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

Ambitable topological groups

A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n bounded topological group is either precompact or ambitable. In the familiar semigroups constructed over ambitable groups, topological centres have an effective characterization.Comment: LaTeX; 12 pages; Changes in versions 2 and 3: New Theorem 3.3 and improvements enabled by it; Changes in version 4: Corrections for Theorems 4.9 and 4.10, added 1 referenc

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

Sleep Quality, Academic Performance, and Personality Examined

I will be examining relationships between sleep quality, academic performance, and personality. Results showed that there was a negative correlation found between the PSQI score and conscientiousness (r = -.223) and between the PSQI score and emotional stability (r = -.445). There was no significant effect for the PSQI score t(76) = -1.6, p = .121, despite women (M = 8.06, SD = 3.49) attaining higher scores than men (M = 6.83, SD = 3.16). This study investigates whether there is a relationship between one’s sleep quality, personality traits, and academic performance. A negative relationship was found between sleep quality and conscientiousness and between sleep quality and emotional stability. No other significant relationships were found. The results are similar to the findings by Alotaibi et al. (2020), who also found no significant relationship between academic performance and sleep quality. For further research, a bigger sample size would be preferred. A more reliable way of obtaining participants’ sleep quality would be better instead of using a self-reflection questionnaire

BONNSAI: a Bayesian tool for comparing stars with stellar evolution models

Powerful telescopes equipped with multi-fibre or integral field spectrographs combined with detailed models of stellar atmospheres and automated fitting techniques allow for the analysis of large number of stars. These datasets contain a wealth of information that require new analysis techniques to bridge the gap between observations and stellar evolution models. To that end, we develop BONNSAI (BONN Stellar Astrophysics Interface), a Bayesian statistical method, that is capable of comparing all available observables simultaneously to stellar models while taking observed uncertainties and prior knowledge such as initial mass functions and distributions of stellar rotational velocities into account. BONNSAI can be used to (1) determine probability distributions of fundamental stellar parameters such as initial masses and stellar ages from complex datasets, (2) predict stellar parameters that were not yet observationally determined and (3) test stellar models to further advance our understanding of stellar evolution. An important aspect of BONNSAI is that it singles out stars that cannot be reproduced by stellar models through $\chi^{2}$ hypothesis tests and posterior predictive checks. BONNSAI can be used with any set of stellar models and currently supports massive main-sequence single star models of Milky Way and Large and Small Magellanic Cloud composition. We apply our new method to mock stars to demonstrate its functionality and capabilities. In a first application, we use BONNSAI to test the stellar models of Brott et al. (2011a) by comparing the stellar ages inferred for the primary and secondary stars of eclipsing Milky Way binaries. Ages are determined from dynamical masses and radii that are known to better than 3%. We find that the stellar models reproduce the Milky Way binaries well. BONNSAI is available through a web-interface at http://www.astro.uni-bonn.de/stars/bonnsai.Comment: Accepted for publication in A&A; 15 pages, 10 figures, 4 tables; BONNSAI is available through a web-interface at http://www.astro.uni-bonn.de/stars/bonnsa

Economic choices can be made using only stimulus values

Decision-making often involves choices between different stimuli, each of which is associated with a different physical action. A growing consensus suggests that the brain makes such decisions by assigning a value to each available option and then comparing them to make a choice. An open question in decision neuroscience is whether the brain computes these choices by comparing the values of stimuli directly in goods space or instead by first assigning values to the associated actions and then making a choice over actions. We used a functional MRI paradigm in which human subjects made choices between different stimuli with and without knowledge of the actions required to obtain the different stimuli. We found neural correlates of the value of the chosen stimulus (a postdecision signal) in ventromedial prefrontal cortex before the actual stimulus–action pairing was revealed. These findings provide support for the hypothesis that the brain is capable of making choices in the space of goods without first transferring values into action space

The relationship between kinship support services and placement outcomes

This study examined the relationship between kinship support services and placement outcomes using secondary data collected by Chang and Liles (2004) in the Counties of San Bernardino and Riverside. This study aimed at assessing kinship care placement outcomes by reviewing the characteristics of kin caregivers and their dependent children, types of financial support and services received, and contact with social workers. This study sample included 130 kinship caregivers and 291 dependent children from the original study (Chang & Liles, 2007)