David J. Allcroft

A latent Gaussian Markov random-field model for spatiotemporal rainfall disaggregation

Summary. Rainfall data are often collected at coarser spatial scales than required for input into hydrology and agricultural models. We therefore describe a spatiotemporal model which allows multiple imputation of rainfall at fine spatial resolutions, with a realistic dependence structure in both space and time and with the total rainfall at the coarse scale consistent with that observed. The method involves the transformation of the fine scale rainfall to a thresholded Gaussian process which we model as a Gaussian Markov random field. Gibbs sampling is then used to generate realizations of rainfall efficiently at the fine scale. Results compare favourably with previous, less elegant methods.

Clustering of Mycobacterium avium subsp. paratuberculosis in Rabbits and the Environment: How Hot Is a Hot Spot?

ABSTRACT Clustering of pathogens in the environment leads to hot spots of diseases at local, regional, national, and international levels. Scotland contains regional hot spots of Johnes disease (caused by Mycobacterium avium subsp. paratuberculosis) in rabbits, and there is increasing evidence of a link between paratuberculosis infections in rabbits and cattle. The spatial and temporal dynamics of paratuberculosis in rabbits within a hot spot region were studied with the overall aim of determining environmental patterns of infection and thus the risk of interspecies transmission to livestock. The specific aims were to determine if prevalence of paratuberculosis in rabbits varies temporally between seasons and whether the heterogeneous spatial environmental distribution of M. avium subsp. paratuberculosis on a large scale (i.e., regional hot spots) is replicated at finer resolutions within a hot spot. The overall prevalence of M. avium subsp. paratuberculosis in rabbits was 39.7%; the temporal distribution of infection in rabbits followed a cyclical pattern, with a peak in spring of 55.4% and a low in summer of 19.4%. Spatially, M. avium subsp. paratuberculosis-infected rabbits and, thus, the risk of interspecies transmission were highly clustered in the environment. However, this is mostly due to the clustered distribution of rabbits. The patterns of M. avium subsp. paratuberculosis infection in rabbits are discussed in relation to the hosts socioecology and risk to livestock.

Risk factors for Johne's disease in Scotland - the results of a survey of farmers

The reported incidence of Johnes disease has been increasing in the east of Scotland since 1993. A postal questionnaire survey was sent to 127 farms to identify potential risk factors for Johnes disease in relation to wildlife and farm management practices, and 86 returns were obtained. Of 22 farms which had been assumed to be free of the disease, on the basis of information held by local veterinary centres, seven (32 per cent) reported cases of Johnes disease in the 1990s, indicating that the disease is under-reported. Logistic regression analyses showed that eight of 63 potentially explanatory variables were significant at the 5 per cent level in affecting the likelihood of farms reporting Johnes disease. Of these, large numbers of livestock and rabbits, and access of wildlife to feed stores were the clearest and most consistent risk factors associated with the disease. The application of manure to grazing pasture, the type of water supply for the cattle and the numbers of crows were also related to the presence of Johnes disease but the nature of these relationships was less clear. Only 38 per cent of the farms reported taking any control measures to combat Johnes disease, but three of the control measures were relevant to risk factors identified as significant by the survey, namely maintaining a clean water supply, controlling rabbits and not spreading manure on to grazing pasture.

THE TEMPORAL STRUCTURE OF FEEDING BEHAVIOR

Meals have long been considered relevant units of feeding behavior. Large data sets of feeding behavior of cattle, pigs, chickens, ducks, turkeys, dolphins, and rats were analyzed with the aims of 1) describing the temporal structure of feeding behavior and 2) developing appropriate methods for estimating meal criteria. Longer (between-meal) intervals were never distributed as the negative exponential assumed by traditional methods, such as log-survivorship analysis, but as a skewed Gaussian, which can be (almost) normalized by log-transformation of interval lengths. Log-transformation can also normalize frequency distributions of within-meal intervals. Meal criteria, i.e., the longest interval considered to occur within meals, can be estimated after fitting models consisting of Gaussian functions alone or of one Weibull and one or more Gaussian functions to the distribution of log-transformed interval lengths. Nonuniform data sets may require disaggregation before this can be achieved. Observations from all species were in conflict with assumptions of random behavior that underlie traditional methods for criteria estimation. Instead, the observed structure of feeding behavior is consistent with 1) a decrease in satiety associated with an increase in the probability of animals starting a meal with time since the last meal and 2) an increase in satiation associated with an increase in the probability of animals ending a meal with the amount of food already consumed. The novel methodology proposed here will avoid biased conclusions from analyses of feeding behavior associated with previous methods and, as demonstrated, can be applied across a range of species to address questions relevant to the control of food intake.

A simulation-based method for model evaluation

We wish to evaluate and compare models that are non-nested and fit to data using different fitting criteria. We first estimate parameters in all models by optimizing goodness-of-fit to a dataset. Then, to assess a candidate model, we simulate a population of datasets from it and evaluate the goodness-of-fit of all the models, without re-estimating parameter values. Finally, we see whether the vector of goodness-of-fit criteria for the original data is compatible with the multivariate distribution of these criteria for the simulated datasets. By simulating from each model in turn, we determine whether any, or several, models are consistent with the data. We apply the method to compare three models, fit at different temporal resolutions to binary time series of animal behaviour data, concluding that a semi-Markov model gives a better fit than latent Gaussian and hidden Markov models.

Analysis of crop lodging using a latent variable model

A method for quantifying treatment comparisons for a situation in which there are too many zeros in the dataset for a conventional analysis of variance to be valid is presented. The method assumes the existence of a latent variable such that zero observations correspond to values below a threshold, and non-zero observations are transformed to fit the part of the distribution above the threshold. The method is known as Tobit analysis in econometrics. Parameters are estimated by maximum likelihood and standard errors obtained, all using standard numerical routines. Use of the method is demonstrated by analysis of a dataset of crop lodging, and it is anticipated to be widely applicable to other types of data for which high numbers of zeros prevent conventional analysis.

A Spectral Estimator of Arma Parameters from Thresholded Data

We consider computationally-fast methods for estimating parameters in ARMA processes from binary time series data, obtained by thresholding the latent ARMA process. All methods involve matching estimated and expected autocorrelations of the binary series. In particular, we focus on the spectral representation of the likelihood of an ARMA process and derive a restricted form of this likelihood, which uses correlations at only the first few lags. We contrast these methods with an efficient but computationally-intensive Markov chain Monte Carlo (MCMC) method. In a simulation study we show that, for a range of ARMA processes, the spectral method is more efficient than variants of least squares and much faster than MCMC. We illustrate by fitting an ARMA(2,1) model to a binary time series of cow feeding data.