Proper local scoring rules on discrete sample spaces

A scoring rule is a loss function measuring the quality of a quoted probability distribution $Q$ for a random variable $X$, in the light of the realized outcome $x$ of $X$; it is proper if the expected score, under any distribution $P$ for $X$, is minimized by quoting $Q=P$. Using the fact that any differentiable proper scoring rule on a finite sample space ${\mathcal{X}}$ is the gradient of a concave homogeneous function, we consider when such a rule can be local in the sense of depending only on the probabilities quoted for points in a nominated neighborhood of $x$. Under mild conditions, we characterize such a proper local scoring rule in terms of a collection of homogeneous functions on the cliques of an undirected graph on the space ${\mathcal{X}}$. A useful property of such rules is that the quoted distribution $Q$ need only be known up to a scale factor. Examples of the use of such scoring rules include Besag's pseudo-likelihood and Hyv\"{a}rinen's method of ratio matching.Comment: Published in at http://dx.doi.org/10.1214/12-AOS972 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electric control of collective atomic coherence in an Erbium doped solid

We demonstrate fast and accurate control of the evolution of collective atomic coherences in an Erbium doped solid using external electric fields. This is achieved by controlling the inhomogeneous broadening of Erbium ions emitting at 1536 nm using an electric field gradient and the linear Stark effect. The manipulation of atomic coherence is characterized with the collective spontaneous emission (optical free induction decay) emitted by the sample after an optical excitation, which does not require any previous preparation of the atoms. We show that controlled dephasing and rephasing of the atoms by the electric field result in collapses and revivals of the optical free induction decay. Our results show that the use of external electric fields does not introduce any substantial additional decoherence and enables the manipulation of collective atomic coherence with a very high degree of precision on the time scale of tens of ns. This provides an interesting resource for photonic quantum state storage and quantum state manipulation.Comment: 10 pages, 5 figure

Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.Comment: 15 pages, article will appear in Scandinavian Journal of Statistic

Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial datasets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article is submitted to the Practice section of the journal with the aim of developing massively scalable Bayesian approaches that can rapidly deliver Bayesian inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (e.g., a standard desktop or laptop) using easily available statistical software packages without requiring message-parsing interfaces or parallel programming paradigms. Key insights are offered regarding assumptions and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table

On the angular momentum dependence of nuclear level densities

Angular momentum dependence of nuclear level densities at finite temperatures are investigated in the static path approximation(SPA) to the partition function using a cranked quadrupole interaction Hamiltonian in the following three schemes: (i) cranking about x-axis, (ii) cranking about z-axis and (iii) cranking about z-axis but correcting for the orientation fluctuation of the axis. Performing numerical computations for an $sd$ and a $pf$ shell nucleus, we find that the x-axis cranking results are satisfactory for reasonably heavy nuclei and this offers a computationally faster method to include the angular momentum dependence at high temperatures in the SPA approach. It also appears that at high spins inclusion of orientation fluctuation correction would be important.Comment: 19 Latex pages, 9 figures(available upon request

Transfer Entropy as a Log-likelihood Ratio

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic chi-squared distribution is established for the transfer entropy estimator. The result generalises the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense

The physical determinants of the thickness of lamellar polymer crystals

Based upon kinetic Monte Carlo simulations of crystallization in a simple polymer model we present a new picture of the mechanism by which the thickness of lamellar polymer crystals is constrained to a value close to the minimum thermodynamically stable thickness. This description contrasts with those given by the two dominant theoretical approaches.Comment: 4 pages, 4 figures, revte

Hierarchical Models for Independence Structures of Networks

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erd\"os-R\'enyi and beta-models to create hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.Comment: 19 pages, 7 figure