Dimension-Independent MCMC Sampling for Inverse Problems with Non-Gaussian Priors

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution may be supported on an infinite dimensional space. In practice this involves the approximation of measures defined on sequences of spaces of increasing dimension. Motivated by an elliptic inverse problem with non-Gaussian prior, we study the design of proposal chains for the Metropolis-Hastings algorithm with dimension independent performance. Dimension-independent bounds on the Monte-Carlo error of MCMC sampling for Gaussian prior measures have already been established. In this paper we provide a simple recipe to obtain these bounds for non-Gaussian prior measures. To illustrate the theory we consider an elliptic inverse problem arising in groundwater flow. We explicitly construct an efficient Metropolis-Hastings proposal based on local proposals, and we provide numerical evidence which supports the theory.Comment: 26 pages, 7 figure

Long-Run Trends of Human Aging and Longevity

Over the last 200 years humans experienced a huge increase of life expectancy. These advances were largely driven by extrinsic improvements of their environment (for example, the available diet, disease prevalence, vaccination, and the state of hygiene and sanitation). In this paper we ask whether future improvements of life-expectancy will be bounded from above by human life-span. Life-span, in contrast to life-expectancy, is conceptualized as a biological measure of longevity driven by the intrinsic rate of bodily deterioration. In order to pursue our question we first present a modern theory of aging and show that immutable life-span would put an upper limit on life-expectancy. We then show for a sample of developed countries that human life-span thus defined was indeed constant until the 1950s but increased since then by about eight years in sync with life-expectancy. In other words, we find evidence for manufactured life-span.human life-span, life-expectancy, aging, compression of mortality, life-span extension

Political Institutions and Human Development Does Democracy Fulfill its 'Constructive' and 'Instrumental' Role?

Institutions are a major field of interest in the study of development processes. The authors contribute to this discussion concentrating our research on political institutions and their effect on the non-income dimensions of human development. First, they elaborate a theoretical argument why and under what conditions democracies compared to autocratic political systems might perform better with regards to the provision of public goods. Due to higher redistributive concerns matched to the needs of the population democracies should show a higher level of human development. In the following they analyze whether our theoretical expectations are supported by empirical facts. The authors perform a static panel analysis over the period of 1970 to 2003. The model confirms that living in a democratic system positively affects human development measured by life expectancy and literacy rates even controlling for GDP. By analyzing interaction effects they find that the performance of democracy is rather independent of the circumstances. However, democracy leads to more redistribution in favor of health provision in more unequal societies.human development; democracy; political institutions; life expectancy; literacy; panel analysis

The Fertility Transition Around the World - 1950-2005

In this paper we analyze the distribution of fertility rates across the world using parametric mixture models. We demonstrate the existence of twin peaks and the division of the world's countries in two distinct components: a high-fertility regime and a low fertility regime. Whereas the significance of twin peaks vanishes over time, the two fertility regimes continue to exists over the whole observation period. In 1950 about two thirds of the world's countries belonged to the high-fertility regime and the rest constituted the low-fertility regime. By the year 2005 this picture has reversed. Within both the low- and the high-fertility regime the average fertility rate declined, with a larger absolute decline within the high-fertility regime. Visually, the two peaks moved closer together. For the low fertility-group we find both ?- and ?- convergence but we cannot establish any convergence pattern for the high fertility regime. Overall our findings are difficult to reconcile with the standard view of a fertility trap but they support the differentiated take-off view established in the Unified Growth literature. --Fertility,Convergence,Twin Peaks,Fertility Regimes,Unified Growth

Bilateral trade flows and income-distribution similarity

This paper accounts for non-homothetic preferences by specifically investigating the role of income per capita and income-distribution differences in the context of the gravity model of trade. A theoretically justified gravity model is estimated for disaggregated trade data using a sample of 104 exporters and 108 importers for 1980-2003 to achieve two main goals. First we are able to empirically test some of the theoretical predictions of Markusen (2010), namely that there is a positive dependence of trade on per capita income and that higher inequality increase trade of more sophisticated goods. Second, and in line with the Linder hypothesis, we hypothesized that a higher demands’ overlap implies a more similar demand structure and therefore more trade. We test this hypothesis with new measures of income-distribution similarity. National income distributions are used to calculate income similarity indices that measure how much each country pair overlaps in terms of income distribution and population. We find that per capita income is positively related to bilateral trade and that on average, a 10 percent increase in incomedistribution similarities increases exports by almost 4 percent being this effect stronger for more sophisticated goods in comparison with more homogenous ones.Exports, Income distribution, Gravity equation, Density estimation, Non-homothetic prefereces.

