entry bias might arise in the analysis of survival data. The purpose of the present article is to develop an appropriate methodology for making inference about data including late entries. We construct a model that includes parameters for the effect of delayed entry bias having no specification for the distribution of entry time. We also discuss likelihood inference based on this model and derive the asymptotic behavior of estimates. A simulation study is conducted for a finite sample size in order to compare the analysis results using our method with those using the standard method, where independence between entry time and failure time is assumed. We apply this method to mortality analysis among atomic bomb survivors defined in a geographical study region.     

An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections. Part II: An application in soil micromorphology

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width of these fissures is of interest. The fissures are mathematically generalized to flat bodies which are defined as stationary weighted surface processes with the weight “thickness”. In a typical point of the surface process suitable, joint parametric distributions of direction and thickness are assumed. The parameters have to be estimated from measurements on vertical sections which are taken from the soil. On these sections only a visible thickness and a visible angle can be observed. The joint distribution of these variables can be expressed by the joint distribution of spatial direction and thickness with the same parameters and in this indirect way the parameters can be estimated. The paper describes how to randomize the vertical section and how to measure the visible variables on the sections. The Chi-Square method is proposed for the parameter estimation. Further it is discussed how to derive good starting values for the numerical procedure. All this is demonstrated in a simulation study using the Bingham-Mardia distribution for the direction and the lognormal distribution for the thickness including a way to correlate the mean thickness and the direction. Finally an application in soil micromorphology is demonstrated for one soil horizon.     

Fragile sites and statistics

Summary A simple and reliable statistical method is proposed to distinguish real fragile sites from the casual accumulation of aberrations that can occur as a consequence of random distribution. It is based on a study of the expected random distribution, assumed to be equal to a Poisson distribution, with the expected value of events per band as the mean.     

Statistical tests for recessive lethal-carriers.

This paper presents a statistical method for testing whether a male mouse is a recessive lethal-carrier. The analysis is based on a back-cross experiment in which the male mouse is mated with some of his daughters. The numbers of total implantations and intrauterine deaths in each litter are recorded. It is assumed that, conditional on the number of total implantations, the number of intrauterine deaths follows a binomial distribution. Using computer-simulated experimentation it is shown that the proposed statistical method, which is sensitive to the pattern of intrauterine death rates, is more powerful than a test based only on the total number of implant deaths. The proposed test requires relatively simple calculations and can be used for a wide range of values of total implantations and background implant mortality rates. For computer-simulated experiments, there was no practical difference between the empirical error rate and the nominal error rate.     

Fitting semiparametric random effects models to large data sets

For large data sets, it can be difficult or impossible to fit models with random effects using standard algorithms due to memory limitations or high computational burdens. In addition, it would be advantageous to use the abundant information to relax assumptions, such as normality of random effects. Motivated by data from an epidemiologic study of childhood growth, we propose a 2-stage method for fitting semiparametric random effects models to longitudinal data with many subjects. In the first stage, we use a multivariate clustering method to identify G相似文献   

Improved parameter estimation for variance-stabilizing transformation of gene-expression microarray data

A gene-expression microarray datum is modeled as an exponential expression signal (log-normal distribution) and additive noise. Variance-stabilizing transformation based on this model is useful for improving the uniformity of variance, which is often assumed for conventional statistical analysis methods. However, the existing method of estimating transformation parameters may not be perfect because of poor management of outliers. By employing an information normalization technique, we have developed an improved parameter estimation method, which enables statistically more straightforward outlier exclusion and works well even in the case of small sample size. Validation of this method with experimental data has suggested that it is superior to the conventional method.     

An illness-death process with time-dependent covariates

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates in order to make an appropriate adjustment for the transition and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown. The method developed is illustrated with data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach with which the effectiveness of the treatment can be compared between the placebo and propranolol treatment groups with respect to fatal and nonfatal events simultaneously.     

