Estimating the kernel parameters of premises-based stochastic models of farmed animal infectious disease epidemics using limited, incomplete, or ongoing data

Three different estimators are presented for the types of parameters present in mathematical models of animal epidemics. The estimators make use of the data collected during an epidemic, which may be limited, incomplete, or under collection on an ongoing basis. When data are being collected on an ongoing basis, the estimated parameters can be used to evaluate putative control strategies. These estimators were tested using simulated epidemics based on a spatial, discrete-time, gravity-type, stochastic mathematical model containing two parameters. Target epidemics were simulated with the model and the three estimators were implemented using various combinations of collected data to independently determine the two parameters.     

A concept of a general computer program for the iterative calculation of maximum likelihood estimators with application to qualitative dose response analyses

In this article we describe the construction of a general computer program for the iterative calculation of maximum likelihood estimators. The program is general in the sense that it allows the maximization of any given likelihood function. The user only has to write a subroutine LKLHD, in which the special likelihood function and their first and second derivatives will be calculated. This subroutine is an input parameter of the optimization program. This enables the user to employ one main program for the maximization of various likelihood functions. This advantage will be shown for the evaluation of qualitative dose response relationships (quantal assays: probit-, logit-analysis).     

Sparse Sampling and Maximum Likelihood Estimation for Boolean Models

A condition for practical independence of contact distribution functions in Boolean models is obtained. This result allows the authors to use maximum likelihcod methods, via sparse sampling, for estimating unknown parameters of an isotropic Boolean model. The second part of this paper is devoted to a simulation study of the proposed method. AMS classification: 60D05     

Maximum Likelihood Methods for Fitting the Burr Type XII Distribution to Life Test Data

This paper describes mathematical and computational methodology for estimating the parameters of the Burr Type XII distribution by the method of maximum likelihood. Expressions for the asymptotic variances and covariances of the parameter estimates are given, and the modality of the log-likelihood and conditional log-likelihood functions is analyzed. As a result of this analysis for various a priori known and unknown parameter combinations, conditions are given which guarantee that the parameter estimates obtained will, indeed, be maximum likelihood estimates. An efficient numerical method for maximizing the conditional log-likelihood function is described, and mathematical expressions are given for the various numerical approximations needed to evaluate the expressions given for the asymptotic variances and covariances of the parameter estimates. The methodology discussed is applied in a numerical example to life test data arising in a clinical setting.     

用空间直观模型是否足以从斑块占据性资料中推断集合种群的动态过程?

在集合种群的研究中,经常要根据空间占据性数据应用斑块模型来推断种群的动态过程,在保护生物学应用中,斑块占据性模型的参数估测对于阐释集合种群动态和预测种群对生境破坏的反应极为重要。我们探讨了一种广泛应用的空间直观模型——率函数模型(Incidence function model)中参数估测的不确定性问题,通过构建由50个斑块组成的网络和两个假想的已知参数的集合种群,应用模拟模型产生集合种群随时间变化的斑块占据性数据系列：即快照(snapshot)。然后,根据这些快照,应用率函数模型和最大似然法估测种群动态参数。此外,我们还给出了传统的率函数模型的一个变形,这个变形包含了目标区效应(Target area effect)：即一个斑块的占据概率不但取决于空间隔离度,也取决于斑块本身面积的大小。结果表明：根据同一个集合种群不同的快照所估测的参数可以有很大差异,一个快照得出的参数提示的是占据性强但存活率低的集合种群,而另一个快照可能反映的是一个占据性弱但存活率高的集合种群。应用传统的率函数模型于一个包含了目标区效应的集合种群,导致斑块大小相关的灭绝率参数估测的正偏差。因此,仅根据一个快照的空间占据性数据来推测集合种群的过程有很大的不确定性[动物学报49(6)：787～794,2003]。     

A Rapid and Efficient Estimation Procedure for the Negative Binomial Distribution

This paper presents a new noniterative procedure for estimating the parameters of a negative binomial distribution. The procedure uses the first moment equation and an equation based on the weighted sample mean, with weights ω_x∝ α^z. The selection of a value for α is examined. A simulation study has been carried out and also the method has been applied to the 35 data sets analysed by Martin and Katti (1965, Biometrics) in order to compare it with the method of moments and with the method of maximum likelihood (ML). We conclude that the new procedure has greater relative efficiency than the method of moments; it gives estimates which are consistently close to ML and are easy to calculate.     

Boolean Models: Maximum Likelihood Estimation from Circular Clumps

This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.