Bayesian nonparametric analysis of reversible Markov chains

We introduce a three-parameter random walk with reinforcement, called the $(\theta,\alpha,\beta)$ scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter $\beta$ smoothly tunes the $(\theta,\alpha,\beta)$ scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters $\alpha$ and $\theta$ modulate how many states are typically visited. Resorting to de Finetti's theorem for Markov chains, we use the $(\theta,\alpha,\beta)$ scheme to define a nonparametric prior for Bayesian analysis of reversible Markov chains. The prior is applied in Bayesian nonparametric inference for species sampling problems with data generated from a reversible Markov chain with an unknown transition kernel. As a real example, we analyze data from molecular dynamics simulations of protein folding.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1102 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Giant Dipole Resonance as a quantitative constraint on the symmetry energy

The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy S(rho), are very much under debate. In the present work, we show that the value of the symmetry energy associated with Skyrme functionals, at densities rho around 0.1 fm^{-3}, is strongly correlated with the value of the centroid of the Giant Dipole Resonance (GDR) in spherical nuclei. Consequently, the experimental value of the GDR in, e.g., 208Pb can be used as a constraint on the symmetry energy, leading to 23.3 MeV < S(rho=0.1 fm^{-3}) < 24.9 MeV.Comment: 5 pages, 2 figures, submitte

Interpretable Model Summaries Using the Wasserstein Distance

Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation phase is a commonly used approach, but less work has focused on selecting subsets of the parameters for interpreting the estimated model -- especially in settings such as Bayesian inference and model averaging. Importantly, many models do not have straightforward interpretations and create another layer of obfuscation. To solve this gap, we introduce a new method that uses the Wasserstein distance to identify a low-dimensional interpretable model projection. After the estimation of complex models, users can budget how many parameters they wish to interpret and the proposed generates a simplified model of the desired dimension minimizing the distance to the full model. We provide simulation results to illustrate the method and apply it to cancer datasets