The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

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Attitudes toward risk were measured in 240 households using two methods: an interview method eliciting certainty equivalents and an experimental gambling approach with real payoffs which, at their maximum, exceeded monthly incomes of unskilled laborers. The interview method is subject to interviewer bias and its results were totally inconsistent with the experimental measures of risk aversion. Experimental measures indicate that, at high payoff levels, virtually all individuals are moderately risk-averse with little variation according to personal characteristics. Wealth tends to reduce risk aversion slightly, but its effect is not statistically significant. Key words: India, psychological experiments, risk aversion, semi-arid tropics. The research reported here was carried out in the semi-arid, tropical areas of India, charac-terized by high climatic risk for agriculture. It was initiated to determine whether differences in behavior between farmers of different wealth levels are the consequence of different attitudes towards risk or of different constraint sets such as limitations on credit or on access to modern inputs. This question is of consid-erable policy importance because policy pre-sumably can affect credit and other con-straints faced by low income farmers more easily than their attitudes toward risk. The basic approach is experimental. It measures attitudes by observing the reactions of indi-viduals to a set of actual one-period gambles. It must be recognized that extrapolating the findings of such an approach to real farm deci-sions may face theoretical challenges. 1 Hans P. Binswanger is an associate of the Agricultural Develop-

The spectre of climate change that is unfolding now is undeniably a cumulative impact of anthropogenic interference in the climate system over the last two centuries. The science is clear and the policy community is being increasingly convinced and galvanised into action to address this emergent challenge in light of the associated economic and human dimensions. The impacts of climate change ranging from sea level rise, melting ice caps and glaciers, severe weather events, drought, flooding, warming, subtle changes in ecosystems – will impinge on every aspect of society and economic life. The costs of inaction will more than outweigh the costs of action. There is only a narrow window of opportunity to redress the situation. The Intergovernmental Panel on Climate Change (IPCC) in its Fourth Assessment Report has

) and sold �rms in the highest decile of the index (weakest rights) would have earned abnormal returns of 8.5 percent per year during the sample period. We �nd that �rms with stronger shareholder rights had higher �rm value, higher pro�ts, higher sales growth, lower capital expenditures, and made fewer

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The paper presents the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM). We will show how the PUFEM can be used to employ the structure of the differential equation under consideration to construct effective and robust methods. Although the method and its theory are valid in n dimensions, a detailed and illustrative analysis will be given for a one dimensional model problem. We identify some classes of non-standard problems which can profit highly from the advantages of the PUFEM and conclude this paper with some open questions concerning implementational aspects of the PUFEM.

We examine "realized" daily equity return volatilities and correlations obtained from high-frequency intraday transaction prices on individual stocks in the Dow Jones

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