A Statistical View of Learning in the Centipede Game

In this article we evaluate the statistical evidence that a population of students learn about the sub-game perfect Nash equilibrium of the centipede game via repeated play of the game. This is done by formulating a model in which a player's error in assessing the utility of decisions changes as they gain experience with the game. We first estimate parameters in a statistical model where the probabilities of choices of the players are given by a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey, 1995, 1996, 1998), but are allowed to change with repeated play. This model gives a better fit to the data than similar models previously considered. However, substantial correlation of outcomes of games having a common player suggests that a statistical model that captures within-subject correlation is more appropriate. Thus we then estimate parameters in a model which allows for within-player correlation of decisions and rates of learning. Through out the paper we also consider and compare the use of randomization tests and posterior predictive tests in the context of exploratory and confirmatory data analyses

Precision cosmology with redshift-space bispectrum: a perturbation theory based model at one-loop order

The large-scale matter distribution in the late-time Universe exhibits gravity-induced non-Gaussianity, and the bispectrum, three-point cumulant is expected to contain significant cosmological information. In particular, the measurement of the bispectrum helps to tighten the constraints on dark energy and modified gravity through the redshift-space distortions (RSD). In this paper, extending the work by Taruya, Nishimichi & Saito (2010, Phys.Rev.D 82, 063522), we present a perturbation theory (PT) based model of redshift-space matter bispectrum that can keep the non-perturbative damping effect under control. Characterizing this non-perturbative damping by a univariate function with single free parameter, the PT model of the redshift-space bispectrum is tested against a large set of cosmological $N$-body simulations, finding that the predicted monopole and quadrupole moments are in a good agreement with simulations at the scales of baryon acoustic oscillations (well beyond the range of agreement of standard PT). The validity of the univariate ansatz of the damping effect is also examined, and with the PT calculation at next-to-leading order, the fitted values of the free parameter is shown to consistently match those obtained from the PT model of power spectrum by Taruya, Nishimichi & Saito (2010).Comment: 21 pages, 13 figure

Error, bias, and long-branch attraction in data for two chloroplast photosystem genes in seed plants

Sequences of two chloroplast photosystem genes, psaA and psbB, together comprising about 3,500 bp, were obtained for all five major groups of extant seed plants and several outgroups among other vascular plants. Strongly supported, but significantly conflicting, phylogenetic signals were obtained in parsimony analyses from partitions of the data into first and second codon positions versus third positions. In the former, both genes agreed on a monophyletic gymnosperms, with Gnetales closely related to certain conifers. In the latter, Gnetales are inferred to be the sister group of all other seed plants, with gymnosperms paraphyletic. None of the data supported the modern ‘‘anthophyte hypothesis,’’ which places Gnetales as the sister group of flowering plants. A series of simulation studies were undertaken to examine the error rate for parsimony inference. Three kinds of errors were examined: random error, systematic bias (both properties of finite data sets), and statistical inconsistency owing to long-branch attraction (an asymptotic property). Parsimony reconstructions were extremely biased for third-position data for psbB. Regardless of the true underlying tree, a tree in which Gnetales are sister to all other seed plants was likely to be reconstructed for these data. None of the combinations of genes or partitions permits the anthophyte tree to be reconstructed with high probability. Simulations of progressively larger data sets indicate the existence of long-branch attraction (statistical inconsistency) for third-position psbB data if either the anthophyte tree or the gymnosperm tree is correct. This is also true for the anthophyte tree using either psaA third positions or psbB first and second positions. A factor contributing to bias and inconsistency is extremely short branches at the base of the seed plant radiation, coupled with extremely high rates in Gnetales and nonseed plant outgroups. M. J. Sanderson,* M. F. Wojciechowski,*† J.-M. Hu,* T. Sher Khan,* and S. G. Brad

Steps towards operationalizing an evolutionary archaeological definition of culture

This paper will examine the definition of archaeological cultures/techno-complexes from an evolutionary perspective, in which culture is defined as a system of social information transmission. A formal methodology will be presented through which the concept of a culture can be operationalized, at least within this approach. It has already been argued that in order to study material culture evolution in a manner similar to how palaeontologists study biological change over time we need explicitly constructed ‘archaeological taxonomic units’ (ATUs). In palaeontology, the definition of such taxonomic units – most commonly species – is highly controversial, so no readily adoptable methodology exists. Here it is argued that ‘culture’, however defined, is a phenomenon that emerges through the actions of individuals. In order to identify ‘cultures’, we must therefore construct them from the bottom up, beginning with individual actions. Chaîne opèratoire research, combined with the formal and quantitative identification of variability in individual material culture behaviour allows those traits critical in the social transmission of cultural information to be identified. Once such traits are identified, quantitative, so-called phylogenetic methods can be used to track material culture change over time. Phylogenetic methods produce nested hierarchies of increasingly exclusive groupings, reflecting descent with modification within lineages of social information transmission. Once such nested hierarchies are constructed, it is possible to define an archaeological culture at any given point in this hierarchy, depending on the scale of analysis. A brief example from the Late Glacial in Southern Scandinavia is presented and it is shown that this approach can be used to operationalize an evolutionary definition of ‘culture’ and that it improves upon traditional, typologically defined technocomplexes. In closing, the benefits and limits of such an evolutionary and quantitative definition of ‘culture’ are discussed

On the motion of the Local Group and its substructures

The problem of the relative motion of the substructures of the Local Group of galaxies revealed via S-tree method, as well as of the velocity of the Local Group itself, is considered. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which uses the information on the radial velocities of the galaxies, but not on their distances. Once the bulk motion of substructures is estimated, in combination with the observed CMB dipole we also consider the mean velocity of the Local Group itself. Assigning the Local Group the mean motion of its main substructures we evaluate its peculiar velocity in Milky Way frame V(LG->MW)= (-7 \pm 303,-15 \pm 155 ,+177 \pm 144) or 178 km/s toward galactic coordinates l=245 and b=+85. Combined with CMB dipole V(MW->CMB), we obtain Local Group velocity in CMB frame: V(LG->CMB) = (-41\pm 303,-497\pm 155,445 \pm 144) or 668 km/s towards l=265 and b=42. This estimation is in good agreement, within 1 sigma level, with the estimation of Yahil et al (1977).Comment: To be published in MNRA