Nonparametric Bayes modeling of count processes

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions. This article proposes a class of nonparametric Bayes count process models, which are constructed through rounding real-valued underlying processes. The proposed class of models accommodates applications in which one observes separate count-valued functional data for each subject under study. Theoretical results on large support and posterior consistency are established, and computational algorithms are developed using Markov chain Monte Carlo. The methods are evaluated via simulation studies and illustrated through application to longitudinal tumor counts and asthma inhaler usage

A Kolmogorov-Smirnov test for the molecular clock on Bayesian ensembles of phylogenies

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS) goodness-of-fit test. In the strict clock case, the method consists in using the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny is clock-like, in other words, if it follows a Poisson law. The ECD is computed from the discretized branch lengths and the parameter $\lambda$ of the expected Poisson distribution is calculated as the average branch length over the ensemble of trees. To compensate for the auto-correlation in the ensemble of trees and pseudo-replication we take advantage of thinning and effective sample size, two features provided by Bayesian inference MCMC samplers. Finally, it is observed that tree topologies with very long or very short branches lead to Poisson mixtures and in this case we propose the use of the two-sample KS test with samples from two continuous branch length distributions, one obtained from an ensemble of clock-constrained trees and the other from an ensemble of unconstrained trees. Moreover, in this second form the test can also be applied to test for relaxed clock models. The use of a statistically equivalent ensemble of phylogenies to obtain the branch lengths ECD, instead of one consensus tree, yields considerable reduction of the effects of small sample size and provides again of power.Comment: 14 pages, 9 figures, 8 tables. Minor revision, additin of a new example and new title. Software: https://github.com/FernandoMarcon/PKS_Test.gi

Customer flow, intermediaries, and the discovery of the equilibrium riskfree rate

Macro announcements change the equilibrium riskfree rate. We find that treasury prices reflect part of the impact instantaneously, but intermediaries rely on their customer order flow in the 15 minutes after the announcement to discover the full impact. We show that this customer flow informativeness is strongest at times when analyst forecasts of macro variables are highly dispersed. We study 30 year treasury futures to identify the customer flow. We further show that intermediaries appear to benefit from privately recognizing informed customer flow, as, in the cross-section, their own-account trade profitability correlates with access to customer orders, controlling for volatility, competition, and the announcement surprise. These results suggest that intermediaries learn about equilibrium riskfree rates through customer orders