Ecoregion classification using a bayesian approach and centre-focused clusters

Ecological regions are increasingly used as a spatial unit for planning and environmental management. It is important to define these regions in a scientifically defensible way to justify any decisions made on the basis that they are representative of broad environmental assets. The paper describes a methodology and tool to identify cohesive bioregions. The methodology applies an elicitation process to obtain geographical descriptions for bioregions, each of these is transformed into a Normal density estimate on environmental variables within that region. This prior information is balanced with data classification of environmental datasets using a Bayesian statistical modelling approach to objectively map ecological regions. The method is called model-based clustering as it fits a Normal mixture model to the clusters associated with regions, and it addresses issues of uncertainty in environmental datasets due to overlapping clusters.

Prediction with Gaussian processes: from linear regression to linear prediction and beyond

The main aim of this paper is to provide a tutorial on regression with Gaussian processes. We start from Bayesian linear regression, and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions, rather than on priors over parameters. This leads in to a more general discussion of Gaussian processes in section 4. Section 5 deals with further issues, including hierarchical modelling and the setting of the parameters that control the Gaussian process, the covariance functions for neural network models and the use of Gaussian processes in classification problems.

Essays in Empirical Operations Management: Bayesian Learning of Service Quality and Structural Estimation of Complementary Product Pricing and Inventory Management

This dissertation contributes to the rapidly growing empirical research area in the field of operations management. It contains two essays, tackling two different sets of operations management questions which are motivated by and built on field data sets from two very different industries --- air cargo logistics and retailing.

The first essay, based on the data set obtained from a world leading third-party logistics company, develops a novel and general Bayesian hierarchical learning framework for estimating customers' spillover learning, that is, customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. We then apply our model to the data set to study how customers' experiences from shipping on a particular route affect their future decisions about shipping not only on that route, but also on other routes serviced by the same logistics company. We find that customers indeed borrow experiences from similar but different services to update their quality beliefs that determine future purchase decisions. Also, service quality beliefs have a significant impact on their future purchasing decisions. Moreover, customers are risk averse; they are averse to not only experience variability but also belief uncertainty (i.e., customer's uncertainty about their beliefs). Finally, belief uncertainty affects customers' utilities more compared to experience variability.

The second essay is based on a data set obtained from a large Chinese supermarket chain, which contains sales as well as both wholesale and retail prices of un-packaged perishable vegetables. Recognizing the special characteristics of this particularly product category, we develop a structural estimation model in a discrete-continuous choice model framework. Building on this framework, we then study an optimization model for joint pricing and inventory management strategies of multiple products, which aims at improving the company's profit from direct sales and at the same time reducing food waste and thus improving social welfare.

Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, insights, and guidance for firms to utilize vast sales and operations data to devise more effective business strategies.

Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.

Daily average temperature and mortality among the elderly : a meta-analysis and systematic review of epidemiological evidence

The impact of climate change on the health of vulnerable groups such as the elderly has been of increasing concern. However, to date there has been no meta-analysis of current literature relating to the effects of temperature fluctuations upon mortality amongst the elderly. We synthesised risk estimates of the overall impact of daily mean temperature on elderly mortality across different continents. A comprehensive literature search was conducted using MEDLINE and PubMed to identify papers published up to December 2010. Selection criteria including suitable temperature indicators, endpoints, study-designs and identification of threshold were used. A two-stage Bayesian hierarchical model was performed to summarise the percent increase in mortality with a 1°C temperature increase (or decrease) with 95% confidence intervals in hot (or cold) days, with lagged effects also measured. Fifteen studies met the eligibility criteria and almost 13 million elderly deaths were included in this meta-analysis. In total, there was a 2-5% increase for a 1°C increment during hot temperature intervals, and a 1-2 % increase in all-cause mortality for a 1°C decrease during cold temperature intervals. Lags of up to 9 days in exposure to cold temperature intervals were substantially associated with all-cause mortality, but no substantial lagged effects were observed for hot intervals. Thus, both hot and cold temperatures substantially increased mortality among the elderly, but the magnitude of heat-related effects seemed to be larger than that of cold effects within a global context.

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.

Ambient temperature and cardiorespiratory morbidity : a systematic review and meta-analysis

BACKGROUND: The effect of extreme temperature has become an increasing public health concern. Evaluating the impact of ambient temperature on morbidity has received less attention than its impact on mortality. METHODS: We performed a systematic literature review and extracted quantitative estimates of the effects of hot temperatures on cardiorespiratory morbidity. There were too few studies on effects of cold temperatures to warrant a summary. Pooled estimates of effects of heat were calculated using a Bayesian hierarchical approach that allowed multiple results to be included from the same study, particularly results at different latitudes and with varying lagged effects. RESULTS: Twenty-one studies were included in the final meta-analysis. The pooled results suggest an increase of 3.2% (95% posterior interval = -3.2% to 10.1%) in respiratory morbidity with 1°C increase on hot days. No apparent association was observed for cardiovascular morbidity (-0.5% [-3.0% to 2.1%]). The length of lags had inconsistent effects on the risk of respiratory and cardiovascular morbidity, whereas latitude had little effect on either. CONCLUSIONS: The effects of temperature on cardiorespiratory morbidity seemed to be smaller and more variable than previous findings related to mortality.

Spatial inequalities in colorectal and breast cancer survival : premature deaths and associated factors

This study examines the influence of cancer stage, distance to treatment facilities and area disadvantage on breast and colorectal cancer spatial survival inequalities. We also estimate the number of premature deaths after adjusting for cancer stage to quantify the impact of spatial survival inequalities. Population-based descriptive study of residents aged <90 years in Queensland, Australia diagnosed with primary invasive breast (25,202 females) or colorectal (14,690 males, 11,700 females) cancers during 1996-2007. Bayesian hierarchical models explored relative survival inequalities across 478 regions. Cancer stage and disadvantage explained the spatial inequalities in breast cancer survival, however spatial inequalities in colorectal cancer survival persisted after adjustment. Of the 6,019 colorectal cancer deaths within 5 years of diagnosis, 470 (8%) were associated with spatial inequalities in non-diagnostic factors, i.e. factors beyond cancer stage at diagnosis. For breast cancers, of 2,412 deaths, 170 (7%) were related to spatial inequalities in non-diagnostic factors. Quantifying premature deaths can increase incentive for action to reduce these spatial inequalities.

Estimating the effects of environmental exposures using a weighted mean of monitoring stations

The health effects of environmental hazards are often examined using time series of the association between a daily response variable (e.g., death) and a daily level of exposure (e.g., temperature). Exposures are usually the average from a network of stations. This gives each station equal importance, and negates the opportunity for some stations to be better measures of exposure. We used a Bayesian hierarchical model that weighted stations using random variables between zero and one. We compared the weighted estimates to the standard model using data on health outcomes (deaths and hospital admissions) and exposures (air pollution and temperature) in Brisbane, Australia. The improvements in model fit were relatively small, and the estimated health effects of pollution were similar using either the standard or weighted estimates. Spatial weighted exposures would be probably more worthwhile when there is either greater spatial detail in the health outcome, or a greater spatial variation in exposure.

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Likelihood‐free inference for transmission rates of nosocomial pathogens

This chapter contains sections titled: Introduction Case study: Estimating transmission rates of nosocomial pathogens Models and methods Data analysis and results Discussion References