An Ecological Study of the Prairie and Sedge Meadow Communities of Richardson Wildlife Foundation

ID: 8259; Issue date not indicated on report.INHS Technical Report prepared for Terry Moyer, Richardson Wildlife Foundatio

Ergodicity, Decisions, and Partial Information

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that one may choose (under a mild integrability assumption) a decision strategy whose pathwise time-average loss is asymptotically smaller than that of any other strategy. The corresponding problem in the case of partial information proves to be much more delicate, however: if the process X is not observable, but decisions must be based on the observation of a different process Y, the existence of pathwise optimal strategies is not guaranteed. The aim of this paper is to exhibit connections between pathwise optimal strategies and notions from ergodic theory. The sequential decision problem is developed in the general setting of an ergodic dynamical system (\Omega,B,P,T) with partial information Y\subseteq B. The existence of pathwise optimal strategies grounded in two basic properties: the conditional ergodic theory of the dynamical system, and the complexity of the loss function. When the loss function is not too complex, a general sufficient condition for the existence of pathwise optimal strategies is that the dynamical system is a conditional K-automorphism relative to the past observations \bigvee_n T^n Y. If the conditional ergodicity assumption is strengthened, the complexity assumption can be weakened. Several examples demonstrate the interplay between complexity and ergodicity, which does not arise in the case of full information. Our results also yield a decision-theoretic characterization of weak mixing in ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page

Single-Particle Self-Excited Oscillator

Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e-, e+, p, and [overline p] magnetic moments

The Epidemiology of Multiple Sclerosis in Scotland: Inferences from Hospital Admissions

PMCID: PMC3029296This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Adverse Selection and Switching Costs in Health Insurance Markets: When Nudging Hurts

This paper investigates consumer switching costs in the context of health insurance markets, where adverse selection is a potential concern. Though previous work has studied these phenomena in isolation, they interact in a way that directly impacts market outcomes and consumer welfare. Our identification strategy leverages a unique natural experiment that occurred at a large firm where we also observe individual-level panel data on health insurance choices and medical claims. We present descriptive results to show that (i) switching costs are large and (ii) adverse selection is present. To formalize this analysis we develop and estimate a choice model that jointly quantifies switching costs, risk preferences, and ex ante health risk. We use these estimates to study the welfare impact of an information provision policy that nudges consumers toward better decisions by reducing switching costs. This policy increases welfare in a naive setting where insurance plan prices are held fixed. However, when insurance prices change endogenously to reflect updated enrollee risk pools, the same policy substantially exacerbates adverse selection and reduces consumer welfare, doubling the existing welfare loss from adverse selection.

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Correction: The Role of Compensatory Mutations in the Emergence of Drug Resistance

Pathogens that evolve resistance to drugs usually have reduced fitness. However, mutations that largely compensate for this reduction in fitness often arise. We investigate how these compensatory mutations affect population-wide resistance emergence as a function of drug treatment. Using a model of gonorrhea transmission dynamics, we obtain generally applicable, qualitative results that show how compensatory mutations lead to more likely and faster resistance emergence. We further show that resistance emergence depends on the level of drug use in a strongly nonlinear fashion. We also discuss what data need to be obtained to allow future quantitative predictions of resistance emergence

Information frictions and adverse selection: policyinterventions in health insurance markets

This paper develops and implements a general framework to study insurance market equilibrium and evaluate policy interventions in the presence of choice frictions. Friction-reducing policies can increase welfare by facilitating better matches between consumers and plans, but can decrease welfare by increasing the correlation between willingness-to-pay and costs, exacerbating adverse selection. We identify relationships between the underlying distributions of consumer (i) costs (ii) surplus from risk protection and (iii) choice frictions that determine whether friction-reducing policies will be on net welfare increasing or reducing. We extend the analysis to study how policies to improve consumer choices interact with the supply-side policy of risk-adjustment transfers and show that the effectiveness of the latter policy can have important implications for the effectiveness of the former. We implement the model empirically using proprietary data on insurance choices, utilization, and consumer information from a large firm. We leverage structural estimates from prior work with these data and highlight how the model's micro-foundations can be estimated in practice. In our specific setting, we find that friction-reducing policies exacerbate adverse selection, essentially leading to the market fully unravelling, and reduce welfare. Risk-adjustment transfers are complementary, substantially mitigating the negative impact of friction-reducing policies, but having little effect in their absence

A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory, while remaining completely within the setting of finite-dimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be found at http://minty.caltech.edu/papers.ph

Smoking and Multiple Sclerosis: An Updated Meta-Analysis

Background: Multiple sclerosis (MS) is a leading cause of disability in young adults. Susceptibility to MS is determined by environmental exposure on the background of genetic risk factors. A previous meta-analysis suggested that smoking was an important risk factor for MS but many other studies have been published since then.Methods/Principal Findings: We performed a Medline search to identify articles published that investigated MS risk following cigarette smoking. A total of 14 articles were included in this study. This represented data on 3,052 cases and 457,619 controls. We analysed these studies in both a conservative (limiting our analysis to only those where smoking behaviour was described prior to disease onset) and non-conservative manner. Our results show that smoking is associated with MS susceptibility (conservative: risk ratio (RR) 1.48, 95% confidence interval (CI) 1.35-1.63, p<10(-15); non-conservative: RR 1.52, 95% CI 1.39-1.66, p<10(-19)). We also analysed 4 studies reporting risk of secondary progression in MS and found that this fell just short of statistical significance with considerable heterogeneity (RR 1.88, 95% CI 0.98-3.61, p = 0.06).Discussion: Our results demonstrate that cigarette smoking is important in determining MS susceptibility but the effect on the progression of disease is less certain. Further work is needed to understand the mechanism behind this association and how smoking integrates with other established risk factors