Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Relative entropy rate based design for linear hybrid system models

Hybrid system representations have been applied to many challenging modeling situations. In these hybrid system representations, a mixture of continuous and discrete states is used to capture the dominating behavioural features of a nonlinear, possible uncertain, model under approximation. Unfortunately, the problem of how to best design a suitable hybrid system model has not yet been fully addressed. This paper proposes a new joint state measurement relative entropy rate based approach for this design purpose. Design examples and simulation studies are presented which highlight the benefits of our proposed design approaches.

The Relative Efficiency of International, Domestic, and Budget Airlines : Nonparametric Evidence

This study determines whether the inclusion of low-cost airlines in a dataset of international and domestic airlines has an impact on the efficiency scores of so-called ‘prestigious’ purportedly ‘efficient’ airlines. This is because while many airline studies concern efficiency, none has truly included a combination of international, domestic and budget airlines. The present study employs the nonparametric technique of data envelopment analysis (DEA) to investigate the technical efficiency of 53 airlines in 2006. The findings reveal that the majority of budget airlines are efficient relative to their more prestigious counterparts. Moreover, most airlines identified as inefficient are so largely because of the overutilization of non-flight assets.

Intolerance of uncertainty and meta-worry : relative importance in discriminating GAD

This study explored whether intolerance of uncertainty and/or meta-worry discriminate between non-clinical individuals and those diagnosed with generalised anxiety disorder (GAD group). The participants were 107 GAD clients and 91 university students. The students were divided into two groups (high and low GAD symptom groups). A multivariate analysis of covariance (MANCOVA) adjusting for age indicated that intolerance of uncertainty distinguished between the low GAD symptom group and the high GAD symptom group, and between the low GAD symptom group and the GAD group. Meta-worry distinguished all three groups. A discriminant function including intolerance of uncertainty and meta-worry classified 94.4% of the GAD group and 97.9% of the low GAD symptom group. Only 6.8% of the high GAD symptom group was classified correctly, 77.3% of the high GAD symptom group was classified as GAD. Findings indicated that intolerance of uncertainty and meta-worry may assist with the diagnosis and treatment of GAD.

An infinite-horizon robust filter for uncertain hidden Markov Models with conditional relative entropy constraints

We consider a robust filtering problem for uncertain discrete-time, homogeneous, first-order, finite-state hidden Markov models (HMMs). The class of uncertain HMMs considered is described by a conditional relative entropy constraint on measures perturbed from a nominal regular conditional probability distribution given the previous posterior state distribution and the latest measurement. Under this class of perturbations, a robust infinite horizon filtering problem is first formulated as a constrained optimization problem before being transformed via variational results into an unconstrained optimization problem; the latter can be elegantly solved using a risk-sensitive information-state based filtering.

The relative importance of factors influencing bicycling crash risk

Government promotion of active transport has renewed interest in cycling safety. Research has shown that bicyclists are up to 20 times more likely to be involved in serious injury crashes than drivers. On-road cycling injuries are under-reported in police data, and many non-serious injuries are not recorded in any official database. This study aims to explore the relationships between rider characteristics and environmental factors that influence per kilometre risk of bicycle-related crash and non-crash injuries.

A note on the ‘Linsanity’ of measuring the relative efficiency of National Basketball Association (NBA) guards

This note examines the productive efficiency of 62 starting guards during the 2011/12 National Basketball Association (NBA) season. This period coincides with the phenomenal and largely unanticipated performance of New York Knicks’ starting point guard Jeremy Lin and the attendant public and media hype known as Linsanity. We employ a data envelopment analysis (DEA) approach that includes allowance for an undesirable output, here turnovers per game, with the desirable outputs of points, rebounds, assists, steals, and blocks per game and an input of minutes per game. The results indicate that depending upon the specification, between 29 and 42 percent of NBA guards are fully efficient, including Jeremy Lin, with a mean inefficiency of 3.7 and 19.2 percent. However, while Jeremy Lin is technically efficient, he seldom serves as a benchmark for inefficient players, at least when compared with established players such as Chris Paul and Dwayne Wade. This suggests the uniqueness of Jeremy Lin’s productive solution and may explain why his unique style of play, encompassing individual brilliance, unselfish play, and team leadership, is of such broad public appeal.

HMM triangle relative entropy concepts in sequential change detection applied to vision-based dim target manoeuvre detection

The quick detection of abrupt (unknown) parameter changes in an observed hidden Markov model (HMM) is important in several applications. Motivated by the recent application of relative entropy concepts in the robust sequential change detection problem (and the related model selection problem), this paper proposes a sequential unknown change detection algorithm based on a relative entropy based HMM parameter estimator. Our proposed approach is able to overcome the lack of knowledge of post-change parameters, and is illustrated to have similar performance to the popular cumulative sum (CUSUM) algorithm (which requires knowledge of the post-change parameter values) when examined, on both simulated and real data, in a vision-based aircraft manoeuvre detection problem.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

The relative risk of second primary cancers in Queensland, Australia: A retrospective cohort study

Background Cancer survivors face an increased likelihood of being subsequently diagnosed with another cancer. The aim of this study was to quantify the relative risk of survivors developing a second primary cancer in Queensland, Australia. Methods Standardised incidence rates stratified by type of first primary cancer, type of second primary cancer, sex, age at first diagnosis, period of first diagnosis and follow-up interval were calculated for residents of Queensland, Australia, who were diagnosed with a first primary invasive cancer between 1982 and 2001 and survived for a minimum of 2 months. Results A total of 23,580 second invasive primary cancers were observed over 1,370,247 years of follow-up among 204,962 cancer patients. Both males (SIR = 1.22; 95% CI = 1.20-1.24) and females (SIR = 1.36; 95% CI = 1.33-1.39) within the study cohort were found to have a significant excess risk of developing a second cancer relative to the incidence of cancer in the general population. The observed number of second primary cancers was also higher than expected within each age group, across all time periods and during each follow-up interval. Conclusions The excess risk of developing a second malignancy among cancer survivors can likely be attributed to factors including similar aetiologies, genetics and the effects of treatment, underlining the need for ongoing monitoring of cancer patients to detect subsequent tumours at an early stage. Education campaigns developed specifically for survivors may be required to lessen the prevalence of known cancer risk factors.