Background Global and regional projections of mortality and burden of disease by cause for the years 2000, 2010, and 2030 were published by Murray and Lopez in 1996 as part of the Global Burden of Disease project. These projections, which are based on 1990 data, continue to be widely quoted, although they are substantially outdated; in particular, they substantially underestimated the spread of HIV/AIDS. To address the widespread demand for information on likely future trends in global health, and thereby to support international health policy and priority setting, we have prepared new projections of mortality and burden of disease to 2030 starting from World Health Organization estimates of mortality and burden of disease for 2002. This paper describes the methods, assumptions, input data, and results. Methods and Findings Relatively simple models were used to project future health trends under three scenarios—baseline, optimistic, and pessimistic—based largely on projections of economic and social development, and using the historically observed relationships of these with cause-specific mortality rates. Data inputs have been updated to take account of the greater availability of death registration data and the latest available projections for HIV/AIDS, income, human capital, tobacco smoking, body mass index, and other inputs. In all three scenarios there is a dramatic shift in the distribution of deaths from younger to older ages and from communicable, maternal, perinatal, and nutritional causes to noncommunicable disease causes. The risk of death for children younger than 5 y is projected to fall by nearly 50% in the baseline scenario between 2002 and 2030. The proportion of deaths due to noncommunicable disease is projected to rise from 59% in 2002 to 69% in 2030. Global HIV/AIDS deaths are projected to rise from 2.8 million in 2002 to 6.5 million in 2030 under the baseline scenario, which assumes coverage with antiretroviral drugs reaches 80% by 2012. Under the optimistic scenario, which also assumes increased prevention activity, HIV/AIDS deaths are projected to drop to 3.7 million in 2030. Total tobacco-attributable deaths are projected to rise from 5.4 million in 2005 to 6.4 million in 2015 and 8.3 million in 2030 under our baseline scenario. Tobacco is projected to kill 50% more people in 2015 than HIV/AIDS, and to be responsible for 10% of all deaths globally. The three leading causes of burden of disease in 2030 are projected to include HIV/AIDS, unipolar depressive disorders, and ischaemic heart disease in the baseline and pessimistic scenarios. Road traffic accidents are the fourth leading cause in the baseline scenario, and the third leading cause ahead of ischaemic heart disease in the optimistic scenario. Under the baseline scenario, HIV/AIDS becomes the leading cause of burden of disease in middle- and low-income countries by 2015. Conclusions These projections represent a set of three visions of the future for population health, based on certain explicit assumptions. Despite the wide uncertainty ranges around future projections, they enable us to appreciate better the implications for health and health policy of currently observed trends, and the likely impact of fairly certain future trends, such as the ageing of the population, the continued spread of HIV/AIDS in many regions, and the continuation of the epidemiological transition in developing countries. The results depend strongly on the assumption that future mortality trends in poor countries will have a relationship to economic and social development similar to those that have occurred in the higher-income countries.

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Projections of Global Mortality and Burden of Disease from 2002 to 2030

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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Modern Applied Statistics With S

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionF if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the ...

/pdf/strictly-proper-scoring-rules-prediction-and-estimation-28cdd1b5ww.pdf

Strictly Proper Scoring Rules, Prediction, and Estimation

This work is motivated by a mobility study conducted in the city of Munich, Germany. The variable of interest is a binary response, which indicates whether public transport has
been utilized or not. One of the central questions is to identify areas of low/high utilization of public transport after adjusting for explanatory factors such as trip, individual and household
attributes. For the spatial effects a modification of a class of Markov Random Fields (MRF) models with proper joint distributions introduced by Pettitt et al. (2002) is developed. It
contains the intrinsic MRF in the limit and allows for efficient Markov Chain Monte Carlo (MCMC) algorithms. Further cluster effects using group and individual approaches are
taken into consideration. The first one models heterogeneity between clusters, while the second one models heterogeneity within clusters. A naive approach to include individual
cluster effects results in an unidentifiable model. It is shown how a re-parametrization gives identifiable parameters. This provides a new approach for modeling heterogeneity within
clusters. Finally the proposed model classes are applied to the mobility study.

Modelling transport mode decisions using hierarchical logistic regression models with spatial and cluster effects

We examine the dependence structure of finite block-maxima of multivariate distributions. We provide a closed form expression for the copula density of the vector of the block-maxima. Further, we show how partial derivatives of three-dimensional vine copulas can be obtained by only one-dimensional integration. Combining these results allows the numerical treatment of the block-maxima of any three-dimensional vine copula for finite block-sizes. We look at certain vine copula specifications and examine how the density of the block-maxima behaves for different block-sizes. Additionally, a real data example from hydrology is considered. In extreme-value theory for multivariate normal distributions, a certain scaling of each variable and the correlation matrix is necessary to obtain a non-trivial limiting distribution when the block-size goes to infinity. This scaling is applied to different three-dimensional vine copula specifications.

/pdf/block-maxima-of-vines-24vfb8607x.pdf

Block-Maxima of Vines

Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a set of candidate models out of which the best one is supposed to be selected. For example, this may arise in the context of non-simplified vine copulas, truncations of vines and other simplifications regarding pair-copula families or the vine structure. With the help of distance measures we develop a parametric bootstrap based testing procedure to decide between copulas from nested model classes. In addition we use distance measures to select among different candidate models. All commonly used distance measures, e.g. the Kullback-Leibler distance, suffer from the curse of dimensionality due to high-dimensional integrals. As a remedy for this problem, Killiches, Kraus and Czado (2017) propose several modifications of the Kullback-Leibler distance. We apply these distance measures to the above mentioned model selection problems and substantiate their usefulness.

Using model distances to investigate the simplifying assumption, model selection and truncation levels for vine copulas

While environmental, social, and governance (ESG) trading activity has been a distinctive feature of financial markets, the debate if ESG scores can also convey information regarding a company's riskiness remains open. Regulatory authorities, such as the European Banking Authority (EBA), have acknowledged that ESG factors can contribute to risk. Therefore, it is important to model such risks and quantify what part of a company's riskiness can be attributed to the ESG scores. This paper aims to question whether ESG scores can be used to provide information on (tail) riskiness. By analyzing the (tail) dependence structure of companies with a range of ESG scores, that is within an ESG rating class, using high-dimensional vine copula modelling, we are able to show that risk can also depend on and be directly associated with a specific ESG rating class. Empirical findings on real-world data show positive not negligible ESG risks determined by ESG scores, especially during the 2008 crisis.

ESG, Risk, and (Tail) Dependence

Modeling dependence among operational loss frequencies is a natural way of trying to capture possible relationships between losses, which are categorized differently with respect to the business line or the event type, but which have occurred simultaneously.We propose a model that explicitly accounts for such dependence and allows modeling it in a heterogeneous way to capture the wide spectrum of dependence structures operational losses exhibit.Our model relies on a pair copula construction, which flexibly combines different bivariate copulas, to estimate efficiently the joint multivariate distribution and then determine the total risk capital.Empirical results on real-world data show that such flexible explicit dependence modeling might have a significant impact on the risk capital, leading to a clear diversification benefit compared to the standard Basel comonotonicity assumption.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2345342_code1208064.pdf?abstractid=2345342&mirid=1&type=2

Claudia Czado

Papers

Modelling transport mode decisions using hierarchical logistic regression models with spatial and cluster effects

Block-Maxima of Vines

Using model distances to investigate the simplifying assumption, model selection and truncation levels for vine copulas

ESG, Risk, and (Tail) Dependence

Modeling Dependence of Operational Loss Frequencies