Gregor Zens - Efficient MCMC for Binary and Categorical Data Regression Models - Methodological Advances & Implementation in R
Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of familiarity with Bayesian statistics or suffer from issues such as low sampling efficiency. To contribute to the accessibility of Bayesian models for binary and categorical data, we introduce novel latent variable representations based on Pólya Gamma random variables for a range of commonly encountered discrete choice models. From these latent variable representations, new Gibbs sampling algorithms for binary, binomial and multinomial logistic regression models are derived. All models allow for a conditionally Gaussian likelihood representation, rendering extensions to more complex modeling frameworks such as state space models straight-forward. However, sampling efficiency may still be an issue in these data augmentation based estimation frameworks. To counteract this, MCMC boosting strategies are developed and discussed in detail. The algorithms are made available in the accompanying R package UPG. It offers a convenient estimation framework for balanced and imbalanced data settings implemented in C++, allowing for rapid parameter estimation. In addition, UPG provides several methods for fast production of output tables and summary plots that are easily accessible to a broad range of users.
Zehra Eksi-Altay - Momentum and mean reversion under partial information
We study a dynamic portfolio optimization problem in which stock returns tend to continue over short horizons, so-called momentum, and revert over longer horizons, so-called mean-reversion or reversal. We extend the continuous-time framework of Koijen et. al. (2009) into a partial information one, where the investor (trader) could not observe in what proportion of the drift uncertainty is attributable to the mean-reversion or momentum. Due to the Gaussian nature of the problem, we use the Kalman filter to obtain the estimated state variables. Since essentially the filtering and stochastic optimal control problems are separable, we obtain the optimal portfolio weights and optimal value function by standard techniques. Finally, we provide a comparison between strategies corresponding to full and partial information settings.
(Joint work with Suhan Altay and Katia Colaneri)