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.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Towards automatic object segmentation with sequential multiple views

Object segmentation is one of the fundamental steps for a number of robotic applications such as manipulation, object detection, and obstacle avoidance. This paper proposes a visual method for incorporating colour and depth information from sequential multiview stereo images to segment objects of interest from complex and cluttered environments. Rather than segmenting objects using information from a single frame in the sequence, we incorporate information from neighbouring views to increase the reliability of the information and improve the overall segmentation result. Specifically, dense depth information of a scene is computed using multiple view stereo. Depths from neighbouring views are reprojected into the reference frame to be segmented compensating for imperfect depth computations for individual frames. The multiple depth layers are then combined with color information from the reference frame to create a Markov random field to model the segmentation problem. Finally, graphcut optimisation is employed to infer pixels belonging to the object to be segmented. The segmentation accuracy is evaluated over images from an outdoor video sequence demonstrating the viability for automatic object segmentation for mobile robots using monocular cameras as a primary sensor.

Modeling random effect and excess zeros in road traffic accident prediction

Poisson distribution has often been used for count like accident data. Negative Binomial (NB) distribution has been adopted in the count data to take care of the over-dispersion problem. However, Poisson and NB distributions are incapable of taking into account some unobserved heterogeneities due to spatial and temporal effects of accident data. To overcome this problem, Random Effect models have been developed. Again another challenge with existing traffic accident prediction models is the distribution of excess zero accident observations in some accident data. Although Zero-Inflated Poisson (ZIP) model is capable of handling the dual-state system in accident data with excess zero observations, it does not accommodate the within-location correlation and between-location correlation heterogeneities which are the basic motivations for the need of the Random Effect models. This paper proposes an effective way of fitting ZIP model with location specific random effects and for model calibration and assessment the Bayesian analysis is recommended.

Practical client puzzles in the standard model

Client puzzles are cryptographic problems that are neither easy nor hard to solve. Most puzzles are based on either number theoretic or hash inversions problems. Hash-based puzzles are very efficient but so far have been shown secure only in the random oracle model; number theoretic puzzles, while secure in the standard model, tend to be inefficient. In this paper, we solve the problem of constucting cryptographic puzzles that are secure int he standard model and are very efficient. We present an efficient number theoretic puzzle that satisfies the puzzle security definition of Chen et al. (ASIACRYPT 2009). To prove the security of our puzzle, we introduce a new variant of the interval discrete logarithm assumption which may be of independent interest, and show this new problem to be hard under reasonable assumptions. Our experimental results show that, for 512-bit modulus, the solution verification time of our proposed puzzle can be up to 50x and 89x faster than the Karame-Capkum puzzle and the Rivest et al.'s time-lock puzzle respectively. In particular, the solution verification tiem of our puzzle is only 1.4x slower than that of Chen et al.'s efficient hash based puzzle.

Finding additional semantic entity information for search engines

Entity-oriented search has become an essential component of modern search engines. It focuses on retrieving a list of entities or information about the specific entities instead of documents. In this paper, we study the problem of finding entity related information, referred to as attribute-value pairs, that play a significant role in searching target entities. We propose a novel decomposition framework combining reduced relations and the discriminative model, Conditional Random Field (CRF), for automatically finding entity-related attribute-value pairs from free text documents. This decomposition framework allows us to locate potential text fragments and identify the hidden semantics, in the form of attribute-value pairs for user queries. Empirical analysis shows that the decomposition framework outperforms pattern-based approaches due to its capability of effective integration of syntactic and semantic features.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration and death are observed across all scales. For example, they govern cellular processes such as wound-healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behaviour. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pair-wise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplication, in the form of a partial differential equation description for the evolution of pair-wise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behaviour in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before, and our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Automatic object segmentation of unstructured scenes using colour and depth maps

This study presents a segmentation pipeline that fuses colour and depth information to automatically separate objects of interest in video sequences captured from a quadcopter. Many approaches assume that cameras are static with known position, a condition which cannot be preserved in most outdoor robotic applications. In this study, the authors compute depth information and camera positions from a monocular video sequence using structure from motion and use this information as an additional cue to colour for accurate segmentation. The authors model the problem similarly to standard segmentation routines as a Markov random field and perform the segmentation using graph cuts optimisation. Manual intervention is minimised and is only required to determine pixel seeds in the first frame which are then automatically reprojected into the remaining frames of the sequence. The authors also describe an automated method to adjust the relative weights for colour and depth according to their discriminative properties in each frame. Experimental results are presented for two video sequences captured using a quadcopter. The quality of the segmentation is compared to a ground truth and other state-of-the-art methods with consistently accurate results.

Short signature without random oracles and the SDH assumption in bilinear groups

We describe a short signature scheme that is strongly existentially unforgeable under an adaptive chosen message attack in the standard security model. Our construction works in groups equipped with an efficient bilinear map, or, more generally, an algorithm for the Decision Diffie-Hellman problem. The security of our scheme depends on a new intractability assumption we call Strong Diffie-Hellman (SDH), by analogy to the Strong RSA assumption with which it shares many properties. Signature generation in our system is fast and the resulting signatures are as short as DSA signatures for comparable security. We give a tight reduction proving that our scheme is secure in any group in which the SDH assumption holds, without relying on the random oracle model.

Cost efficiency of Japanese steam power generation companies : a Bayesian comparison of random and fixed frontier models

This study analyses and compares the cost efficiency of Japanese steam power generation companies using the fixed and random Bayesian frontier models. We show that it is essential to account for heterogeneity in modelling the performance of energy companies. Results from the model estimation also indicate that restricting CO2 emissions can lead to a decrease in total cost. The study finally discusses the efficiency variations between the energy companies under analysis, and elaborates on the managerial and policy implications of the results.

An MRF based abnormal event detection approach using motion and appearance features

Abnormal event detection has attracted a lot of attention in the computer vision research community during recent years due to the increased focus on automated surveillance systems to improve security in public places. Due to the scarcity of training data and the definition of an abnormality being dependent on context, abnormal event detection is generally formulated as a data-driven approach where activities are modeled in an unsupervised fashion during the training phase. In this work, we use a Gaussian mixture model (GMM) to cluster the activities during the training phase, and propose a Gaussian mixture model based Markov random field (GMM-MRF) to estimate the likelihood scores of new videos in the testing phase. Further-more, we propose two new features: optical acceleration, and the histogram of optical flow gradients; to detect the presence of any abnormal objects and speed violations in the scene. We show that our proposed method outperforms other state of the art abnormal event detection algorithms on publicly available UCSD dataset.

Pre-processing for approximate Bayesian computation in image analysis

Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.

Bayesian computational methods for spatial analysis of images

This thesis introduces a new way of using prior information in a spatial model and develops scalable algorithms for fitting this model to large imaging datasets. These methods are employed for image-guided radiation therapy and satellite based classification of land use and water quality. This study has utilized a pre-computation step to achieve a hundredfold improvement in the elapsed runtime for model fitting. This makes it much more feasible to apply these models to real-world problems, and enables full Bayesian inference for images with a million or more pixels.

Scalable Bayesian Computation for intractable likelihoods in image analysis

The inverse temperature hyperparameter of the hidden Potts model governs the strength of spatial cohesion and therefore has a substantial influence over the resulting model fit. The difficulty arises from the dependence of an intractable normalising constant on the value of the inverse temperature, thus there is no closed form solution for sampling from the distribution directly. We review three computational approaches for addressing this issue, namely pseudolikelihood, path sampling, and the approximate exchange algorithm. We compare the accuracy and scalability of these methods using a simulation study.