Statistical theory of extreme values and some practical applications; a series of lectures.

Bibliography: p. 48-49.

On the detection of human influence in extreme precipitation over India

Climate change is expected to influence extreme precipitation which in turn might affect risks of pluvial flooding. Recent studies on extreme rainfall over India vary in their definition of extremes, scales of analyses and conclusions about nature of changes in such extremes. Fingerprint-based detection and attribution (D&A) offer a formal way of investigating the presence of anthropogenic signals in hydroclimatic observations. There have been recent efforts to quantify human effects in the components of the hydrologic cycle at large scales, including precipitation extremes. This study conducts a D&A analysis on precipitation extremes over India, considering both univariate and multivariate fingerprints, using a standardized probability-based index (SPI) from annual maximum one-day (RX1D) and five-day accumulated (RX5D) rainfall. The pattern-correlation based fingerprint method is used for the D&A analysis. Transformation of annual extreme values to SPI and subsequent interpolation to coarser grids are carried out to facilitate comparison between observations and model simulations. Our results show that in spite of employing these methods to address scale and physical processes mismatch between observed and model simulated extremes, attributing changes in regional extreme precipitation to anthropogenic climate change is difficult. At very high (95%) confidence, no signals are detected for RX1D, while for the RX5D and multivariate cases only the anthropogenic (ANT) signal is detected, though the fingerprints are in general found to be noisy. The findings indicate that model simulations may underestimate regional climate system responses to increasing human forcings for extremes, and though anthropogenic factors may have a role to play in causing changes in extreme precipitation, their detection is difficult at regional scales and not statistically significant. (C) 2015 Elsevier B.V. All rights reserved.

Factors contributing to the development of extreme North Atlantic cyclones and their relationship with the NAO

The occurrence of extreme cyclones is analysed in terms of their relationship to the NAO phase and the dominating environmental variables controlling their intensification. These are latent energy (equivalent potential temperature 850 hPa is used as an indicator), upper-air baroclinicity, horizontal divergence and jet stream strength. Cyclones over the North Atlantic are identified and tracked using a numerical algorithm, permitting a detailed analysis of their life cycles. Extreme cyclones are selected as the 10% most severe in terms of intensity. Investigations focus on the main strengthening phase of each cyclone. The environmental factors are related to the NAO, which affects the location and orientation of the cyclone tracks, thus explaining why extreme cyclones occur more (less) frequently during strong positive (negative) NAO phases. The enhanced number of extreme cyclones in positive NAO phases can be explained by the larger area with suitable growth conditions, which is better aligned with the cyclone tracks and is associated with increased cyclone life time and intensity. Moreover, strong intensification of cyclones is frequently linked to the occurrence of extreme values of growth factors in the immediate vicinity of the cyclone centre. Similar results are found for ECHAM5/OM1 for present day conditions, demonstrating that relationships between the environment factors and cyclones are also valid in the GCM. For future climate conditions (following the SRES A1B scenario), the results are similar, but a small increase of the frequency of extreme values is detected near the cyclone cores. On the other hand, total cyclone numbers decrease by 10% over the North Atlantic. An exception is the region near the British Isles, which features increased track density and intensity of extreme cyclones irrespective of the NAO phase. These changes are associated with an intensified jet stream close to Europe. Moreover, an enhanced frequency of explosive developments over the British Isles is found, leading to more frequent windstorms affecting Europe.

Non-stationary frequency analysis of extreme daily rainfall in Sao Paulo, Brazil

This work is an assessment of frequency of extreme values (EVs) of daily rainfall in the city of Sao Paulo. Brazil, over the period 1933-2005, based on the peaks-over-threshold (POT) and Generalized Pareto Distribution (GPD) approach. Usually. a GPD model is fitted to a sample of POT Values Selected With a constant threshold. However. in this work we use time-dependent thresholds, composed of relatively large p quantities (for example p of 0.97) of daily rainfall amounts computed from all available data. Samples of POT values were extracted with several Values of p. Four different GPD models (GPD-1, GPD-2, GPD-3. and GDP-4) were fitted to each one of these samples by the maximum likelihood (ML) method. The shape parameter was assumed constant for the four models, but time-varying covariates were incorporated into scale parameter of GPD-2. GPD-3, and GPD-4, describing annual cycle in GPD-2. linear trend in GPD-3, and both annual cycle and linear trend in GPD-4. The GPD-1 with constant scale and shape parameters is the simplest model. For identification of the best model among the four models WC used rescaled Akaike Information Criterion (AIC) with second-order bias correction. This criterion isolates GPD-3 as the best model, i.e. the one with positive linear trend in the scale parameter. The slope of this trend is significant compared to the null hypothesis of no trend, for about 98% confidence level. The non-parametric Mann-Kendall test also showed presence of positive trend in the annual frequency of excess over high thresholds. with p-value being virtually zero. Therefore. there is strong evidence that high quantiles of daily rainfall in the city of Sao Paulo have been increasing in magnitude and frequency over time. For example. 0.99 quantiles of daily rainfall amount have increased by about 40 mm between 1933 and 2005. Copyright (C) 2008 Royal Meteorological Society

