Comment: Bayesian Checking of the Second Level of Hierarchical Models: Cross-Validated Posterior Predictive Checks Using Discrepancy Measures

Comment: Bayesian Checking of the Second Level of Hierarchical Models [arXiv:0802.0743]Comment: Published in at http://dx.doi.org/10.1214/07-STS235B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Algorithm Instance Games

This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of the algorithm's description influence agents' strategic behavior? We analyze two versions of an AIG based on the set-cover optimization problem. In these games, joint strategies correspond to instances of the set-cover problem, with each subset (of a given universe of elements) representing the strategy of a single agent. Outcomes are covers computed from the joint strategies by a set-cover algorithm. In one variant of this game, outcomes are computed by a deterministic greedy algorithm, and the other variant utilizes a non-deterministic form of the greedy algorithm. We characterize Nash equilibrium strategies for both versions of the game, finding that agents' strategies can vary considerably between the two settings. In particular, we find that the version of the game based on the deterministic algorithm only admits Nash equilibrium in which agents choose strategies (i.e., subsets) containing at most one element, with no two agents picking the same element. On the other hand, in the version of the game based on the non-deterministic algorithm, Nash equilibrium strategies can include agents with zero, one, or every element, and the same element can appear in the strategies of multiple agents.Comment: 14 page

Strangeness production in heavy ion collisions at SPS and RHIC within two-source statistical model

The experimental data on hadron yields and ratios in central Pb+Pb and Au+Au collisions at SPS and RHIC energies, respectively, are analysed within a two-source statistical model of an ideal hadron gas. These two sources represent the expanding system of colliding heavy ions, where the hot central fireball is embedded in a larger but cooler fireball. The volume of the central source increases with rising bombarding energy. Results of the two-source model fit to RHIC experimental data at midrapidity coincide with the results of the one-source thermal model fit, indicating the formation of an extended fireball, which is three times larger than the corresponding core at SPS.Comment: Talk at "Strange Quarks in Matter" Conference (Strangeness'2001), September 2001, Frankfurt a.M., German

Bayesian inferences of galaxy formation from the K-band luminosity and HI mass functions of galaxies: constraining star formation and feedback

We infer mechanisms of galaxy formation for a broad family of semi-analytic models (SAMs) constrained by the K-band luminosity function and HI mass function of local galaxies using tools of Bayesian analysis. Even with a broad search in parameter space the whole model family fails to match to constraining data. In the best fitting models, the star formation and feedback parameters in low-mass haloes are tightly constrained by the two data sets, and the analysis reveals several generic failures of models that similarly apply to other existing SAMs. First, based on the assumption that baryon accretion follows the dark matter accretion, large mass-loading factors are required for haloes with circular velocities lower than 200 km/s, and most of the wind mass must be expelled from the haloes. Second, assuming that the feedback is powered by Type-II supernovae with a Chabrier IMF, the outflow requires more than 25% of the available SN kinetic energy. Finally, the posterior predictive distributions for the star formation history are dramatically inconsistent with observations for masses similar to or smaller than the Milky-Way mass. The inferences suggest that the current model family is still missing some key physical processes that regulate the gas accretion and star formation in galaxies with masses below that of the Milky Way.Comment: 17 pages, 9 figures, 1 table, accepted for publication in MNRA