Estimating stochastic volatility diffusion using conditional moments of integrated volatility

We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps. © 2002 Elsevier Science B.V. All rights reserved.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Stochastic E2F activation and reconciliation of phenomenological cell-cycle models.

The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.

Man's search for meaning: The case of Legos

We investigate how perceived meaning influences labor supply. In a laboratory setting, we manipulate the perceived meaning of simple, repetitive tasks and find a strong influence on subjects' labor supply. Despite the fact that the wage and the task are identical across the conditions in each experiment, subjects in the less meaningful conditions exhibit reservation wages that are consistently much higher than the subjects in the more meaningful conditions. The result replicates across different types of tasks. Moreover, in the more meaningful conditions, subjects' productivity influences labor supply more strongly. © 2008 Elsevier B.V. All rights reserved.

Rare targets are rarely missed in correctable search.

Failing to find a tumor in an x-ray scan or a gun in an airport baggage screening can have dire consequences, making it fundamentally important to elucidate the mechanisms that hinder performance in such visual searches. Recent laboratory work has indicated that low target prevalence can lead to disturbingly high miss rates in visual search. Here, however, we demonstrate that misses in low-prevalence searches can be readily abated. When targets are rarely present, observers adapt by responding more quickly, and miss rates are high. Critically, though, these misses are often due to response-execution errors, not perceptual or identification errors: Observers know a target was present, but just respond too quickly. When provided an opportunity to correct their last response, observers can catch their mistakes. Thus, low target prevalence may not be a generalizable cause of high miss rates in visual search.

Comprehensive search for new phases and compounds in binary alloy systems based on platinum-group metals, using a computational first-principles approach

We report a comprehensive study of the binary systems of the platinum-group metals with the transition metals, using high-throughput first-principles calculations. These computations predict stability of new compounds in 28 binary systems where no compounds have been reported in the literature experimentally and a few dozen of as-yet unreported compounds in additional systems. Our calculations also identify stable structures at compound compositions that have been previously reported without detailed structural data and indicate that some experimentally reported compounds may actually be unstable at low temperatures. With these results, we construct enhanced structure maps for the binary alloys of platinum-group metals. These maps are much more complete, systematic, and predictive than those based on empirical results alone.

BAYESIAN MODEL SEARCH AND MULTILEVEL INFERENCE FOR SNP ASSOCIATION STUDIES.

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally "validated" in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.

Postoperative statin use and risk of biochemical recurrence following radical prostatectomy: results from the Shared Equal Access Regional Cancer Hospital (SEARCH) database.

OBJECTIVE: To investigate the effect of statin use after radical prostatectomy (RP) on biochemical recurrence (BCR) in patients with prostate cancer who never received statins before RP. PATIENTS AND METHODS: We conducted a retrospective analysis of 1146 RP patients within the Shared Equal Access Regional Cancer Hospital (SEARCH) database. Multivariable Cox proportional hazards analyses were used to examine differences in risk of BCR between post-RP statin users vs nonusers. To account for varying start dates and duration of statin use during follow-up, post-RP statin use was treated as a time-dependent variable. In a secondary analysis, models were stratified by race to examine the association of post-RP statin use with BCR among black and non-black men. RESULTS: After adjusting for clinical and pathological characteristics, post-RP statin use was significantly associated with 36% reduced risk of BCR (hazard ratio [HR] 0.64, 95% confidence interval [CI] 0.47-0.87; P = 0.004). Post-RP statin use remained associated with reduced risk of BCR after adjusting for preoperative serum cholesterol levels. In secondary analysis, after stratification by race, this protective association was significant in non-black (HR 0.49, 95% CI 0.32-0.75; P = 0.001) but not black men (HR 0.82, 95% CI 0.53-1.28; P = 0.384). CONCLUSION: In this retrospective cohort of men undergoing RP, post-RP statin use was significantly associated with reduced risk of BCR. Whether the association between post-RP statin use and BCR differs by race requires further study. Given these findings, coupled with other studies suggesting that statins may reduce risk of advanced prostate cancer, randomised controlled trials are warranted to formally test the hypothesis that statins slow prostate cancer progression.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Improvement in visual search with practice: mapping learning-related changes in neurocognitive stages of processing.

Practice can improve performance on visual search tasks; the neural mechanisms underlying such improvements, however, are not clear. Response time typically shortens with practice, but which components of the stimulus-response processing chain facilitate this behavioral change? Improved search performance could result from enhancements in various cognitive processing stages, including (1) sensory processing, (2) attentional allocation, (3) target discrimination, (4) motor-response preparation, and/or (5) response execution. We measured event-related potentials (ERPs) as human participants completed a five-day visual-search protocol in which they reported the orientation of a color popout target within an array of ellipses. We assessed changes in behavioral performance and in ERP components associated with various stages of processing. After practice, response time decreased in all participants (while accuracy remained consistent), and electrophysiological measures revealed modulation of several ERP components. First, amplitudes of the early sensory-evoked N1 component at 150 ms increased bilaterally, indicating enhanced visual sensory processing of the array. Second, the negative-polarity posterior-contralateral component (N2pc, 170-250 ms) was earlier and larger, demonstrating enhanced attentional orienting. Third, the amplitude of the sustained posterior contralateral negativity component (SPCN, 300-400 ms) decreased, indicating facilitated target discrimination. Finally, faster motor-response preparation and execution were observed after practice, as indicated by latency changes in both the stimulus-locked and response-locked lateralized readiness potentials (LRPs). These electrophysiological results delineate the functional plasticity in key mechanisms underlying visual search with high temporal resolution and illustrate how practice influences various cognitive and neural processing stages leading to enhanced behavioral performance.

VizMaps: A Bayesian Topic Modeling Based PubMed Search Interface

A common challenge that users of academic databases face is making sense of their query outputs for knowledge discovery. This is exacerbated by the size and growth of modern databases. PubMed, a central index of biomedical literature, contains over 25 million citations, and can output search results containing hundreds of thousands of citations. Under these conditions, efficient knowledge discovery requires a different data structure than a chronological list of articles. It requires a method of conveying what the important ideas are, where they are located, and how they are connected; a method of allowing users to see the underlying topical structure of their search. This paper presents VizMaps, a PubMed search interface that addresses some of these problems. Given search terms, our main backend pipeline extracts relevant words from the title and abstract, and clusters them into discovered topics using Bayesian topic models, in particular the Latent Dirichlet Allocation (LDA). It then outputs a visual, navigable map of the query results.