Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

Maintenance optimisation of a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals

This paper presents a maintenance optimisation method for a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals. The objective function considered in the paper is the average revenue per unit time calculated based on the semi-regenerative theory and the universal generating function (UGF). A new algorithm using the stochastic ordering is also developed in this paper to reduce the search space of maintenance strategies and to enhance the efficiency of optimisation algorithms. A numerical simulation is presented in the study to evaluate the efficiency of the proposed maintenance strategy and optimisation algorithms. The simulation result reveals that maintenance strategies with opportunistic maintenance and state-dependent inspection intervals are more cost-effective when the influence of economic dependence and inspection cost is significant. The study further demonstrates that the optimisation algorithm proposed in this paper has higher computational efficiency than the commonly employed heuristic algorithms.

Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Beyond point forecasting : evaluation of alternative prediction intervals for tourist arrivals

This paper evaluates the performances of prediction intervals generated from alternative time series models, in the context of tourism forecasting. The forecasting methods considered include the autoregressive (AR) model, the AR model using the bias-corrected bootstrap, seasonal ARIMA models, innovations state space models for exponential smoothing, and Harvey’s structural time series models. We use thirteen monthly time series for the number of tourist arrivals to Hong Kong and Australia. The mean coverage rates and widths of the alternative prediction intervals are evaluated in an empirical setting. It is found that all models produce satisfactory prediction intervals, except for the autoregressive model. In particular, those based on the biascorrected bootstrap perform best in general, providing tight intervals with accurate coverage rates, especially when the forecast horizon is long.

Exact parametric confidence intervals for Bland-Altman limits of agreement

Purpose The previous literature on Bland-Altman analysis only describes approximate methods for calculating confidence intervals for 95% Limits of Agreement (LoAs). This paper describes exact methods for calculating such confidence intervals, based on the assumption that differences in measurement pairs are normally distributed. Methods Two basic situations are considered for calculating LoA confidence intervals: the first where LoAs are considered individually (i.e. using one-sided tolerance factors for a normal distribution); and the second, where LoAs are considered as a pair (i.e. using two-sided tolerance factors for a normal distribution). Equations underlying the calculation of exact confidence limits are briefly outlined. Results To assist in determining confidence intervals for LoAs (considered individually and as a pair) tables of coefficients have been included for degrees of freedom between 1 and 1000. Numerical examples, showing the use of the tables for calculating confidence limits for Bland-Altman LoAs, have been provided. Conclusions Exact confidence intervals for LoAs can differ considerably from Bland and Altman’s approximate method, especially for sample sizes that are not large. There are better, more precise methods for calculating confidence intervals for LoAs than Bland and Altman’s approximate method, although even an approximate calculation of confidence intervals for LoAs is likely to be better than none at all. Reporting confidence limits for LoAs considered as a pair is appropriate for most situations, however there may be circumstances where it is appropriate to report confidence limits for LoAs considered individually.

Methods for constructing uncertainty intervals for queries of Bayesian nets

In this paper the issue of finding uncertainty intervals for queries in a Bayesian Network is reconsidered. The investigation focuses on Bayesian Nets with discrete nodes and finite populations. An earlier asymptotic approach is compared with a simulation-based approach, together with further alternatives, one based on a single sample of the Bayesian Net of a particular finite population size, and another which uses expected population sizes together with exact probabilities. We conclude that a query of a Bayesian Net should be expressed as a probability embedded in an uncertainty interval. Based on an investigation of two Bayesian Net structures, the preferred method is the simulation method. However, both the single sample method and the expected sample size methods may be useful and are simpler to compute. Any method at all is more useful than none, when assessing a Bayesian Net under development, or when drawing conclusions from an ‘expert’ system.

An extravariation model for improving confidence intervals of population size estimates from removal data

We propose a new model for estimating the size of a population from successive catches taken during a removal experiment. The data from these experiments often have excessive variation, known as overdispersion, as compared with that predicted by the multinomial model. The new model allows catchability to vary randomly among samplings, which accounts for overdispersion. When the catchability is assumed to have a beta distribution, the likelihood function, which is refered to as beta-multinomial, is derived, and hence the maximum likelihood estimates can be evaluated. Simulations show that in the presence of extravariation in the data, the confidence intervals have been substantially underestimated in previous models (Leslie-DeLury, Moran) and that the new model provides more reliable confidence intervals. The performance of these methods was also demonstrated using two real data sets: one with overdispersion, from smallmouth bass (Micropterus dolomieu), and the other without overdispersion, from rat (Rattus rattus).

Cross-correlations between weather variables in Australia

The information on climate variations is essential for the research of many subjects, such as the performance of buildings and agricultural production. However, recorded meteorological data are often incomplete. There may be a limited number of locations recorded, while the number of recorded climatic variables and the time intervals can also be inadequate. Therefore, the hourly data of key weather parameters as required by many building simulation programmes are typically not readily available. To overcome this gap in measured information, several empirical methods and weather data generators have been developed. They generally employ statistical analysis techniques to model the variations of individual climatic variables, while the possible interactions between different weather parameters are largely ignored. Based on a statistical analysis of 10 years historical hourly climatic data over all capital cities in Australia, this paper reports on the finding of strong correlations between several specific weather variables. It is found that there are strong linear correlations between the hourly variations of global solar irradiation (GSI) and dry bulb temperature (DBT), and between the hourly variations of DBT and relative humidity (RH). With an increase in GSI, DBT would generally increase, while the RH tends to decrease. However, no such a clear correlation can be found between the DBT and atmospheric pressure (P), and between the DBT and wind speed. These findings will be useful for the research and practice in building performance simulation.

