Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison

In this paper we show that fully likelihood-based estimation and comparison of multivariate stochastic volatility (SV) models can be easily performed via a freely available Bayesian software called WinBUGS. Moreover, we introduce to the literature several new specifications which are natural extensions to certain existing models, one of which allows for time varying correlation coefficients. Ideas are illustrated by fitting, to a bivariate time series data of weekly exchange rates, nine multivariate SV models, including the specifications with Granger causality in volatility, time varying correlations, heavytailed error distributions, additive factor structure, and multiplicative factor structure. Empirical results suggest that the most adequate specifications are those that allow for time varying correlation coefficients.Multivariate stochastic volatility; Granger causality in volatility; Heavy-tailed distributions; Time varying correlations; Factors; MCMC; DIC.

Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among processes. By extending the results by Chow and Liu on dependence tree approximations, we show that the best causal dependence tree approximation is the one which maximizes the sum of directed informations on its edges, where best is defined in terms of minimizing the KL-divergence between the original and the approximate distribution. Moreover, we describe a low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure

Learning Optimal Biomarker-Guided Treatment Policy for Chronic Disorders

Electroencephalogram (EEG) provides noninvasive measures of brain activity and is found to be valuable for diagnosis of some chronic disorders. Specifically, pre-treatment EEG signals in alpha and theta frequency bands have demonstrated some association with anti-depressant response, which is well-known to have low response rate. We aim to design an integrated pipeline that improves the response rate of major depressive disorder patients by developing an individualized treatment policy guided by the resting state pre-treatment EEG recordings and other treatment effects modifiers. We first design an innovative automatic site-specific EEG preprocessing pipeline to extract features that possess stronger signals compared with raw data. We then estimate the conditional average treatment effect using causal forests, and use a doubly robust technique to improve the efficiency in the estimation of the average treatment effect. We present evidence of heterogeneity in the treatment effect and the modifying power of EEG features as well as a significant average treatment effect, a result that cannot be obtained by conventional methods. Finally, we employ an efficient policy learning algorithm to learn an optimal depth-2 treatment assignment decision tree and compare its performance with Q-Learning and outcome-weighted learning via simulation studies and an application to a large multi-site, double-blind randomized controlled clinical trial, EMBARC

Meta Learning for Causal Direction

The inaccessibility of controlled randomized trials due to inherent constraints in many fields of science has been a fundamental issue in causal inference. In this paper, we focus on distinguishing the cause from effect in the bivariate setting under limited observational data. Based on recent developments in meta learning as well as in causal inference, we introduce a novel generative model that allows distinguishing cause and effect in the small data setting. Using a learnt task variable that contains distributional information of each dataset, we propose an end-to-end algorithm that makes use of similar training datasets at test time. We demonstrate our method on various synthetic as well as real-world data and show that it is able to maintain high accuracy in detecting directions across varying dataset sizes