Investigating the collision energy dependence of η\eta/s in RHIC beam energy scan using Bayesian statistics

We determine the probability distributions of shear viscosity over the entropy density ratio $\eta/s$ in Au+Au collisions at $\sqrt{s_{NN}}=19.6, 39$, and $62.4$ GeV, using Bayesian inference and Gaussian process emulators for a model-to-data statistical analysis that probes the full input parameter space of a transport+viscous hydrodynamics hybrid model. We find the most likely value of $\eta/s$ to be larger at smaller $\sqrt{s_{NN}}$, although the uncertainties still allow for a constant value between 0.10 and 0.15 for the investigated collision energy range.Comment: 44 pages, 34 figures. Submitted to Phys. Rev.

Flow in small and large quark-gluon plasma droplets: the role of nucleon substructure

We study the effects of nucleon substructure on bulk observables in proton-lead collisions at the LHC using Bayesian methodology. Substructure is added to the TRENTO parametric initial condition model using Gaussian nucleons with a variable number of Gaussian partons. We vary the number and width of these partons while recovering the desired inelastic proton-proton cross section and ensemble averaged proton density. We then run the model through a large number of minimum bias hydrodynamic simulations and measure the response of final particle production and azimuthal particle correlations to initial state properties. Once these response functions are determined, we calibrate free parameters of the model using established Bayesian methodology. We comment on the implied viability of the partonic model for describing hydrodynamic behavior in small systems.Comment: proceedings for Quark Matter 201

Bootstrap-Based Improvements for Inference with Clustered Errors

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (5-30) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo and Mullainathan (2004). Rejection rates of ten percent using standard methods can be reduced to the nominal size of five percent using our methods.

Robust Inference with Multi-way Clustering

In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.