Proactive detection of high collision concentration locations on highways

In previous research (Chung et al., 2009), the potential of the continuous risk profile (CRP) to proactively detect the systematic deterioration of freeway safety levels was presented. In this paper, this potential is investigated further, and an algorithm is proposed for proactively detecting sites where the collision rate is not sufficiently high to be classified as a high collision concentration location but where a systematic deterioration of safety level is observed. The approach proposed compares the weighted CRP across different years and uses the cumulative sum (CUSUM) algorithm to detect the sites where changes in collision rate are observed. The CRPs of the detected sites are then compared for reproducibility. When high reproducibility is observed, a growth factor is used for sequential hypothesis testing to determine if the collision profiles are increasing over time. Findings from applying the proposed method using empirical data are documented in the paper together with a detailed description of the method.

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

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.

Asymptotic minimax robust and misspecified Lorden quickest change detection for dependent stochastic processes

The quick detection of an abrupt unknown change in the conditional distribution of a dependent stochastic process has numerous applications. In this paper, we pose a minimax robust quickest change detection problem for cases where there is uncertainty about the post-change conditional distribution. Our minimax robust formulation is based on the popular Lorden criteria of optimal quickest change detection. Under a condition on the set of possible post-change distributions, we show that the widely known cumulative sum (CUSUM) rule is asymptotically minimax robust under our Lorden minimax robust formulation as a false alarm constraint becomes more strict. We also establish general asymptotic bounds on the detection delay of misspecified CUSUM rules (i.e. CUSUM rules that are designed with post- change distributions that differ from those of the observed sequence). We exploit these bounds to compare the delay performance of asymptotically minimax robust, asymptotically optimal, and other misspecified CUSUM rules. In simulation examples, we illustrate that asymptotically minimax robust CUSUM rules can provide better detection delay performance at greatly reduced computation effort compared to competing generalised likelihood ratio procedures.

Outbreak detection algorithms for seasonal disease data : a case study using Ross River virus disease

Background Detection of outbreaks is an important part of disease surveillance. Although many algorithms have been designed for detecting outbreaks, few have been specifically assessed against diseases that have distinct seasonal incidence patterns, such as those caused by vector-borne pathogens. Methods We applied five previously reported outbreak detection algorithms to Ross River virus (RRV) disease data (1991-2007) for the four local government areas (LGAs) of Brisbane, Emerald, Redland and Townsville in Queensland, Australia. The methods used were the Early Aberration Reporting System (EARS) C1, C2 and C3 methods, negative binomial cusum (NBC), historical limits method (HLM), Poisson outbreak detection (POD) method and the purely temporal SaTScan analysis. Seasonally-adjusted variants of the NBC and SaTScan methods were developed. Some of the algorithms were applied using a range of parameter values, resulting in 17 variants of the five algorithms. Results The 9,188 RRV disease notifications that occurred in the four selected regions over the study period showed marked seasonality, which adversely affected the performance of some of the outbreak detection algorithms. Most of the methods examined were able to detect the same major events. The exception was the seasonally-adjusted NBC methods that detected an excess of short signals. The NBC, POD and temporal SaTScan algorithms were the only methods that consistently had high true positive rates and low false positive and false negative rates across the four study areas. The timeliness of outbreak signals generated by each method was also compared but there was no consistency across outbreaks and LGAs. Conclusions This study has highlighted several issues associated with applying outbreak detection algorithms to seasonal disease data. In lieu of a true gold standard, a quantitative comparison is difficult and caution should be taken when interpreting the true positives, false positives, sensitivity and specificity.

Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.