Investment Decisions with Endogeneity: A Dirichlet Tree Analysis

Ignoring endogeneity when assessing investors’ decisions carries the risk of biased estimates for the influence of exogeneous marketing variables. This study shows how to overcome this challenge by using Pólya trees in the quantification of impacts on investors’ decisions. A total of 2255 investors recruited for this study received and opened a digital marketing newsletter about investing daily. Given the nature of investors’ decisions characterized by heterogeneity and endogeneity, the response model is assessed with the Dirichlet process mixture and estimated with the Markov chain Monte Carlo method. Digital marketing substantially exceeds the impact of investor experience, but both have a significant positive impact on investors’ trading volume. Findings obtained with the Dirichlet process mixture as a flexible model indicate that digital marketing even with latent endogenous factors makes an underlying contribution to the investors’ actions in the stock market.

Estimation of Receiver Operating Characteristic Surface Using Mixtures of Finite Polya Trees (MFPT)

Generalisation of Receiver operating characteristic (ROC) curve has become increasingly useful in evaluating the performance of diagnostic tests that have more than binary outcomes. While parametric approaches have been widely used over the years, the limitations associated with parametric assumptions often make it difficult to modelling the volume under surface for data that do not meet criteria under parametric distributions. As such, estimation of ROC surface using nonparametric approaches have been proposed to obtained insights on available data. One of the common approaches to non-parametric estimation is the use of Bayesian models where assumptions about priors can be made then posterior distributions obtained which can then be used to model the data. This study uses Polya tree priors where mixtures of Polya trees approach was used to model simulated three-way ROC data. The results of VUS estimation which is considered a suitable inference in evaluating performance of a diagnostic test, indicated that the mixtures of Polya trees model fitted well the ROC surface data. Further, the model performed relatively well compared to parametric and semiparametric models under similar assumptions.  

Multiscale stick-breaking mixture models

Bayesian nonparametric density estimation is dominated by single-scale methods, typically exploiting mixture model specifications, exception made for Pólya trees prior and allied approaches. In this paper we focus on developing a novel family of multiscale stick-breaking mixture models that inherits some of the advantages of both single-scale nonparametric mixtures and Pólya trees. Our proposal is based on a mixture specification exploiting an infinitely deep binary tree of random weights that grows according to a multiscale generalization of a large class of stick-breaking processes; this multiscale stick-breaking is paired with specific stochastic processes generating sequences of parameters that induce stochastically ordered kernel functions. Properties of this family of multiscale stick-breaking mixtures are described. Focusing on a Gaussian specification, a Markov Chain Monte Carlo algorithm for posterior computation is introduced. The performance of the method is illustrated analyzing both synthetic and real datasets consistently showing competitive results both in scenarios favoring single-scale and multiscale methods. The results suggest that the method is well suited to estimate densities with varying degree of smoothness and local features.

Protection numbers in simply generated trees and Pólya trees

We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P?lya trees, and in unlabelled non-plane binary trees, when the number of vertices tends to infinity. Moreover, we compute expectation and variance of the protection number of a randomly chosen vertex in all those tree classes. We obtain exact formulas as sum representations, where the obtained sums are rapidly converging thus allowing an efficient numerical computation of high accuracy.

Bayesian analysis and decisions in nuclear power plant maintenance

This article discusses the results of a study in Bayesian analysis and decision making in the maintenance and reliability of nuclear power plants. It demonstrates the use of Bayesian parametric and semiparametric methodology to analyse the failure times of components that belong to an auxiliary feedwater system in a nuclear power plant at the South Texas Project (STP) Electric Generation Station. The parametric models produce estimates of the hazard functions that are compared to the output from a mixture of Polya trees model. The statistical output is used as the most critical input in a stochastic optimization model which finds the optimal replacement time for a system that randomly fails over a finite horizon. The article first introduces the model for maintenance and reliability analysis before presenting the optimization results. It also examines the nuclear power plant data to be used in the Bayesian models.