Identifiability of parameters in latent structure models with many observed variables

While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models and random graph mixture models, and lead to a number of new results and improvements to old ones. In the parametric setting, this approach indicates that for such models, the classical definition of identifiability is typically too strong. Instead generic identifiability holds, which implies that the set of nonidentifiable parameters has measure zero, so that parameter inference is still meaningful. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to have nonidentifiable parameters. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions.Comment: Published in at http://dx.doi.org/10.1214/09-AOS689 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Demand Elasticities for Fresh Fruit at the Retail Level

The obesity epidemic in the US and elsewhere has re-doubled efforts to understand determinants of the quality of consumers' diets. Part of the discussion has centered on the potential of "fat taxes" and/or the subsidization of the purchase of fresh fruits and vegetables to coax consumers to better diets. Whether this discussion has merit or not, fundamental to the debate are the demand elasticities of the commodities involved. This study employs weekly data from several retail stores on fruit prices and sales to estimate elasticities of individual fruits. Estimates show consumers are more responsive to price than has been found previously.Consumer/Household Economics,

Who are Rural Students? How Definitions of Rurality Affect Research on College Completion

Given a revived national discourse about rural populations, more educational research on rural students is necessary, including ways that rural students transition to college and the success (or lack thereof) that they experience once there. However, the National Center for Education Statistics (NCES) has changed the definition of rurality used in each iterative dataset over the last few decades, casting doubt on the consistency of what is meant by the term rural. The purpose of this study is to: (a) communicate to the educational research audience various ways of defining rural students, and specifically how NCES has changed their definition of rurality over their last three major data collections; (b) demonstrate how conclusions about rural students’ and their college degree completion may differ based on these alternate NCES definitions; and (c) discuss how this specific example using NCES data relates to the wider landscape of research on rural students. Results show that conclusions about college degree completion change depending on the definition of rurality used for analysis. Therefore, the education research community should consider the options for defining rural students, report transparently about the choices made, consider the sensitivity of results to the definition of rurality, and ultimately build a more robust body of literature concerning rural students’ college success. Gaining definitional clarity will be beneficial, particularly for those who wish to translate their research into practical action for the benefit of rural students

The design and evaluation of a sonically enhanced tool palette

This paper describes an experiment to investigate the effectiveness of adding sound to tool palettes. Palettes have usability problems because users need to see the information they present, but they are often outside the area of visual focus. We used nonspeech sounds called earcons to indicate the current tool and when tool changes occurred so that users could tell what tool they were in wherever they were looking. Results showed a significant reduction in the number of tasks performed with the wrong tool. Therefore, users knew what the current tool was and did not try to perform tasks with the wrong one. All of this was not at the expense of making the tool palettes any more annoying to use

Theory of Combined Photoassociation and Feshbach Resonances in a Bose-Einstein Condensate

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate, where the shared dissociation continuum allows for quantum interference in losses from the condensate, as well as a dispersive-like shift of resonance. A simple analytical model, based on the limit of weakly bound molecules, agrees well with numerical experiments that explicitly include dissociation to noncondensate modes. For a resonant laser and an off-resonant magnetic field, constructive interference enables saturation of the photoassociation rate at user-friendly intensities, at a value set by the interparticle distance. This rate limit is larger for smaller condensate densities and, near the Feshbach resonance, approaches the rate limit for magnetoassociation alone. Also, we find agreement with the unitary limit--set by the condensate size--only for a limited range of near-resonant magnetic fields. Finally, for a resonant magnetic field and an off-resonant laser, magnetoassociation displays similar quantum interference and a dispersive-like shift. Unlike photoassociation, interference and the fieldshift in resonant magnetoassociation is tunable with both laser intensity and detuning. Also, the dispersive-like shift of the Feshbach resonance depends on the size of the Feshbach molecule, and is a signature of non-universal physics in a strongly interacting system.Comment: 10 pages, 5 figures, 82 reference

Echocardiographic evaluation of velocity ratio, velocity time integral ratio, and pulmonary valve area in dogs with pulmonary valve stenosis.

BackgroundVelocity ratio, velocity time integral (VTI) ratio, and pulmonary valve area indexed to body surface area (iPVA) are methods of assessment of pulmonary valve stenosis (PS) severity that are less dependent on blood flow. Studies evaluating these methods are limited.ObjectivesTo determine the effects of butorphanol, atenolol, and balloon valvuloplasty (BV) on velocity ratio, VTI ratio, iPVA, mean PG, and max PG.AnimalsTwenty-seven dogs with PS (max PG >50 mm Hg).MethodsProspective study. All dogs underwent an echocardiogram at baseline, 5-minutes after administration of butorphanol (0.2-0.25 mg/kg IV), and 2-to-4 weeks after atenolol (1-1.5 mg/kg q12h). Twenty-one of these were evaluated 24-hours after BV.ResultsThere were no significant differences (P > .05) amongst any of the methods of assessment of PS severity after butorphanol. After atenolol, mean (SD) of mean (57.0 [21.0] mm Hg) and max PG (93.1 [33.8] mm Hg) were significantly decreased (P ≤ .047) compared with baseline (65.2 [26.2] mm Hg and 108 [44.4] mm Hg, respectively). After atenolol, there were no significant (P ≥ .12) differences in velocity ratio (0.29 [0.09]), VTI ratio (0.18 [0.05]), or iPVA (0.43 [0.16] cm2 /m2 ) compared with baseline (0.30 [0.09], 0.19 [0.09], 0.44 [0.17] cm2 /m2 , respectively).Conclusions and clinical importanceAtenolol might reduce mean and max PG but does not alter less flow-dependent methods of assessment of PS severity (velocity ratio, VTI ratio, and iPVA) in dogs with PS. Results support an integrative approach to assessment of PS severity that includes less flow-dependent methods, particularly in states of altered flow or right ventricular function

Extended Hubbard model on a C20_{20} molecule

The electronic correlations on a C$_{20}$ molecule, as described by an extended Hubbard Hamiltonian with a nearest neighbor Coulomb interaction of strength $V$, are studied using quantum Monte Carlo and exact diagonalization methods. For electron doped C$_{20}$, it is known that pair-binding arising from a purely electronic mechanism is absent within the standard Hubbard model (V=0). Here we show that this is also the case for hole doping for $0<U/t\leq 3$ and that, for both electron and hole doping, the effect of a non-zero $V$ is to work against pair-binding. We also study the magnetic properties of the neutral molecule, and find transitions between spin singlet and triplet ground states for either fixed $U$ or $V$ values. In addition, spin, charge and pairing correlation functions on C$_{20}$ are computed. The spin-spin and charge-charge correlations are very short-range, although a weak enhancement in the pairing correlation is observed for a distance equal to the molecular diameter.Comment: 9 pages, 8 figures, 4 table

Order in a Spatially Anisotropic Triangular Antiferromagnet

The phase diagram of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice of weakly coupled chains, a model relevant to Cs2CuCl4, is investigated using a renormalization group analysis, which includes marginal couplings important for connecting to numerical studies of this model. In particular, the relative stability of incommensurate spiral spin-density order and collinear antiferromagnetic order is studied. While incommensurate spiral order is found to exist over most of the phase diagram in the presence of a Dzyaloshinskii-Moriya (DM) interaction, at small interchain and extremely weak DM couplings, collinear antiferromagnetic order can survive. Our results imply that Cs2CuCl4 is well within the part of the phase diagram where spiral order is stable. The implications of the renormalization group analysis for numerical studies, many of which have found spin-liquidlike behavior, are discussed.Comment: 10 pages, 7 figures, minor edits and reference adde