Using Proxies for the Short Rate: When are Three Months Like an Instant?

The dynamics of the unobservable "short" or "instantaneous" rate of interest are frequently estimated using a proxy variable. We show the biases resulting from this practice (the "proxy" problem) are related to the derivatives of the proxy with respect to the short rate and the (inverse) function from the proxy to the short rate. Analytic results show that the proxy problem is not economically significant for single- factor affine models, for parameter values consistent with US data. In addition, for the two-factor affine model of Longstaff and Schwartz (1992), the proxy problem is only economically significant for pricing discount bonds with maturities of more than 5 years. We also describe two different procedures which can be used to assess the magnitude of the proxy problem in more general interest rate models. Numerical evaluation of a nonlinear single-factor model suggests that the proxy problem can significantly affect both estimates of the diffusion function and discount bond prices.interest rates, proxies, term structure

A Statistical Description of Neural Ensemble Dynamics

The growing use of multi-channel neural recording techniques in behaving animals has produced rich datasets that hold immense potential for advancing our understanding of how the brain mediates behavior. One limitation of these techniques is they do not provide important information about the underlying anatomical connections among the recorded neurons within an ensemble. Inferring these connections is often intractable because the set of possible interactions grows exponentially with ensemble size. This is a fundamental challenge one confronts when interpreting these data. Unfortunately, the combination of expert knowledge and ensemble data is often insufficient for selecting a unique model of these interactions. Our approach shifts away from modeling the network diagram of the ensemble toward analyzing changes in the dynamics of the ensemble as they relate to behavior. Our contribution consists of adapting techniques from signal processing and Bayesian statistics to track the dynamics of ensemble data on time-scales comparable with behavior. We employ a Bayesian estimator to weigh prior information against the available ensemble data, and use an adaptive quantization technique to aggregate poorly estimated regions of the ensemble data space. Importantly, our method is capable of detecting changes in both the magnitude and structure of correlations among neurons missed by firing rate metrics. We show that this method is scalable across a wide range of time-scales and ensemble sizes. Lastly, the performance of this method on both simulated and real ensemble data is used to demonstrate its utility

Matching the Statistical Model to the Research Question for Dental Caries Indices with Many Zero Counts

Marginalized zero-inflated count regression models have recently been introduced for the statistical analysis of dental caries indices and other zero-inflated count data as alternatives to traditional zero-inflated and hurdle models. Unlike the standard approaches, the marginalized models directly estimate overall exposure or treatment effects by relating covariates to the marginal mean count. This article discusses model interpretation and model class choice according to the research question being addressed in caries research. Two datasets, one consisting of fictional dmft counts in two groups and the other on DMFS among schoolchildren from a randomized clinical trial (RCT) comparing three toothpaste formulations to prevent incident dental caries, are analysed with negative binomial hurdle (NBH), zero-inflated negative binomial (ZINB), and marginalized zero-inflated negative binomial (MZINB) models. In the first example, estimates of treatment effects vary according to the type of incidence rate ratio (IRR) estimated by the model. Estimates of IRRs in the analysis of the RCT were similar despite their distinctive interpretations. Choice of statistical model class should match the study’s purpose, while accounting for the broad decline in children’s caries experience, such that dmft and DMFS indices more frequently generate zero counts. Marginalized (marginal mean) models for zero-inflated count data should be considered for direct assessment of exposure effects on the marginal mean dental caries count in the presence of high frequencies of zero counts

Stability of High-Density Two-Dimensional Excitons against a Mott Transition in High Magnetic Fields Probed by Coherent Terahertz Spectroscopy

We have performed time-resolved terahertz absorption measurements on photoexcited electron-hole pairs in undoped GaAs quantum wells in magnetic fields. We probed both unbound- and bound-carrier responses via cyclotron resonance and intraexciton resonance, respectively. The stability of excitons, monitored as the pair density was systematically increased, was found to dramatically increase with increasing magnetic field. Specifically, the 1$s$-2$p_-$ intraexciton transition at 9 T persisted up to the highest density, whereas the 1$s$-2$p$ feature at 0 T was quickly replaced by a free-carrier Drude response. Interestingly, at 9 T, the 1$s$-2$p_-$ peak was replaced by free-hole cyclotron resonance at high temperatures, indicating that 2D magnetoexcitons do dissociate under thermal excitation, even though they are stable against a density-driven Mott transition.Comment: 5 pages, 4 figure

