A quasi-likelihood approach for ordered categorical data with overdispersion

Quasi-likelihood (QL) methods are often used to account for overdispersion in categorical data. This paper proposes a new way of constructing a QL function that stems from the conditional mean-variance relationship. Unlike traditional QL approaches to categorical data, this QL function is, in general, not a scaled version of the ordinary log-likelihood function. A simulation study is carried out to examine the performance of the proposed QL method. Fish mortality data from quantal response experiments are used for illustration.

Delineating environmental envelopes to improve mapping of species distributions, via a hurdle model with CART &/or MaxEnT

Species distribution modelling (SDM) typically analyses species’ presence together with some form of absence information. Ideally absences comprise observations or are inferred from comprehensive sampling. When such information is not available, then pseudo-absences are often generated from the background locations within the study region of interest containing the presences, or else absence is implied through the comparison of presences to the whole study region, e.g. as is the case in Maximum Entropy (MaxEnt) or Poisson point process modelling. However, the choice of which absence information to include can be both challenging and highly influential on SDM predictions (e.g. Oksanen and Minchin, 2002). In practice, the use of pseudo- or implied absences often leads to an imbalance where absences far outnumber presences. This leaves analysis highly susceptible to ‘naughty-noughts’: absences that occur beyond the envelope of the species, which can exert strong influence on the model and its predictions (Austin and Meyers, 1996). Also known as ‘excess zeros’, naughty noughts can be estimated via an overall proportion in simple hurdle or mixture models (Martin et al., 2005). However, absences, especially those that occur beyond the species envelope, can often be more diverse than presences. Here we consider an extension to excess zero models. The two-staged approach first exploits the compartmentalisation provided by classification trees (CTs) (as in O’Leary, 2008) to identify multiple sources of naughty noughts and simultaneously delineate several species envelopes. Then SDMs can be fit separately within each envelope, and for this stage, we examine both CTs (as in Falk et al., 2014) and the popular MaxEnt (Elith et al., 2006). We introduce a wider range of model performance measures to improve treatment of naughty noughts in SDM. We retain an overall measure of model performance, the area under the curve (AUC) of the Receiver-Operating Curve (ROC), but focus on its constituent measures of false negative rate (FNR) and false positive rate (FPR), and how these relate to the threshold in the predicted probability of presence that delimits predicted presence from absence. We also propose error rates more relevant to users of predictions: false omission rate (FOR), the chance that a predicted absence corresponds to (and hence wastes) an observed presence, and the false discovery rate (FDR), reflecting those predicted (or potential) presences that correspond to absence. A high FDR may be desirable since it could help target future search efforts, whereas zero or low FOR is desirable since it indicates none of the (often valuable) presences have been ignored in the SDM. For illustration, we chose Bradypus variegatus, a species that has previously been published as an exemplar species for MaxEnt, proposed by Phillips et al. (2006). We used CTs to increasingly refine the species envelope, starting with the whole study region (E0), eliminating more and more potential naughty noughts (E1–E3). When combined with an SDM fit within the species envelope, the best CT SDM had similar AUC and FPR to the best MaxEnt SDM, but otherwise performed better. The FNR and FOR were greatly reduced, suggesting that CTs handle absences better. Interestingly, MaxEnt predictions showed low discriminatory performance, with the most common predicted probability of presence being in the same range (0.00-0.20) for both true absences and presences. In summary, this example shows that SDMs can be improved by introducing an initial hurdle to identify naughty noughts and partition the envelope before applying SDMs. This improvement was barely detectable via AUC and FPR yet visible in FOR, FNR, and the comparison of predicted probability of presence distribution for pres/absence.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Bayesian mixture model estimation of aerosol particle size distributions

In this paper, we examine approaches to estimate a Bayesian mixture model at both single and multiple time points for a sample of actual and simulated aerosol particle size distribution (PSD) data. For estimation of a mixture model at a single time point, we use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to estimate mixture model parameters including the number of components which is assumed to be unknown. We compare the results of this approach to a commonly used estimation method in the aerosol physics literature. As PSD data is often measured over time, often at small time intervals, we also examine the use of an informative prior for estimation of the mixture parameters which takes into account the correlated nature of the parameters. The Bayesian mixture model offers a promising approach, providing advantages both in estimation and inference.

Hospital in the Nursing Home program reduces emergency department presentations and hospital admissions from residential aged care facilities in Queensland, Australia: A quasi-experimental study

Background There has been considerable publicity regarding population ageing and hospital emergency department (ED) overcrowding. Our study aims to investigate impact of one intervention piloted in Queensland Australia, the Hospital in the Nursing Home (HiNH) program, on reducing ED and hospital attendances from residential aged care facilities (RACFs). Methods A quasi-experimental study was conducted at an intervention hospital undertaking the program and a control hospital with normal practice. Routine Queensland health information system data were extracted for analysis. Results Significant reductions in the number of ED presentations per 1000 RACF beds (rate ratio (95 % CI): 0.78 (0.67–0.92); p = 0.002), number of hospital admissions per 1000 RACF beds (0.62 (0.50–0.76); p < 0.0001), and number of hospital admissions per 100 ED presentations (0.61 (0.43–0.85); p = 0.004) were noticed in the experimental hospital after the intervention; while there were no significant differences between intervention and control hospitals before the intervention. Pre-test and post-test comparison in the intervention hospital also presented significant decreases in ED presentation rate (0.75 (0.65–0.86); p < 0.0001) and hospital admission rate per RACF bed (0.66 (0.54–0.79); p < 0.0001), and a non-significant reduction in hospital admission rate per ED presentation (0.82 (0.61–1.11); p = 0.196). Conclusions Hospital in the Nursing Home program could be effective in reducing ED presentations and hospital admissions from RACF residents. Implementation of the program across a variety of settings is preferred to fully assess the ongoing benefits for patients and any possible cost-savings.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

A geometric approach to stationary defect solutions in one space dimension

In this manuscript, we consider the impact of a small jump-type spatial heterogeneity on the existence of stationary localized patterns in a system of partial dierential equations in one spatial dimension...

Flood risk information, actual floods and property values: A quasi-experimental analysis

Hedonic property price analysis tells us that property prices can be affected by natural hazards such as floods. This paper examines the impact of flood-related variables (among other factors) on property values, and examines the effect of the release of flood risk map information on property values by comparing the impact with the effect of an actual flood incidence. An examination of the temporal variation of flood impacts on property values is also made. The study is the first of its kind where the impact of the release of flood risk map information to the public is compared with an actual flood incident. In this study, we adopt a spatial quasi-experimental analysis using the release of flood risk maps by Brisbane City Council in Queensland, Australia, in 2009 and the actual floods of 2011. The results suggest that property buyers are more responsive to the actual incidence of floods than to the disclosure of information to the public on the risk of floods.