Robust parameter estimation of density functions under fuzzy interval observations

International audienceThis study deals with the derivation of a probabilistic parametric model from interval data using the maximum likelihood principle. In contrast with classical techniques such as the EM algorithm, that define a precise likelihood function by computing the probability of observations viewed as a collection of non-elementary events, our approach presupposes that each imprecise observation underlies a precise one, and that the uncertainty that pervades its observation is epistemic, rather than representing noise. We define an interval-valued likelihood function and apply robust optimisation methods to find a safe plausible estimate of the statistical parameters. The approach is extended to fuzzy data by optimizing the average of lower likelikoods over a collection of data sets obtained from cuts of the fuzzy intervals, as a trade off between optimistic and pessimistic interpretations of fuzzy data. The principles of this method are compared with those of other existing approaches to handle incompleteness of observations, especially the EM technique

Variations on the Theme of Conning in Mathematical Economics

The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard xed point theorems in orthodox mathematical economics

Forum Bauinformatik 2009 : 23. bis 25. September 2009, Universität Karlsruhe (TH)

Tagungsband des 21. Forum Bauinformatik am 23. bis 25. September 2009 an der Universität Karlsruhe (TH). Beiträge von jungen Wissenschaftlern aus den Bereichen Simulationsmodelle, Numerische Methoden, Visualisierung, Informationsvermittlung, Prozess- und Produktmodellierung sowie weiterer informationstechnischer Anwendungen im Bauwesen

Essays on the economics of networks

Networks (collections of nodes or vertices and graphs capturing their linkages) are a common object of study across a range of fields includ- ing economics, statistics and computer science. Network analysis is often based around capturing the overall structure of the network by some reduced set of parameters. Canonically, this has focused on the notion of centrality. There are many measures of centrality, mostly based around statistical analysis of the linkages between nodes on the network. However, another common approach has been through the use of eigenfunction analysis of the centrality matrix. My the- sis focuses on eigencentrality as a property, paying particular focus to equilibrium behaviour when the network structure is fixed. This occurs when nodes are either passive, such as for web-searches or queueing models or when they represent active optimizing agents in network games. The major contribution of my thesis is in the applica- tion of relatively recent innovations in matrix derivatives to centrality measurements and equilibria within games that are function of those measurements. I present a series of new results on the stability of eigencentrality measures and provide some examples of applications to a number of real world examples

microeconomic theory: general equilibrium

survey of some issues in chapter 17 and following of mas colell et alias 1995 microeconomic textbook; general equilibrium, spot markets, linear and dynamic programming; discrete choice models (logit and probit) applied to a trademark valuation for a mechanical fir