Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Spatial mapping and map exploitation : a bio-inspired engineering perspective

Probabilistic robot mapping techniques can produce high resolution, accurate maps of large indoor and outdoor environments. However, much less progress has been made towards robots using these maps to perform useful functions such as efficient navigation. This paper describes a pragmatic approach to mapping system development that considers not only the map but also the navigation functionality that the map must provide. We pursue this approach within a bio-inspired mapping context, and use esults from robot experiments in indoor and outdoor environments to demonstrate its validity. The research attempts to stimulate new research directions in the field of robot mapping with a proposal for a new approach that has the potential to lead to more complete mapping and navigation systems.

Ordering of Ge islands on Si(001) substrates patterned by nanoindentation

Spatial organization of Ge islands, grown by physical vapor deposition, on prepatterned Si(001) substrates has been investigated. The substrates were patterned prior to Ge deposition by nanoindentation. Characterization of Ge dots is performed by atomic force microscopy and scanning electron microscopy. The nanoindents act as trapping sites, allowing ripening of Ge islands at those locations during subsequent deposition and diffusion of Ge on the surface. The results show that island ordering is intrinsically linked to the nucleation and growth at indented sites and it strongly depends on pattern parameters.

Changes in Level of Virus Accumulation and Incidence of Infection are Critical in the Characterization of Rice Tungro Bacilliform Virus (RTBV) Resistance in Rice

Analysis by enzyme-linked immunosorbent assay showed that Rice tungro bacilliform virus (RTBV) accumulated in a cyclic pattern from early to late stages of infection in tungro-susceptible variety, Taichung Native 1 (TN1), and resistant variety, Balimau Putih, singly infected with RTBV or co-infected with RTBV+Rice tungro spherical virus (RTSV). These changes in virus accumulation resulted in differences in RTBV levels and incidence of infection. The virus levels were expressed relative to those of the susceptible variety and the incidence of infection was assessed at different weeks after inoculation. At a particular time point, RTBV levels in TN1 or Balimau Putih singly infected with RTBV were not significantly different from the virus level in plants co-infected with RTBV+RTSV. The relative RTBV levels in Balimau Putih either singly infected with RTBV or co-infected with RTBV+RTSV were significantly lower than those in TN1. The incidence of RTBV infection varied at different times in Balimau Putih but not in TN1, and to determine the actual infection, the number of plants that became infected at least once anytime during the 4wk observation period was considered. Considering the changes in RTBV accumulation, new parameters for analyzing RTBV resistance were established. Based on these parameters, Balimau Putih was characterized having resistance to virus accumulation although the actual incidence of infection was >75%.