Margaret Donald

3-D imaging and quantitative comparison of human dentitions and simulated bite marks

This study presents a technique developed for 3-D imaging and quantitative comparison of human dentitions and simulated bite marks. A sample of 42 study models and the corresponding bites, made by the same subjects in acrylic dental wax, were digitised by laser scanning. This technique allows image comparison of a 3-D dentition with a 3-D bite mark, eliminating distortion due to perspective as experienced in conventional photography. Cartesian co-ordinates of a series of landmarks were used to describe the dentitions and bite marks, and a matrix was created to compare all possible combinations of matches and non-matches using cross-validation techniques. An algorithm, which estimated the probability of a dentition matching its corresponding bite mark, was developed. A receiver operating characteristic graph illustrated the relationship between values for specificity and sensitivity. This graph also showed for this sample that 15% of non-matches could not be distinguished from the true match, translating to a 15% probability of falsely convicting an innocent person.

Bayesian Network for Risk of Diarrhea Associated with the Use of Recycled Water

Estimating potential health risks associated with recycled (reused) water is highly complex given the multiple factors affecting water quality. We take a conceptual model, which represents the factors and pathways by which recycled water may pose a risk of contracting gastroenteritis, convert the conceptual model to a Bayesian net, and quantify the model using one experts opinion. This allows us to make various predictions as to the risks posed under various scenarios. Bayesian nets provide an additional way of modeling the determinants of recycled water quality and elucidating their relative influence on a given disease outcome. The important contribution to Bayesian net methodology is that all model predictions, whether risk or relative risk estimates, are expressed as credible intervals.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond. We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

A Four Dimensional Spatio-Temporal Analysis of an Agricultural Dataset

While a variety of statistical models now exist for the spatio-temporal analysis of two-dimensional (surface) data collected over time, there are few published examples of analogous models for the spatial analysis of data taken over four dimensions: latitude, longitude, height or depth, and time. When taking account of the autocorrelation of data within and between dimensions, the notion of closeness often differs for each of the dimensions. Here, we consider a number of approaches to the analysis of such a dataset, which arises from an agricultural experiment exploring the impact of different cropping systems on soil moisture. The proposed models vary in their representation of the spatial correlation in the data, the assumed temporal pattern and choice of conditional autoregressive (CAR) and other priors. In terms of the substantive question, we find that response cropping is generally more effective than long fallow cropping in reducing soil moisture at the depths considered (100 cm to 220 cm). Thus, if we wish to reduce the possibility of deep drainage and increased groundwater salinity, the recommended cropping system is response cropping.

Potential for using soil particle-size data to infer geological parent material in the Sydney Region

Ecological communities are more than assemblages of species. In assessing the presence of many ecological communities, interpretation of soil properties and associated parent material has become a definitive component under environmental legislation worldwide, and particularly in Australia. The hypothesis tested here is that the geological parent material of a soil sample can be determined from particle size fraction data of the Marshall soil texture diagram. Supervised statistical classifiers were built from data for four particle-size fractions from four soil landscape publications. These methods were modified by taking into account possible autocorrelation between samples from the same site. The soil samples could not be classified with certainty as being derived from Wianamatta Group Shale or Hawkesbury Sandstone parent material. The classification of alluvial/fluvial-derived soils was no better than chance alone. A good classifier using four-fraction compositional data could not be built to determine geological parent material. Hence, the three size fractions of the Marshall soil texture diagram are insufficient to determine the geological parent material of a soil sample.