Inconsistency of Pitman-Yor process mixtures for the number of components

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).Comment: This is a general treatment of the problem discussed in our related article, "A simple example of Dirichlet process mixture inconsistency for the number of components", Miller and Harrison (2013) arXiv:1301.270

Exact Enumeration and Sampling of Matrices with Specified Margins

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling

Exact sampling and counting for fixed-margin matrices

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1131 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1104.032

THEORETICAL AND EMPIRICAL CONSIDERATIONS OF ELICITING PREFERENCES AND MODEL ESTIMATION IN CONJOINT ANALYSIS

The theoretical underpinnings associated with eliciting consumer preferences and statistical properties of alternative models in conjoint analysis are examined. Results show that model selection makes little difference in the context of sign and significance of coefficients. However, results show that tobit is a better predictor of ordinal ranking relative to the probit model.Demand and Price Analysis,

The Neighbor's Portfolio: Word-of-Mouth Effects in the Holdings and Trade of Money Managers

A mutual-fund manager is more likely to hold (or buy, or sell) a particular stock in any quarter if other managers in the same city are holding (or buying, or selling) that same stock. This pattern shows up even when controlling for the distance between the fund manager and the stock in question, so it is distinct from a local-preference effect. It is also robust to a variety of controls for investment styles. These results can be interpreted in terms of an epidemic model in which investors spread information about stocks to one another by word of mouth.

Analysis of Cardinal and Ordinal Assumptions in Conjoint Analysis

Of twenty-three agricultural economics conjoint analyses conducted between 1990 and 2001, seventeen used interval-rating scales, with estimation procedures varying widely. This study tests cardinality assumptions in conjoint analysis when interval-rating scales are used, and tests whether the ordered probit or two-limit tobit model is the most valid. Results indicate that cardinality assumptions are invalid, but estimates of the underlying utility scale for the two models do not differ. Thus, while the ordered probit model is theoretically more appealing, the two-limit tobit model may be more useful in practice, especially in cases with limited degrees of freedom, such as with individual-level conjoint models.ordered probit, two-limit probit, conjoint analysis, cardinality, Research Methods/ Statistical Methods,

Social Interaction and Stock-Market Participation

We investigate the idea that stock-market participation is influenced by social interaction. We build a simple model in which any given 'social' investor finds it more attractive to invest in the market when the participation rate among his peers is higher. The model predicts higher participation rates among social investors than among 'non-socials'. It also admits the possibility of multiple social equilibria. We then test the theory using data from the Health and Retirement Study. Social households - defined as those who interact with their neighbors, or who attend church - are indeed substantially more likely to invest in the stock market than non-social households, controlling for other factors like wealth, race, education and risk tolerance. Moreover, consistent with a peer-effects story, the impact of sociability is stronger in states where stock-market participation rates are higher.