Radiographic outcomes over time after endoscopic anterior scoliosis correction

A prospective, consecutive series of 106 patients receiving endoscopic anterior scoliosis correction. The aim was to analyse changes in radiographic parameters and rib hump in the two years following surgery. Endoscopic anterior scoliosis correction is a level sparing approach, therefore it is important to assess the amount of decompensation which occurs after surgery. All patients received a single anterior rod and vertebral body screws using a standard compression technique. Cleared disc spaces were packed with either mulched femoral head allograft or rib head/iliac crest autograft. Radiographic parameters (major, instrumented, minor Cobb, T5-T12 kyphosis) and rib hump were measured at 2,6,12 and 24 months after surgery. Paired t-tests and Wilcoxon signed ranks tests were used to assess the statistical significant of changes between adjacent time intervals.----- Results: Mean loss of major curve correction from 2 to 24 months after surgery was 4 degrees. Mean loss of rib hump correction was 1.4 degrees. Mean sagittal kyphosis increased from 27 degrees at 2 months to 30.6 degrees at 24 months. Rod fractures and screw-related complications resulted in several degrees less correction than patients without complications, but overall there was no clinically significant decompensation following complications. The study concluded that there are small changes in deformity measures after endoscopic anterior scoliosis surgery, which are statistically significant but not clinically significant.

Does psychological stress mediate social deprivation in tooth loss?

It is unclear which theoretical dimension of psychological stress affects health status. We hypothesized that both distress and coping mediate the relationship between socio-economic position and tooth loss. Cross-sectional data from 2915 middle-aged adults evaluated retention of < 20 teeth, behaviors, psychological stress, and sociodemographic characteristics. Principal components analysis of the Perceived Stress Scale (PSS) extracted 'distress' (a = 0.85) and 'coping' (a =0.83) factors, consistent with theory. Hierarchical entry of explanatory variables into age- and sex-adjusted logistic regression models estimated odds ratios (OR) and 95% confidence intervals [95% CI] for retention of < 20 teeth. Analysis of the separate contributions of distress and coping revealed a significant main effect of coping (OR = 0.7 [95% CI = 0.7-0.8]), but no effect for distress (OR = 1.0 [95% CI = 0.9-1.1]) or for the interaction of coping and distress. Behavior and psychological stress only modestly attenuated socio-economic inequality in retention of < 20 teeth, providing evidence to support a mediating role of coping.

Increased body temperature following subarachnoid haemorrhage : a retrospective correlational study

Introduction: Nursing clinicians are primarily responsible for the monitoring and treatment of increased body temperature. The body temperature of patients during their acute care hospital stay is measured at regular repeated intervals. In the event a patient is assessed with an elevated temperature, a multitude of decisions are required. The action of instigating temperature reducing strategies is based upon the assumption that elevated temperature is harmful and that the strategy employed will have some beneficial effect. Background and Significance: The potential harmful effects of increased body temperature (fever, hyperthermia) following neurological insult are well recognised. Although few studies have investigated this phenomenon in the diagnostic population of non-traumatic subarachnoid haemorrhage, it has been demonstrated that increased body temperature occurs in 41 to 72% of patients with poor clinical outcome. However, in the Australian context the frequency, or other characteristics of increased body temperature, as well as the association between increased body temperature with poor clinical outcome has not been established. Design: This study used a correlational study design to: describe the frequency, duration and timing of increased body temperature; determine the association between increased body temperature and clinical outcome; and describe the clinical interventions used to manage increased body temperature in patients with non-traumatic subarachnoid haemorrhage. A retrospective clinical chart audit was conducted on 43 patients who met the inclusion criteria. Findings: The major findings of this study were: increased body temperature occurred frequently; persisted for a long time; and onset did not occur until 20 hours after primary insult; increased body temperature was associated with death or dependent outcome; and no intervention was recorded in many instances. Conclusion: This study has quantified in a non-traumatic subarachnoid haemorrhage patient population the characteristics of increased body temperature, established an association between increased body temperature with death or dependent outcome and described the current management of elevated temperatures in the Australian context to improve nursing practice, education and research.

The impact of perceived stage of cancer on carers’ anxiety and depression during the patients’ final year of life

Objective: This paper explores the effects of perceived stage of cancer (PSOC) on carers' anxiety and depression during the patients' final year. Methods: A consecutive sample of patients and carers (N=98) were surveyed at regular intervals regarding PSOC, and anxiety and depression using the Hospital Anxiety and Depression Scale. Means were compared by gender using the Mann-Whitney U-test. The chi-square was used to analyse categorical data. Agreement between carers' and patients' PSOC was estimated using kappa statistics. Correlations between carers' PSOC and their anxiety and depression were calculated using the Spearman's rank correlation. Results: Over time, an increasing proportion of carers reported that the cancer was advanced, culminating at 43% near death. Agreement regarding PSOC was fair (kappa=0.29-0.34) until near death (kappa=0.21). Carers' anxiety increased over the year; depression increased in the final 6 months. Females were more anxious (p=0.049, 6 months; p=0.009, 3 months) than males, and more depressed until 1 month to death. The proportion of carers reporting moderate-severe anxiety almost doubled over the year to 27%, with more females in this category at 6 months (p=0.05). Carers with moderate-severe depression increased from 6 to 15% over the year. Increased PSOC was weakly correlated with increased anxiety and depression. Conclusions: Carers' anxiety exceeded depression in severity during advanced cancer. Females generally experienced greater anxiety and depression. Carers were more realistic than patients regarding the ultimate outcome, which was reflected in their declining mental health, particularly near the end.