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Multiple imputation and maximum likelihood estimation (via the expectation- maximization algorithm) are two well-known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation-maximization approximation to the likelihood. In this thesis we show how these two methods are equivalent, and further, exploit this result to show that familiar likelihood-based approaches can be used to enhance multiple imputation’s performance in: (1) model selection, where familiar Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) can be used to choose the imputation model that best fits the observed data; (2) hypothesis testing, where the familiar likelihood-ratio statistic can be used to perform composite hypothesis testing with multiple imputed data; (3) measurement error modelling, where familiar functional methods, such as Simulation-extrapolation and Corrected score, can be used to account for measurement error with multiple imputed data. We verify these results empirically and demonstrate the use of the methods on several classical missing data examples.

This study examined the assisted natural restoration of native vegetation in an Australian floodplain wetland where flows were reinstated and the river was reconnected to the floodplain, following cessation of agricultural cultivation. Extant vegetation was surveyed three times during an inundation event at plots with different land‐use histories. Restoration rate was more influenced by past land use than long‐term inundation frequency and success decreased with antecedent land‐use intensity. Prolonged land‐use history (>3 years cultivation) restricted restoration success. Sites with longer cultivation histories tended to have fewer aquatic species, more terrestrial species and exotic species. For example, amphibious responders with floating leaves were found only in reference plots and less frequently in farmed treatment plots. In this scenario, increased persistence of exotics and dryland species suggested alternative trajectories. Fields with a short land‐use history (1–3 years of clearing and cultivation) resembled undisturbed floodplain communities, consistent with a ‘field of dreams’ hypothesis. Although river–floodplain reconnections can restore wetlands, legacy effects of past land use may limit the pace and outcomes of restoration.

Spatial climate variables are routinely used in species distribution models (SDMs) without accounting for the fact that they have been predicted with uncertainty, which can lead to biased estimates, erroneous inference and poor performances when predicting to new settings - for example under climate change scenarios. We show how information on uncertainty associated with spatial climate variables can be obtained from climate data models. We then explain different types of uncertainty (i.e. classical and Berkson error) and use two statistical methods that incorporate uncertainty in climate variables into SDMs by means of (i) hierarchical modelling and (ii) simulation-extrapolation. We used simulation to study the consequences of failure to account for measurement error. When uncertainty in explanatory variables was not accounted for, we found that coefficient estimates were biased and the SDM had a loss of statistical power. Further, this bias led to biased predictions when projecting change in distribution under climate change scenarios. The proposed errors-in-variables methods were less sensitive to these issues. We also fit the proposed models to real data (presence/absence data on the Carolina wren, Thryothorus ludovicianus), as a function of temperature variables. The proposed framework allows for many possible extensions and improvements to SDMs. If information on the uncertainty of spatial climate variables is available to researchers, we recommend the following: (i) first identify the type of uncertainty; (ii) consider whether any spatial autocorrelation or independence assumptions are required; and (iii) attempt to incorporate the uncertainty into the SDM through established statistical methods and their extensions.

Population demographics such as, population size or survival rates, can be estimated from capture-recapture data collected on individuals from the population. These estimates are of particular interest to ecologists, biologists, sociologists and epidemiologists who rely on accurate inferences so that management and conservation of the population is well maintained. Due to rapid advances in computational power and speed, a growing number of modern statistical techniques, such as penalized smoothing splines, have allowed for more flexibility to construct models from complex data. In summary, this thesis presents: (1.) the development of new and flexible methodologies using modern statistical techniques to enhance and robustify inference for capture-recapture studies, (2.) a comprehensive analysis on various real capture-recapture data sets using both classical and new capture-recapture models; (3.) the performance of new models by conducting simulations resembling real data; and (4.) a new statistical software designed for analysing capture-recapture data. The examples presented in this thesis primarily use capture-recapture data sets collected on Little Penguins Eudyptula minor from a colony located at Summerland Beach on the western end of Phillip Island, Victoria, Australia.