2,634 research outputs found
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
. Noting the mixture model description of the MMNL, we employ a Bayesian
nonparametric approach, using nonparametric priors on the unknown mixing
distribution , 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 -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
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
Beam breakup instability in an annular electron beam
It is shown that an annular electron beam may carry six times as much current as a pencil beam for the same beam breakup (BBU) growth. This finding suggests that the rf magnetic field of the breakup mode is far more important than the rf electric field in the excitation of BBU. A proofâofâprinciple experiment is suggested, and the implications explored.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71057/2/JAPIAU-74-9-5877-1.pd
Effects of a series resistor on electron emission from a field emitter
Universal curves are constructed that provide an immediate determination of the effect of a series resistor on the electron emission from a field emitter. These curves are applicable to both the low current and high current regime. The effects of space charge and of the series resistor are apparent from these curves, which are applicable to a large class of materials. An example is given to illustrate their use. © 1996 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70468/2/APPLAB-69-18-2770-1.pd
Inverse clustering of Gibbs Partitions via independent fragmentation and dual dependent coagulation operators
Gibbs partitions of the integers generated by stable subordinators of index
form remarkable classes of random partitions where in
principle much is known about their properties, including practically
effortless obtainment of otherwise complex asymptotic results potentially
relevant to applications in general combinatorial stochastic processes, random
tree/graph growth models and Bayesian statistics. This class includes the
well-known models based on the two-parameter Poisson-Dirichlet distribution
which forms the bulk of explicit applications. This work continues efforts to
provide interpretations for a larger classes of Gibbs partitions by embedding
important operations within this framework. Here we address the formidable
problem of extending the dual, infinite-block, coagulation/fragmentation
results of Jim Pitman (1999, Annals of Probability), where in terms of
coagulation they are based on independent two-parameter Poisson-Dirichlet
distributions, to all such Gibbs (stable Poisson-Kingman) models. Our results
create nested families of Gibbs partitions, and corresponding mass partitions,
over any We primarily focus on the fragmentation
operations, which remain independent in this setting, and corresponding
remarkable calculations for Gibbs partitions derived from that operation. We
also present definitive results for the dual coagulation operations, now based
on our construction of dependent processes, and demonstrate its relatively
simple application in terms of Mittag-Leffler and generalized gamma models. The
latter demonstrates another approach to recover the duality results in Pitman
(1999)
- âŠ