Validation Results: Utah and Western Sierra Variants of the Forest Vegetation Simulator

The Forest Vegetation Simulator (FVS) is the most widely available and used growth and yield model in the US. It is used in both forest management and research and the basic model framework is integrated with post-processors which can be used for many useful analyses (e.g., fire effects, bark beetle susceptibility, etc.). Recent identification of the nomenclature and a basic validation procedure has resulted in a nation-wide effort to objectively test individual FVS variants following a specific protocol (FVS Validation Subcommittee 2009). Despite the huge range of possibilities for model use, and some independent testing of various model components, (e.g., Pokharel and Froese 2009; Vacchiano et al. 2008) and variants (Lacerte et al. 2004) a comprehensive evaluation of the basic model output has yet to be done. In this project, deliverables identified as necessary to inform an appropriate model testing procedure included: (1) data set description; (2) model verification; (3) model validation; and (4) model sensitivity analysis

The Distance to the Cygnus Loop from Hubble Space Telescope Imaging of the Primary Shock Front

We present a Hubble Space Telescope/WFPC2 narrow-band H-alpha image of a region on the northeastern limb of the Cygnus Loop supernova remnant. This location provides a detailed example of where the primary blast wave first encounters the surrounding interstellar medium. The filament structure is seen in exquisite detail in this image, which was obtained primarily as an EARLY ACQuisition image for a follow-up spectroscopic program. We compare the HST image to a digitized version of the POSS-I red plate to measure the proper motion of this filament. By combining this value for the proper motion with previous measurements of the shock velocity at this position we find that the distance to the Cygnus Loop is 440 (+130, -100) pc, considerably smaller than the canonical value of 770 pc. We briefly discuss the ramifications of this new distance estimate for our understanding of this prototypical supernova remnant.Comment: 18 pages, 3 Figures (2 JPEG and one Postscript

An Algebraic Framework for Stock & Flow Diagrams and Dynamical Systems Using Category Theory

Mathematical modeling of infectious disease at scale is important, but challenging. Some of these difficulties can be alleviated by an approach that takes diagrams seriously as mathematical formalisms in their own right. Stock & flow diagrams are widely used as broadly accessible building blocks for infectious disease modeling. In this chapter, rather than focusing on the underlying mathematics, we informally use communicable disease examples created by the implemented software of StockFlow.jl to explain the basics, characteristics, and benefits of the categorical framework. We first characterize categorical stock & flow diagrams, and note the clear separation between the syntax of stock & flow diagrams and their semantics, demonstrating three examples of semantics already implemented in the software: ODEs, causal loop diagrams, and system structure diagrams. We then establish composition and stratification frameworks and examples for stock & flow diagrams. Applying category theory, these frameworks can build large diagrams from smaller ones in a modular fashion. Finally, we introduce the open-source ModelCollab software for diagram-centric real-time collaborative modeling. Using the graphical user interface, this web-based software allows the user to undertake the types of categorically-rooted operations discussed above, but without any knowledge of their categorical foundations

Evidence for Placoderms from the Mid-Palaeozoic Sandon Beds of North-western New South Wales, Australia

Armoured jawed fishes known as placoderms are a well-documented group with a fossil record spanning the Silurian to end-Devonian. They have a global distribution and a marked diversity within Devonian deposits of Australia. Despite their notable Gondwanan fossil record, new material is occasionally identified and can present important stratigraphic information for otherwise under-explored deposits. A unique find from the so-called Sandon beds is presented here and expands the record of placoderms from New South Wales. This specimen presents insight into a previously unknown macrofossil record from the deposit and suggests a more Devonian age for the unit, rather than the previously suggested Carboniferous date. We also summarise the macrovertebrate record of Devonian placoderms from Australia, highlighting and discussing changes in their Gondwanan taxonomic diversity across the time period