Non-stationary frequency analysis of extreme daily rainfall in São Paulo, Brazil

This work is an assessment of frequency of extreme values (EVs) of daily rainfall in the city of São Paulo. Brazil, over the period 1933-2005, based on the peaks-over-threshold (POT) and Generalized Pareto Distribution (GPD) approach. Usually. a GPD model is fitted to a sample of POT Values Selected With a constant threshold. However. in this work we use time-dependent thresholds, composed of relatively large p quantities (for example p of 0.97) of daily rainfall amounts computed from all available data. Samples of POT values were extracted with several Values of p. Four different GPD models (GPD-1, GPD-2, GPD-3. and GDP-4) were fitted to each one of these samples by the maximum likelihood (ML) method. The shape parameter was assumed constant for the four models, but time-varying covariates were incorporated into scale parameter of GPD-2. GPD-3, and GPD-4, describing annual cycle in GPD-2. linear trend in GPD-3, and both annual cycle and linear trend in GPD-4. The GPD-1 with constant scale and shape parameters is the simplest model. For identification of the best model among the four models WC used rescaled Akaike Information Criterion (AIC) with second-order bias correction. This criterion isolates GPD-3 as the best model, i.e. the one with positive linear trend in the scale parameter. The slope of this trend is significant compared to the null hypothesis of no trend, for about 98% confidence level. The non-parametric Mann-Kendall test also showed presence of positive trend in the annual frequency of excess over high thresholds. with p-value being virtually zero. Therefore. there is strong evidence that high quantiles of daily rainfall in the city of São Paulo have been increasing in magnitude and frequency over time. For example. 0.99 quantiles of daily rainfall amount have increased by about 40 mm between 1933 and 2005. Copyright (C) 2008 Royal Meteorological Society

Statistical assessment of annual patterns in coastal extreme wave conditions

[EN]The annual cycle in extreme values of significant wave height is examined by transforming the timing ofthe storm peaks in a circular variable, with the aim of taking advantage of the many tests devised to explore uniformity on the circle. The use of four different but complementary uniformity tests makes possible a robust assessment of the annual cycle statistical significance. Seasonality of storms in a long time series of significant wave heights, measured in a coastal zone, is examined. The presence of a seasonal pattem is statistically beyond doubt.

Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.

Evaluation of the cost-effectiveness of strategies claiming to reduce the risk of surgical site infections following primary total hip arthroplasty

Background Total hip arthroplasty (THA) is a commonly performed procedure and numbers are increasing with ageing populations. One of the most serious complications in THA are surgical site infections (SSIs), caused by pathogens entering the wound during the procedure. SSIs are associated with a substantial burden for health services, increased mortality and reduced functional outcomes in patients. Numerous approaches to preventing these infections exist but there is no gold standard in practice and the cost-effectiveness of alternate strategies is largely unknown. Objectives The aim of this project was to evaluate the cost-effectiveness of strategies claiming to reduce deep surgical site infections following total hip arthroplasty in Australia. The objectives were: 1. Identification of competing strategies or combinations of strategies that are clinically relevant to the control of SSI related to hip arthroplasty 2. Evidence synthesis and pooling of results to assess the volume and quality of evidence claiming to reduce the risk of SSI following total hip arthroplasty 3. Construction of an economic decision model incorporating cost and health outcomes for each of the identified strategies 4. Quantification of the effect of uncertainty in the model 5. Assessment of the value of perfect information among model parameters to inform future data collection Methods The literature relating to SSI in THA was reviewed, in particular to establish definitions of these concepts, understand mechanisms of aetiology and microbiology, risk factors, diagnosis and consequences as well as to give an overview of existing infection prevention measures. Published economic evaluations on this topic were also reviewed and limitations for Australian decision-makers identified. A Markov state-transition model was developed for the Australian context and subsequently validated by clinicians. The model was designed to capture key events related to deep SSI occurring within the first 12 months following primary THA. Relevant infection prevention measures were selected by reviewing clinical guideline recommendations combined with expert elicitation. Strategies selected for evaluation were the routine use of pre-operative antibiotic prophylaxis (AP) versus no use of antibiotic prophylaxis (No AP) or in combination with antibiotic-impregnated cement (AP & ABC) or laminar air operating rooms (AP & LOR). The best available evidence for clinical effect size and utility parameters was harvested from the medical literature using reproducible methods. Queensland hospital data were extracted to inform patients’ transitions between model health states and related costs captured in assigned treatment codes. Costs related to infection prevention were derived from reliable hospital records and expert opinion. Uncertainty of model input parameters was explored in probabilistic sensitivity analyses and scenario analyses and the value of perfect information was estimated. Results The cost-effectiveness analysis was performed from a health services perspective using a hypothetical cohort of 30,000 THA patients aged 65 years. The baseline rate of deep SSI was 0.96% within one year of a primary THA. The routine use of antibiotic prophylaxis (AP) was highly cost-effective and resulted in cost savings of over $1.6m whilst generating an extra 163 QALYs (without consideration of uncertainty). Deterministic and probabilistic analysis (considering uncertainty) identified antibiotic prophylaxis combined with antibiotic-impregnated cement (AP & ABC) to be the most cost-effective strategy. Using AP & ABC generated the highest net monetary benefit (NMB) and an incremental $3.1m NMB compared to only using antibiotic prophylaxis. There was a very low error probability that this strategy might not have the largest NMB (<5%). Not using antibiotic prophylaxis (No AP) or using both antibiotic prophylaxis combined with laminar air operating rooms (AP & LOR) resulted in worse health outcomes and higher costs. Sensitivity analyses showed that the model was sensitive to the initial cohort starting age and the additional costs of ABC but the best strategy did not change, even for extreme values. The cost-effectiveness improved for a higher proportion of cemented primary THAs and higher baseline rates of deep SSI. The value of perfect information indicated that no additional research is required to support the model conclusions. Conclusions Preventing deep SSI with antibiotic prophylaxis and antibiotic-impregnated cement has shown to improve health outcomes among hospitalised patients, save lives and enhance resource allocation. By implementing a more beneficial infection control strategy, scarce health care resources can be used more efficiently to the benefit of all members of society. The results of this project provide Australian policy makers with key information about how to efficiently manage risks of infection in THA.