The iterated auxiliary particle filter

We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of "twisted" models: each member is specified by a sequence of positive functions psi and has an associated psi-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence psi* that is optimal in the sense that the psi*-auxiliary particle filter's estimate of L has zero variance. In practical applications, psi* is unknown so the psi*-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate psi*, and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm

Intersection Bounds: Estimation and Inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest

A Snapshot of the Age, Growth, and Reproductive Status of Gray Triggerfish (Balistes Capriscus, Gmelin 1789) on Three Artificial Reefs in the Northwest Gulf of Mexico

Age, growth, and reproductive status of gray triggerfish (Balistes capriscus) were identified from 2015-2016 on artificial reefs in the northwest Gulf of Mexico. Individuals ranged from 232-432 mm fork length with and a mean fork length of 319 mm. Individuals from age 0.2 to 5.2 yrs were observed with a weight to length relationship of Wg = 1.1 x -104 x FL2.7 (r2 = 0.94, n = 112), where FL = fork length (mm) and Wg = weight (g). A von Bertalanffy growth equation of Lt = 326(1 - e - 0.9 (t + 1.71)) was calculated irrespective of sex. Gonadosomatic index and histological characterization of reproductive tissue identified June-August as the peak spawning season. A female length to batch fecundity (BF) relationship of Log BF = 2.79 x Log (FL 0.81) (r2 = 0.28) was identified. Continued management of gray triggerfish on artificial reefs is necessary to increase the stock and eventually lead to robust and sustainable fisheries

Can disorder enhance incoherent exciton diffusion?

Recent experiments aimed at probing the dynamics of excitons have revealed that semiconducting films composed of disordered molecular subunits, unlike expectations for their perfectly ordered counterparts, can exhibit a time-dependent diffusivity in which the effective early time diffusion constant is larger than that of the steady state. This observation has led to speculation about what role, if any, microscopic disorder may play in enhancing exciton transport properties. In this article, we present the results of a model study aimed at addressing this point. Specifically, we present a general model, based upon F\"orster theory, for incoherent exciton diffusion in a material composed of independent molecular subunits with static energetic disorder. Energetic disorder leads to heterogeneity in molecule-to-molecule transition rates which we demonstrate has two important consequences related to exciton transport. First, the distribution of local site-specific diffusivity is broadened in a manner that results in a decrease in average exciton diffusivity relative to that in a perfectly ordered film. Second, since excitons prefer to make transitions that are downhill in energy, the steady state distribution of exciton energies is biased towards low energy molecular subunits, those that exhibit reduced diffusivity relative to a perfectly ordered film. These effects combine to reduce the net diffusivity in a manner that is time dependent and grows more pronounced as disorder is increased. Notably, however, we demonstrate that the presence of energetic disorder can give rise to a population of molecular subunits with exciton transfer rates exceeding that of subunits in an energetically uniform material. Such enhancements may play an important role in processes that are sensitive to molecular-scale fluctuations in exciton density field.Comment: 15 pages, 3 figure

Nonequilibrium dynamics of localized and delocalized excitons in colloidal quantum dot solids

Self-assembled quantum dot (QD) solids are a highly tunable class of materials with a wide range of applications in solid-state electronics and optoelectronic devices. In this perspective, we highlight how the presence of microscopic disorder in these materials can influence their macroscopic optoelectronic properties. Specifically, we consider the dynamics of excitons in energetically disordered QD solids using a theoretical model framework for both localized and delocalized excitonic regimes. In both cases, we emphasize the tendency of energetic disorder to promote nonequilibrium relaxation dynamics and discuss how the signatures of these nonequilibrium effects manifest in time-dependent spectral measurements. Moreover, we describe the connection between the microscopic dynamics of excitons within the material and the measurement of material specific parameters, such as emission linewidth broadening and energetic dissipation rate.Comment: 4 figure

Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

A Nonclassical Dihydrogen Adduct of S = ½ Fe(I)

We have exploited the capacity of the “(SiP^(iPr)_3)Fe(I)” scaffold to accommodate additional axial ligands and characterized the mononuclear S = 1/2 H_2 adduct complex (SiP^(iPr)_3)Fe^I(H_2). EPR and ENDOR data, in the context of X-ray structural results, revealed that this complex provides a highly unusual example of an open-shell metal complex that binds dihydrogen as a ligand. The H2 ligand at 2 K dynamically reorients within the ligand-binding pocket, tunneling among the energy minima created by strong interactions with the three Fe–P bonds

Census Snapshot: Illinois

Using data from the U.S. Census Bureau, this report provides demographic and economic information about same-sex couples and same-sex couples raising children in Illinois. We compare same-sex "unmarried partners," which the Census Bureau defines as an unmarried couple who "shares living quarters and has a close personal relationship," to different-sex married couples in Illinois

Census Snapshot: Michigan

Using data from the U.S. Census Bureau, this report provides demographic and economic information about same-sex couples and same-sex couples raising children in Michigan. We compare same-sex "unmarried partners," which the Census Bureau defines as an unmarried couple who "shares living quarters and has a close personal relationship," to different-sex married couples in Michigan