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.

The potential to mitigate global warming with no-tillage management is only realized when practised in the long term

No-tillage (NT) management has been promoted as a practice capable of offsetting greenhouse gas (GHG) emissions because of its ability to sequester carbon in soils. However, true mitigation is only possible if the overall impact of NT adoption reduces the net global warming potential (GWP) determined by fluxes of the three major biogenic GHGs (i.e. CO2, N2O, and CH4). We compiled all available data of soil-derived GHG emission comparisons between conventional tilled (CT) and NT systems for humid and dry temperate climates. Newly converted NT systems increase GWP relative to CT practices, in both humid and dry climate regimes, and longer-term adoption (>10 years) only significantly reduces GWP in humid climates. Mean cumulative GWP over a 20-year period is also reduced under continuous NT in dry areas, but with a high degree of uncertainty. Emissions of N2O drive much of the trend in net GWP, suggesting improved nitrogen management is essential to realize the full benefit from carbon storage in the soil for purposes of global warming mitigation. Our results indicate a strong time dependency in the GHG mitigation potential of NT agriculture, demonstrating that GHG mitigation by adoption of NT is much more variable and complex than previously considered, and policy plans to reduce global warming through this land management practice need further scrutiny to ensure success.

Multi-criteria ranking and receptor modelling of airborne fine particles at three sites in the Pearl River Delta region of China

The multi-criteria decision making methods, Preference METHods for Enrichment Evaluation (PROMETHEE) and Graphical Analysis for Interactive Assistance (GAIA), and the two-way Positive Matrix Factorization (PMF) receptor model were applied to airborne fine particle compositional data collected at three sites in Hong Kong during two monitoring campaigns held from November 2000 to October 2001 and November 2004 to October 2005. PROMETHEE/GAIA indicated that the three sites were worse during the later monitoring campaign, and that the order of the air quality at the sites during each campaign was: rural site > urban site > roadside site. The PMF analysis on the other hand, identified 6 common sources at all of the sites (diesel vehicle, fresh sea salt, secondary sulphate, soil, aged sea salt and oil combustion) which accounted for approximately 68.8 ± 8.7% of the fine particle mass at the sites. In addition, road dust, gasoline vehicle, biomass burning, secondary nitrate, and metal processing were identified at some of the sites. Secondary sulphate was found to be the highest contributor to the fine particle mass at the rural and urban sites with vehicle emission as a high contributor to the roadside site. The PMF results are broadly similar to those obtained in a previous analysis by PCA/APCS. However, the PMF analysis resolved more factors at each site than the PCA/APCS. In addition, the study demonstrated that combined results from multi-criteria decision making analysis and receptor modelling can provide more detailed information that can be used to formulate the scientific basis for mitigating air pollution in the region.