Determining particle density distribution of expanded bed adsorbents

This study presents an experimental approach to measure the density distribution of expanded bed adsorption (EBA) matrices. We report on the use of a series of solutions of caesium trifluoroacetate (CsTFA) of varying density spun in a laboratory centrifuge so as to separate representative matrix samples on the basis of bead density. Mass data was used to plot a decumulative density distribution for the matrix. By performing laser light scattering-based measurements on the same samples of matrix the variation in particle size with density was determined. Particle settling velocity distributions were then calculated using these data and compared with a settling velocity distribution calculated on the basis of an assumed constant bead density. The study demonstrates a reliable and simple method for the characterisation of matrix density distribution. For the case of the Streamline matrices tested the particle size distribution is constant with varying bead density. Bead densities varied from 1.5 to 2.1 g/cm3 in the CsTFA solutions. These were then adjusted using bead porosity to give a density range of 1.11-1.33 g/cm3 in aqueous buffer (assumed 1.0 g/cm3) The differences in resultant settling velocity distributions when based upon measured density distribution than when based upon an assumed mean density value were shown to be insignificant. This result confirms experimentally that an assumption of a single constant mean density for EBA particles is acceptable for hydrodynamic modelling and performance prediction purposes.     

A method for the estimation of parameters for natural stage-structured populations

A relatively simple method is proposed for the estimation of parameters of stage-structured populations from sample data for situation where (a) unit time survival rates may vary with time, and (b) the distribution of entry times to stage 1 is too complicated to be fitted with a simple parametric model such as a normal or gamma distribution. The key aspects of this model are that the entry time distribution is approximated by an exponential function withp parameters, the unit time survival rates in stages are approximated by anr parameter exponential polynomial in the stage number, and the durations of stages are assumed to be the same for all individuals. The new method is applied to four Zooplankton data sets, with parametric bootstrapping used to assess the bias and variation in estimates. It is concluded that good estimates of demographic parameters from stagefrequency data from natural populations will usually only be possible if extra information such as the durations of stages is known.     

Assessing mortality changes from size‐frequency curves

The relationship between the instantaneous mortality rate ( Z ) and the instantaneous change in length‐frequency distribution of organisms per unit of animal size (μ _L ) takes the following form: Z  = μ _L k ( L _∞ −  L ) +  k , where k and L _∞ are coefficients of the von Bertalanffy equation, and L is organism size (length). Z and μ_L change coherently when they are measured for a specific size or age class. Therefore, observations of μ _L can provide information on the relative changes in mortality. This is useful when no precise information about animal growth is available and growth curve is assumed to be invariable. This method was tested on a heavily exploited population of St Peter's fish (mango tilapia) Sarotherodon galilaeus in Lake Kinneret, Israel, where large fluctuations in the size structure of the catch have occurred over the past few years. Analysis of the changes in the length‐frequency distributions showed that the changes in μ _L over multiple years estimated for fully exploited fish reflected the respective changes in Z .     

Estimating parameters of the family-size distribution in ascertainment sampling schemes: numerical results

It is argued that, in any ascertainment sampling scheme using data from families of various sizes, there is never any need to assume a particular form for the (unknown) family-size distribution. There exists a simple conditional method, making no assumptions about the family-size distribution, that is always preferable to the assumption of any particular distributional form. Furthermore, the simplicity of the conditional method gives insights into properties of estimates of genetic and ascertainment parameters, which are not available when a particular form for the family-size distribution is assumed.     

Analyzing k (2 x 2) tables under cluster sampling

In many data analytic applications, such as ophthalmologic, longitudinal, or periodontal studies, multiple observations are recorded over several sites (or timepoints) within the same subject, bringing about dependence between measurements. This correlation, in turn, precludes the use of standard statistical methods that assume independence between outcome measurements. For example, the Mantel-Haenszel statistic, used to assess association between a binary outcome and a binary exposure while adjusting for a categorical covariate, does not follow the usual chi-squared distribution under the null hypothesis when there is correlation between observations. A modified Mantel-Haenszel procedure, which makes adjustment for dependence, is proposed. No particular correlation structure is assumed for responses within a cluster. This closed-form adjustment stems from Liang and Zeger's (1986, Biometrika 73, 13-22) generalized estimating equations approach for clustered data. The difference between this tabular (i.e., noniterative) technique and many earlier tabular methods is that the current method allows for consideration of site-specific exposure and covariate information. An example from a periodontal research study illustrates application of the method.     

