Ruth Marcus

Efficiency of Multivariate Control Variates in Monte Carlo Simulation

This paper considers some statistical aspects of applying control variates to achieve variance reduction in the estimation of a vector of response variables in Monte Carlo simulation. It gives a result that quantifies the loss in variance reduction caused by the estimation of the optimal control matrix. For the one-dimensional case, we derive analytically the optimal size of the vector of control variates under specific assumptions on the covariance matrix. For the multidimensional case, our numerical results show that good variance reduction is achieved when the number of control variates is relatively small approximately of the same order as the number of unknown parameters. Finally, we give some recommendations for future research.

Epidemiological and economic models for spread and control of citrus tristeza virus disease

Citrus tristeza virus (CTV) causes a most destructive citrus disease in many parts of the world, and indications of natural spread were found in Israel in 1970. The strategy for controlling the disease in Israel is based on the eradication of virus-infected trees, detected by test plants or immunological methods. Mathematical models for CTV infection and spread were developed and used to assess the cost-effectiveness of the eradication policy. It was concluded that the discovery-eradication program is economically justified and superior to allowing the disease to progress unchecked.

On the spatial distribution of citrus tristeza virus disease

The spatial spread of citrus tristeza virus (CTV) disease was studied using data from two infected groves. Statistical analysis indicated a spatial grouping of infected trees. A gamma distribution was fitted to the empirical distribution of the distances between nearest infected neighbors. The findings suggest that, after locating a newly infected tree, additional inspections to detect CTV should be carried out mainly on trees within 14 m of that tree.

A model for spread of plant disease with periodic removals

A deterministic model for the spread of infectious disease in a plant population consisting of N interacting groups with periodic removals of the infected plants is considered. In the case of two interacting groups with low infection levels, the problem is solved analytically. In the case of N interacting groups arranged in line, where the interaction between the groups decreases exponentially with distance, the mathematical model consists of N nonlinear equations. Numerical solution of these equations for some values of the parameters shows a pattern similar to the solution for the two interacting groups.

Simultaneous confidence intervals for umbrella contrasts of normal means

Abstract Two procedures for obtaining simultaneous confidence intervals for “umbrella” contrasts of normal means of the form Σciμi, where c1 ⩽ ⋯ ⩽ ch ⩾ ⋯ ⩾ ck and Σci = 0, are described. One procedure employs critical values of the likelihood ratio statistic proposed by Shi (1988) for testing homogeneity of normal means against an umbrella ordering, HU,h: μ1 ⩽ ⋯ ⩽ μh ⩾ ⋯ ⩾ μk), with h known. The second employs critical values of the statistics μ h – min( μ 1, μ k), where { μ i} are the maximum likelihood estimators of {μi under HU,h. The null distribution of the statistic is investigated by the Monte Carlo technique, and some percentiles are provided. The interval lengths obtained by these procedures are compared for different types of umbrella contrasts. Improved confidence bounds are generated when the means satisfy an umbrella ordering.

Deterministic and stochastic logistic models for describing increase of plant diseases

Abstract Deterministic and stochastic versions of the logistic model were applied for describing increase of plant diseases. The stochastic version of the logistic model is based on the addition of a random component to the growth rate per unit infection, as previously used for analysis of insect population abundance. The models were fitted to disease progress curves derived from a real data set consisting of disease assessments of melon plants in Israel infected by zucchini yellow mosaic virus (ZYMV). The results showed that the random component in the stochastic version was estimated as being small. The autocorrelations of the residuals were lower for the stochastic version of the logistic model than the corresponding values of the deterministic logistic model. For small data sets the statistical advantages of the stochastic version of the logistic model over the (simpler) deterministic version were not significant.

Model for the spread of non-persistent virus diseases

This study considers the buildup of virus infection within a crop area. The virus is transmitted by aphid vectors which acquire virus from source plants and inoculate the sensitive crop. The model relates the increase of infection to the behaviour of incoming vectors and of vectors moving from plant to plant within the crop area. The model is implemented using some data available on spread of cucumber mosaic virus in a pepper plot in Israel. The effect of control means is considered.

On testing homogeneity of t normal means against ordered alternatives in r groups

Given k=rt normal populations with a common but unknown variance consisting of t treatments applied to r different groups of units, and supposing that in each group the means are monoto-nically non-decreasing (or non-increasing), then the likelihood ratio test of homogeneity of the means in each group against the simple order alternative is considered. Critical values are provided when one observation is drawn from each of the k populations.

Parameter estimation in differential equations, using random time transformations

Differential equations with measurements subject to errors are usually handled by Least Squares methods or by Likelihood methods based on diffusion-type stochastic modifications of the differential equation. We study the performance of likelihood methods based on substituting a Gaussian random time transformation as argument in the solution of the original deterministic differential equation. This method may be applied to the simultaneous estimation of parameters describing a number of differential equations, based on data with dependent measurement errors. The model is fitted to disease progress curves derived from a real data set consisting of disease assessments of melon plants infected by Zucchini Yellow Mosaic Virus (ZYMV).

d-Isoascorbic acid fed to Spodoptera littoralis moths, induces sterility due to spermatophore malformation

Abstract d -Isoascorbic acid ( d -araboascorbic acid; d -erythorbic acid) fed to Spodoptera littoralis (Boisduval) moths causes males to produce malformed spermatophores with no reduction in their mating capacity. Males fed daily on the analogue, induced sterility in females paired with them. Female fertility and fecundity were markedly reduced compared with the reproductive potential of females mated to males fed either l -ascorbic acid or sucrose only. Spermatophore pathology originated in failure to inflate the spermatophore corpus at the time of mating. This failure was produced by a single male in two females independently, when males only had access to the analogue. Thus, the effect on the spermatophore seems linked to male ingestion of the analogue. When d -isoascorbic acid-feeding of males was discontinued after 48 hr, egg fertility was restored. When l -ascorbic acid followed the analogue, the effect of spermatophore malformation was not completely erased. The mode of action of this ascorbic acid analogue is discussed.