Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Did Brisbane grow smartly? Drivers of city growth 1991-2001 and lessons for current policies

Urban areas are growing unsustainably around the world; however, the growth patterns and their associated drivers vary between contexts. As a result, research has highlighted the need to adopt case study based approaches to stimulate the development of new theoretic understandings. Using land-cover data sets derived from Landsat images (30 m × 30 m), this research identifies both patterns and drivers of urban growth in a period (1991-2001) when a number of policy acts were enacted aimed at fostering smart growth in Brisbane, Australia. A linear multiple regression model was estimated using the proportion of lands that were converted from non-built-up (1991) to built-up usage (2001) within a suburb as a dependent variable to identify significant drivers of land-cover changes. In addition, the hot spot analysis was conducted to identify spatial biases of land-cover changes, if any. Results show that the built-up areas increased by 1.34% every year. About 19.56% of the non-built-up lands in 1991 were converted into built-up lands in 2001. This conversion pattern was significantly biased in the northernmost and southernmost suburbs in the city. This is due to the fact that, as evident from the regression analysis, these suburbs experienced a higher rate of population growth, and had the availability of habitable green field sites in relatively flat lands. The above findings suggest that the policy interventions undertaken between the periods were not as effective in promoting sustainable changes in the environment as they were aimed for.

A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

The BAD project: data mining, database and prediction of protein adsorption on surfaces

Protein adsorption at solid-liquid interfaces is critical to many applications, including biomaterials, protein microarrays and lab-on-a-chip devices. Despite this general interest, and a large amount of research in the last half a century, protein adsorption cannot be predicted with an engineering level, design-orientated accuracy. Here we describe a Biomolecular Adsorption Database (BAD), freely available online, which archives the published protein adsorption data. Piecewise linear regression with breakpoint applied to the data in the BAD suggests that the input variables to protein adsorption, i.e., protein concentration in solution; protein descriptors derived from primary structure (number of residues, global protein hydrophobicity and range of amino acid hydrophobicity, isoelectric point); surface descriptors (contact angle); and fluid environment descriptors (pH, ionic strength), correlate well with the output variable-the protein concentration on the surface. Furthermore, neural network analysis revealed that the size of the BAD makes it sufficiently representative, with a neural network-based predictive error of 5% or less. Interestingly, a consistently better fit is obtained if the BAD is divided in two separate sub-sets representing protein adsorption on hydrophilic and hydrophobic surfaces, respectively. Based on these findings, selected entries from the BAD have been used to construct neural network-based estimation routines, which predict the amount of adsorbed protein, the thickness of the adsorbed layer and the surface tension of the protein-covered surface. While the BAD is of general interest, the prediction of the thickness and the surface tension of the protein-covered layers are of particular relevance to the design of microfluidics devices.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Rejected! The harmful effects of workgroup mistreatment and the moderating role of organisational norms

This program of research investigated the harmful effects of mistreatment by the workgroup, and the role of perceived rejection as a critical mediator linking mistreatment and outcomes. This research program had three primary purposes. First, the research aimed to examine the important role of workgroup mistreatment as an independent predictor of negative outcomes, over and above the influence of supervisor mistreatment. Second, the research aimed to examine the effect of perceived rejection as an explanatory variable linking workgroup mistreatment and outcomes. Finally, the moderating effect of organizational norms on the relationship between workgroup mistreatment and perceived rejection was examined. The relationships of interest were examined over four studies, using multiple methods of data collection, across part-time and full-time working samples. In Study 1 (Chapter 2), the independent role of workgroup mistreatment and the mediating role of perceived rejection were examined. One hundred and forty two part-time working participants took part in the study. The participants completed a questionnaire on workplace behaviors in their organizations. The results of hierarchical regression analyses revealed a strong harmful effect of workgroup mistreatment, independent of mistreatment by the supervisor. In addition, the results showed that perceived rejection fully mediated the relationship between workgroup mistreatment and depression and organizational based self esteem. The study highlighted that perceived rejection acts as a key underlying psychological mechanism involved in the effect of workgroup mistreatment. This study has been published in the Journal of Occupational Health Psychology. Study 2 and Study 3 were presented as one paper in Chapter 3. The aims of these two studies was to explore the effects of workgroup mistreatment on a wider range of individual and organizational level outcomes, and to provide further evidence of the mediating role of perceived rejection as observed in Study 1. The results from both studies demonstrated that workgroup mistreatment had a significant and independent role in predicting negative individual and organizational level outcomes, providing support for the findings of Study 1. In the first study, 189 participants received scenarios manipulating workgroup mistreatment and supervisor mistreatment. The results of hierarchical regression analyses revealed that workgroup mistreatment harmfully affected participants, over and above that of the supervisor. The results also demonstrated that perceived rejection mediated the positive relationships between workgroup mistreatment and depression and organizational deviance, and also the negative relationships between workgroup mistreatment and organizational based self esteem and organizational citizenship behaviors. The second study included an additional aim, to examine the moderating role of supportive organizational norms. Two hundred and twenty nine participants read scenarios that manipulated workgroup mistreatment, supervisor mistreatment and organizational norms. The results of hierarchical regression analyses revealed the significant harmful effects of workgroup mistreatment, over and above the influence of supervisor mistreatment. The results also revealed the mediating role of perceived rejection. The direct effect of positive organizational norms also emerged, consistent with previous research. In addition, the result revealed that employees who experienced supportive organizational norms were more likely to reconcile with their workgroup members after experiencing mistreatment compared to employees who experienced hostile organizational norms. Finally, an unexpected pattern on the key affective variables of depression and organizational based self esteem emerged, such that mistreatment led to more negative outcomes in the supportive norms condition than in the hostile condition, where employees appeared to be desensitized. This paper is currently under review at the Journal of Applied Social Psychology. In Study 4 (Chapter 4), the overall model of workplace mistreatment was tested on a sample of full-time workers in an applied setting. One hundred and seventy two adults took part in the study. Participants were required to evaluate their workplace regarding mistreatment and organizational norms and to report their own psychological, behavioral and organizational outcomes. The results revealed that workgroup mistreatment was associated with increased depression, stress and avoidance, over and above supervisor mistreatment. In addition, the results revealed that perceived rejection acted as an explanatory variable linking workgroup mistreatment to a number of outcomes. Furthermore, the moderating role of hostile organizational norms emerged on depression, stress, reconciliation and avoidance. This paper is currently under review at the Journal of Occupational Health Psychology. Overall, the four studies provided empirical support for the majority of the hypotheses. The effects were demonstrated for a range of psychological, behavioral, and organizational level outcomes, using multiple methods of data collection, across part-time and full-time workers. At the conclusion of the thesis (Chapter 5), an overall summary is provided of the findings across all four studies, practical and theoretical implications and research directions.