Simultaneous estimation of aerosol cloud concentration and spectral backscatter from multiple-wavelength lidar data

Warren, Russell E.; Vanderbeek, Richard G.; Ben‐David, Avishai; Ahl, Jeffrey L.

doi:10.1364/ao.47.004309

Cited by 21 publications

(6 citation statements)

References 4 publications

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“…For each cloud i = 1, …, 30 at 50 time periods (called bursts), which are sampled at one second apart, and various CO 2 laser wavelengths, the background corrected received signal is observed at 250 equally spaced range values. Here we concentrate on the (range invariant) backscatter efficiency of the true signal as estimated using the algorithm of Warren et al (2008, 2009), but applied to the observed data rather than the deconvolved data.…”

Section: Discussionmentioning

confidence: 99%

Significance tests for functional data with complex dependence structure

Staicu

Lahiri

Carroll

2015

Journal of Statistical Planning and Inference

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We propose an L2-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups–clusters or subjects–units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients. The asymptotic null distribution of the test statistic is developed, under mild regularity conditions. To our knowledge this is the first work that studies hypothesis testing, when data have such complex multilevel functional and spatial structure. Two small-sample alternatives, including a novel block bootstrap for functional data, are proposed, and their performance is examined in simulation studies. The paper concludes with an illustration of a motivating experiment.

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Section: Discussionmentioning

confidence: 99%

Significance tests for functional data with complex dependence structure

Staicu

Lahiri

Carroll

2015

Journal of Statistical Planning and Inference

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“…The data are described in detail by Carroll et al (2012), and the estimation of spectral backscatter uses the algorithm of Warren et al (2008, 2009), but applied to the observed data rather than the deconvolved data. Our main goal is to estimate the probability of high spectral backscatter at different wavelengths.…”

Section: Discussionmentioning

confidence: 99%

Multilevel Cross-Dependent Binary Longitudinal Data

2013

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We provide insights into new methodology for the analysis of multilevel binary data observed longitudinally, when the repeated longitudinal measurements are correlated. The proposed model is logistic functional regression conditioned on three latent processes describing the within- and between-variability, and describing the cross-dependence of the repeated longitudinal measurements. We estimate the model components without employing mixed-effects modeling but assuming an approximation to the logistic link function. The primary objectives of this paper are to highlight the challenges in the estimation of the model components, to compare two approximations to the logistic regression function, linear and exponential, and to discuss their advantages and limitations. The linear approximation is computationally efficient whereas the exponential approximation applies for rare events functional data. Our methods are inspired by and applied to a scientific experiment on spectral backscatter from long range infrared light detection and ranging (LIDAR) data. The models are general and relevant to many new binary functional data sets, with or without dependence between repeated functional measurements.

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“…We have access to a small subset of long range infrared light detection and ranging (LIDAR) data described by Warren, et al (2008, 2009, 2010). A comic describing the LIDAR data is given in Figure 3.…”

Section: Applicationmentioning

confidence: 99%

Parameter Estimation of Partial Differential Equation Models

Xun

Cao

Mallick

et al. 2013

Journal of the American Statistical Association

126

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Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

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Simultaneous estimation of aerosol cloud concentration and spectral backscatter from multiple-wavelength lidar data

Cited by 21 publications

References 4 publications

Significance tests for functional data with complex dependence structure

Significance tests for functional data with complex dependence structure

Multilevel Cross-Dependent Binary Longitudinal Data

Parameter Estimation of Partial Differential Equation Models

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