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Now showing 1 - 10 of 511
  • Publication
    A Stochastic Model of Fragmentation in Dynamic Storage Allocation
    (1985-05-01) Coffman, E. G; Kadota, T. T; Shepp, Larry A
    We study a model of dynamic storage allocation in which requests for single units of memory arrive in a Poisson stream at rate λ and are accommodated by the first available location found in a linear scan of memory. Immediately after this first-fit assignment, an occupied location commences an exponential delay with rate parameter μ, after which the location again becomes available. The set of occupied locations (identified by their numbers) at time t forms a random subset St of {1,2, . . .}. The extent of the fragmentation in St, i.e. the alternating holes and occupied regions of memory, is measured by (St) - |St |. In equilibrium, the number of occupied locations, |S|, is known to be Poisson distributed with mean ρ = λ/μ. We obtain an explicit formula for the stationary distribution of max (S), the last occupied location, and by independent arguments we show that (E max (S) - E|S|)/E|S| → 0 as the traffic intensity ρ → ∞. Moreover, we verify numerically that for any ρ the expected number of wasted locations in equilibrium is never more than 1/3 the expected number of occupied locations. Our model applies to studies of fragmentation in paged computer systems, and to containerization problems in industrial storage applications. Finally, our model can be regarded as a simple concrete model of interacting particles [Adv. Math., 5 (1970), pp. 246–290].
  • Publication
    Evidence-Based Forecasting for Climate Change
    (2013-02-01) Green, Kesten C; Soon, Willie; Armstrong, J. Scott
    Following Green, Armstrong and Soon’s (IJF 2009) (GAS) naïve extrapolation, Fildes and Kourentzes (IJF 2011) (F&K) found that each of six more-sophisticated, but inexpensive, extrapolation models provided forecasts of global mean temperature for the 20 years to 2007 that were more accurate than the “business as usual” projections provided by the complex and expensive “General Circulation Models” used by the U.N.’s Intergovernmental Panel on Climate Change (IPCC). Their average trend forecast was .007°C per year, and diminishing; less than a quarter of the IPCC’s .030°C projection. F&K extended previous research by combining forecasts from evidence-based short-term forecasting methods. To further extend this work, we suggest researchers: (1) reconsider causal forces; (2) validate with more and longer-term forecasts; (3) adjust validation data for known biases and use alternative data; and (4) damp forecasted trends to compensate for the complexity and uncertainty of the situation. We have made a start in following these suggestions and found that: (1) uncertainty about causal forces is such that they should be avoided in climate forecasting models; (2) long term forecasts should be validated using all available data and much longer series that include representative variations in trend; (3) when tested against temperature data collected by satellite, naïve forecasts are more accurate than F&K’s longer-term (11-20 year) forecasts; and (4) progressive damping improves the accuracy of F&K’s forecasts. In sum, while forecasting a trend may improve the accuracy of forecasts for a few years into the future, improvements rapidly disappear as the forecast horizon lengthens beyond ten years. We conclude that predictions of dangerous manmade global warming and of benefits from climate policies fail to meet the standards of evidence-based forecasting and are not a proper basis for policy decisions.
  • Publication
    Surrogate Markers for Time-Varying Treatments and Outcomes
    (2015-08-01) Hsu, Jesse Y; Kennedy, Edward H; Roy, Jason A; Stephens-Shields, Alisa J; Small, Dylan S; Joffe, Marshall M
    BACKGROUND: A surrogate marker is a variable commonly used in clinical trials to guide treatment decisions when the outcome of ultimate interest is not available. A good surrogate marker is one where the treatment effect on the surrogate is a strong predictor of the effect of treatment on the outcome. We review the situation when there is one treatment delivered at baseline, one surrogate measured at one later time point, and one ultimate outcome of interest and discuss new issues arising when variables are time-varying. METHODS: Most of the literature on surrogate markers has only considered simple settings with one treatment, one surrogate, and one outcome of interest at a fixed time point. However, more complicated time-varying settings are common in practice. In this article, we describe the unique challenges in two settings, time-varying treatments and time-varying surrogates, while relating the ideas back to the causal-effects and causal-association paradigms. CONCLUSION: In addition to discussing and extending popular notions of surrogacy to time-varying settings, we give examples illustrating that one can be misled by not taking into account time-varying information about the surrogate or treatment. We hope this article has provided some motivation for future work on estimation and inference in such settings.