A method for determining minimal sets of markers for the estimation of center of mass,linear and angular momentum

A new method is proposed for finding small sets of points on the body giving sufficient information for estimating the whole body center of mass (CoM), as well as the linear momenta (LM) and angular momenta (AM). In the underlying model each point (whose trajectory is tracked by a marker) is a point mass: Hence the body is represented by a simple system of point masses. The first step is to determine the appropriate set of points and the mass of each point, which is assumed to be specific for the movement performed. The distribution of the mass to each marker is determined from training data for which the true (or reference) trajectories of the CoM, LM or AM are known. This leads to a quadratic optimization problem with inequality constraints. The use of the method is demonstrated on data from discus throw. Results indicate reasonably small errors, considering the magnitude of other error sources, in CoM position (average magnitude of estimation error 1–2 cm), and moderate errors in AM (13–20% of peak value).     

A method to estimate demographic intensities via cumulative incidence rates

In many situations it is impossible to calculate the occurrence/exposure rates which are so important for analysis in demography, epidemiology, and other fields, because the only information available for each age group is the occurrences and total exposure, but not the distribution of the latter over the various separate statuses. The literature contains a method to estimate the occurrence/ exposure rates from cumulative incidence rates for closed cohorts in some simple situations of this kind. The purpose of this paper is to justify the method by a probabilistic argument, to generalize it to cover a much broader set of cases, described as time-continuous Markov chains, and to illustrate it with some new sets of data. The method is originally based on an assumption of nondifferential mortality, but our findings suggest that it is strongly robust against deviations from this assumption. We also comment upon the effect of migration.     

Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis

Summary .  In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose–response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose–response analysis.     

Theory of ligand binding to heterogeneous receptor populations: Characterization of the free-energy distribution function

We present a method for characterizing the free-energy and affinity distributions of a heterogeneous population of molecules interacting with a homogeneous population of ligands, by driving expressions for the moments as functions of experimental binding curve characteristics, and then constructing the distribution as an expansion over a Gaussian basis set. Although the method provides the complete distribution in principle, in practice it is restricted by experimental noise, inaccuracies in data fitting, and the severity with which the distribution deviates from a Gaussian. Limitations imposed by experimental inaccuracies and the requirement of an appropriate analytic function for data fitting were evaluated by Monte Carlo simulations of binding experiments with various degrees of error in the data. Thus a distribution was assumed, binding curves with random errors were generated, and the technique was applied in order to determine the extent to which the characteristics of the assumed distribution could be recovered. Typical inaccuracies in the first two moments fell within experimental error, whereas inaccuracies in the third and fourth were generally larger than standard deviations in the data. The accuracy of these higher-order moments was invarient for experimental errors ranging from 2 to 10% and may thus be limited, within this range, primarily by the curve fitting procedure. The other aspect of the problem, accurate inference of the distribution, is limited in part by inaccuracies in the moments but more importantly by the extent to which the distribution deviates from a Gaussian. The extensive statistical literature on the problem of inference enables the delineation of specific criteria for estimating the efficiency of construction, as well as for deciding whether certain features of the inferred distribution, such as bimodality, are artifacts of the procedure. In spite of the limitations of the method, the results indicate that the mean and standard deviation are obtainable with greater accuracy than by a Sipsian analysis. This difference is particularly important when the distribution is narrow and width detection is beyond the sensitivity of the Sips plot. The method should be more accurate than the latter as an assay for homogeneity as well as for characterizing the moments, though equally easy to apply.     

Note on a mechanism of the distribution of wealth

A population of individuals is considered to be characterized by a distribution of wealth which is the result of gain and loss from the outside as well as a result of exchange. The population is assumed to be uniform except for the variation in a parameter determining the manner of partition during exchange. The parameter is assumed to be normally distributed over the population. The resulting distribution of wealth is calculated for some special cases and it is found to be very asymmetric.