Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models

This paper develops nonparametric estimation for discrete choice models based on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution $G$. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution $G$, to estimate choice probabilities. We provide an important theoretical support for the use of the proposed methodology by investigating consistency of the posterior distribution for a general nonparametric prior on the mixing distribution. Consistency is defined according to an $L_1$-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy-to-use blocked Gibbs sampling procedures. These procedures are based on approximations of the random probability measure by classes of finite stick-breaking processes. A simulation study is also performed to investigate the performance of the proposed methods.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ233 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Els primers cristians. Del Divendres Sant (any 30) al Concili de Nicea (any 325) (Reseña)

Reseña del libro de Jesús MESTRE I GODES, Els primers cristians. Del Divendres Sant (any 30) al Concili de Nicea (any 325), 62 («Llibres a l'Abast» 300), Barcelona 1997, 401 pp

On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E

Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models

This paper develops nonparametric estimation for discrete choice models based on the Mixed Multinomial Logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution G. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution G, to estimate the unknown choice probabilities. Theoretical support for the use of the proposed methodology is provided by establishing strong consistency of a general nonparametric prior on G under simple sufficient conditions. Consistency is defined according to a L1-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy to use blocked Gibbs sampling procedures. A simulation study is also performed to illustrate the proposed methods and the exibility they achieve with respect to parametric Gaussian MMNL models.Bayesian consistency, Bayesian nonparametrics, Blocked Gibbs sampler, Discrete choice models, Mixed Multinomial Logit, Random probability measures, Stick-breaking priors

General Solution Of Linear Vector Supersymmetry

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example.Comment: 18 pages, LaTeX, no figure

Comment on the ``θ\theta-term renormalization in the (2+1)-dimensional CPN−1CP^{N-1} model with θ\theta term''

It is found that the recently published first coefficient of nonzero $\beta$-function for the Chern-Simons term in the $1/N$ expansion of the $CP^{N-1}$ model is untrue numerically. The correct result is given. The main conclusions of Park's paper are not changed.Comment: 3 pages, LATE