Perspectives on the World Income Distribution - Beyond Twin Peaks Towards Welfare Conclusions

This paper contributes towards the growing debate concerning the world distribution of income and its evolution over that past three to four decades. Our methodological approach is twofold. First, we formally test for the number of modes in a cross-sectional analysis where each country is represented by one observation. We contribute to existing studies with technical improvements of the testing procedure, enabling us to draw new conclusions, and an extension of the time horizon being analyzed. Second, we estimate a global distribution of income from national log-normal distributions of income, as well as a global distribution of log-income as a mixture of national normal distributions of log-income. From this distribution we obtain measures for global inequality and poverty as well as global growth incidence curves.Convergence, Silverman\'s test, non-parametric statistics, bimodal, global income distribution, poverty, inequality, growth incidence curves

Efficient MCMC and posterior consistency for Bayesian inverse problems

Many mathematical models used in science and technology often contain parameters that are not known a priori. In order to match a model to a physical phenomenon, the parameters have to be adapted on the basis of the available data. One of the most important statistical concepts applied to inverse problems is the Bayesian approach which models the a priori and a posteriori uncertainty through probability distributions, called the prior and posterior, respectively. However, computational methods such as Markov Chain Monte Carlo (MCMC) have to be used because these probability measures are only given implicitly. This thesis deals with two major tasks in the area of Bayesian inverse problems: the improvement of the computational methods, in particular, different kinds of MCMC algorithms, and the properties of the Bayesian approach to inverse problems such as posterior consistency. In inverse problems, the unknown parameters are often functions and therefore elements of infinite dimensional spaces. For this reason, we have to discretise the underlying problem in order to apply MCMC methods to it. Finer discretisations lead to a higher dimensional state space and usually to a slower convergence rate of the Markov chain. We study these convergence rates rigorously and show how they deteriorate for standard methods. Moreover, we prove that slightly modified methods exhibit a dimension independent performance constituting one of the first dimension independent convergence results for locally moving MCMC algorithms. The second part of the thesis concerns numerical and analytical investigations of the posterior based on artificially generated data corresponding to a true set of parameters. In particular, we study the behaviour of the posterior as the amount of data increases or the noise in the data decreases. Posterior consistency describes the phenomenon that a sequence of posteriors concentrates around the truth. In this thesis, we present one of the first posterior consistency results for non-linear infinite dimensional inverse problems. We also study a multiscale elliptic inverse problem in detail. In particular, we show that it is not posterior consistent but the posterior concentrates around a manifold

A Contribution to the Empirics of Economic and Human Development

This book contributes to the empirical literature on economic and human development from five different perspectives: the first chapter provides a new statistical test for bimodality of densities with an application to income data. The second chapter analyzes the worlds cross-country distribution of income and challenges the so called Twin Peaks-claim. The third chapter focuses on the world income distribution and resulting implications for poverty reduction, pro-poor growth and the evolution of global inequality. The fourth chapter estimates the welfare effects of recently negotiated Economic Partnership Agreements between the EU and African countries. Finally, the fifth chapter investigates whether democracy leads to higher levels of health and education

Competitiveness – A Comparison of China and Mexico

Latin American countries have lost competitiveness in world markets in comparison to China over the last two decades. The main purpose of this study is to examine the causes of this development. To this end an augmented Ricardian model is estimated using panel data. The explanatory variables considered are productivity, unit labor costs, unit values, trade costs, price levels (in PPP), and real exchange rates in relative terms. Due to data restrictions, China’s relative exports (to the US, Argentina, Japan, Korea, UK, Germany, and Spain) will be compared to Mexico’s exports for a number of sectors over a period of eleven years. Panel and pooled estimation techniques (SUR-estimation, panel Feasible Generalized Least Squares (panel/pooled FGLS)) will be utilized to better control for country-specific effects (differences between American, Argentinian, Japanese, Korean, German, British, and Spanish markets), cross-section specific (sector-specific) effects, and correlation over time.Ricardian model of trade, panel data models, panel Feasible Generalized Least Squares, Seemingly Unrelated (SUR) estimation