  • Publication
    Competing With Strategies
    (2013-01-01) Han, Wei; Rakhlin, Alexander; Sridharan, Karthik
    We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the standard methods for minimizing the usual notion of regret fail, through our analysis we demonstrate existence of regret-minimization methods that compete with such sets of strategies as: autoregressive algorithms, strategies based on statistical models, regularized least squares, and follow the regularized leader strategies. In several cases we also derive efficient learning algorithms
  • Publication
    Diffusion, Cell Mobility, and Bandlimited Functions
    (1984-12-01) Landau, H. J; Logan, B. F; Shepp, Larry A; Bauman, N.
    The mechanism by which leukocytes steer toward a chemical attractant is not fully resolved. Experimental data suggest that these cells detect differences in concentration of chemoattractant over their surface and "walk" up the gradient. The problem has been considered theoretically only in stationary media, where the distribution of attractant is determined solely by diffusion. Experimentally, bulk flow has been allowed only unintentionally. Since bulk flow is characteristic of real systems, we examine a simple two-dimensional model incorporating both diffusion and an additional drift. The latter problem leads to an integral equation which is central also in the study of weighted Hilbert spaces of bandlimited functions. We find asymptotic expressions for the required solution by a Wiener-Hopf method adapted to a finite interval. We conclude that, without drift, the concentration does not vary detectably around the cell, but that drift inceases this variation substantially. Thus over model suggests that drift may play an important role in the cell's chemotactic response.
  • Publication
    Design Sensitivity in Observational Studies
    (2007-01-01) Brown, Lawrence D
    Outside the field of statistics, the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal, such as multiple operationalism or a dose-response relationship. These useful suggestions are typically informal and qualitative. A quantitative measure, design sensitivity, is proposed for measuring the contribution such strategies are then evaluated in terms of their contribution to design sensitivity. A related method for computing the power of a sensitivity analysis is also developed.
  • Publication
    Testing Behavioral Hypotheses Using an Integrated Model of Grocery Store Shopping Path and Purchase Behavior
    (2009-10-01) Hui, Sam K; Bradlow, Eric T; Fader, Peter S
    We examine three sets of established behavioral hypotheses about consumers' in-store behavior using field data on grocery store shopping paths and purchases. Our results provide field evidence for the following empirical regularities. First, as consumers spend more time in the store, they become more purposeful—they are less likely to spend time on exploration and more likely to shop/buy. Second, consistent with “licensing” behavior, after purchasing virtue categories, consumers are more likely to shop at locations that carry vice categories. Third, the presence of other shoppers attracts consumers toward a store zone but reduces consumers' tendency to shop there.
  • Publication
    Predictive Density Estimation for Multiple Regression
    (2008-04-01) George, Edward I; Xu, Xinyi
    Suppose we observe X ~ Nm(Aβ, σ2I) and would like to estimate the predictive density p(y|β) of a future Y ~ Nn(Bβ, σ2I). Evaluating predictive estimates by Kullback–Leibler loss, we develop and evaluate Bayes procedures for this problem. We obtain general sufficient conditions for minimaxity and dominance of the “noninformative” uniform prior Bayes procedure. We extend these results to situations where only a subset of the predictors in A is thought to be potentially irrelevant. We then consider the more realistic situation where there is model uncertainty and this subset is unknown. For this situation we develop multiple shrinkage predictive estimators and obtain general minimaxity and dominance conditions. Finally, we provide an explicit example of a minimax multiple shrinkage predictive estimator based on scaled harmonic priors.
  • Publication
    Comment: The Place of Death in the Quality of Life
    (2006-01-01) Rosenbaum, Paul R
  • Publication
    Large-Scale Multiple Testing of Correlations
    (2016-05-05) Cai, T. Tony; Liu, Weidong
    Multiple testing of correlations arises in many applications including gene coexpression network analysis and brain connectivity analysis. In this article, we consider large-scale simultaneous testing for correlations in both the one-sample and two-sample settings. New multiple testing procedures are proposed and a bootstrap method is introduced for estimating the proportion of the nulls falsely rejected among all the true nulls. We investigate the properties of the proposed procedures both theoretically and numerically. It is shown that the procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level. Simulation results show that the methods perform well numerically in terms of both the size and power of the test and it significantly outperforms two alternative methods. The two-sample procedure is also illustrated by an analysis of a prostate cancer dataset for the detection of changes in coexpression patterns between gene expression levels. Supplementary materials for this article are available online.