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A survey of Monte Carlo algorithms for maximizing the likelihood of a twostage hierarchical model
, 2001
"... Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternati ..."
Abstract

Cited by 15 (8 self)
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Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternative approach is to approximate the intractable integrals using Monte Carlo averages. Several dierent algorithms based on this idea have been proposed. In this paper we discuss the relative merits of simulated maximum likelihood, Monte Carlo EM, Monte Carlo NewtonRaphson and stochastic approximation. Key words and phrases : Eciency, Monte Carlo EM, Monte Carlo NewtonRaphson, Rate of convergence, Simulated maximum likelihood, Stochastic approximation All three authors partially supported by NSF Grant DMS0072827. 1 1
Noname manuscript No. (will be inserted by the editor) Competition Among Providers in Loss Networks
"... Abstract Communication networks are becoming ubiquitous and more and more competitive among revenuemaximizing providers, operating on potentially different technologies. In this paper, we propose to analyze the competition of providers playing with access prices and fighting for customers. Consid ..."
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Abstract Communication networks are becoming ubiquitous and more and more competitive among revenuemaximizing providers, operating on potentially different technologies. In this paper, we propose to analyze the competition of providers playing with access prices and fighting for customers. Considering a slottedtime model, the part of demand exceeding capacity is lost and has to be resent. We consider an access price for submitted packets, thus inducing a congestion pricing through losses. Customers therefore choose the provider with the cheapest average price per correctly transmitted unit of traffic. The model is a twolevel game, the lower level for the distribution of customers among providers, and the upper level for the competition on prices among providers, taking into account what the subsequent repartition at the lower level will be. We prove that the upper level has a unique Nash equilibrium, for which the user repartition among different available providers is also unique, and efficient in the sense of social welfare. Moreover, even when adding a higher level game on capacity disclosure with a possibility of lying for providers, providers are better off being truthful, and the unique Nash equilibrium is thus unchanged.