Modern Mathematical Statistics with Applications

Devore, Jay L.; Berk, Kenneth N.

doi:10.1007/978-3-030-55156-8

Cited by 51 publications

(26 citation statements)

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“… Note . R values rows are shaded by the strength of correlation (not correlated in gray |R| < 0.25, light brown for weak 0.25 ≤ |R| < 0.5, and medium brown for moderate 0.5 ≤ |R| < 0.8 (Devore & Berk, 2012). …”

Section: Methodsmentioning

confidence: 99%

Seasonal Differences and Variability of Concentrations, Chemical Composition, and Cloud Condensation Nuclei of Marine Aerosol Over the North Atlantic

et al. 2020

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The majority of the aerosol particle number (condensation nuclei or CN) in the marine boundary layer (MBL) consists of sulfate and organic compounds that have been shown to provide a large fraction of the cloud condensation nuclei (CCN). Here we use submicron non-refractory Aerosol Mass Spectrometer (AMS) and filter measurements of organic and sulfate components of aerosol particles measured during four North Atlantic Aerosol and Marine Ecosystems Study (NAAMES) research cruises to assess the sources and contributions of submicron organic and sulfate components for CCN concentrations in the MBL during four different seasons. Submicron hydroxyl group organic mass (OM) correlated strongly to sodium concentrations during clean marine periods (R ¼ 0.9), indicating that hydroxyl group OM can serve as a proxy for sea-spray OM in ambient measurements. Sea-spray OM contributed 45% of the sum of sea-spray OM and sea salt during late spring (biomass climax phase) compared to <20% for other seasons, but the seasonal difference was not statistically significant. The contribution of noncombustion sources during clean marine periods to submicron OM was 47 to 88% and to non-sea-salt sulfate 31 to 86%, with likely sources being marine and biogenic. The remaining submicron OM and sulfate were likely associated with ship or continental sources, including biomass burning, even during clean marine periods. The seasonal contribution from secondary sulfate and OM components to submicron aerosol mass was highest during late spring (60%), when biogenic emissions are expected to be highest, and lowest during winter (18%). Removing submicron sea-spray OM decreased CCN concentrations by <10% because of competing effects from increased hygroscopicity and decreased particle size. During all seasons, adding biogenic secondary sulfate increased hygroscopicity, particle size, and CCN concentrations at 0.1-0.3% supersaturations by 5-66%. The largest change was during early spring when the fraction of hygroscopic sulfate components in the 0.1-0.2 μm size range was highest (80%). During continental periods, the increased contribution from low-hygroscopicity organic components to 0.1-0.2 μm diameter particles reduces the CCN/CN by 20-100% for three seasons despite the increased CN and mass concentrations. These results illustrate the important role of the chemical composition of particles with diameters 0.1-0.2 μm for controlling CCN in the MBL.

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Section: Methodsmentioning

confidence: 99%

Seasonal Differences and Variability of Concentrations, Chemical Composition, and Cloud Condensation Nuclei of Marine Aerosol Over the North Atlantic

et al. 2020

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“…Define the output distribution of the network in the forward direction to be q ( d , z ; θ ):

q (boldd, boldz; θ) = p (m) / true| d e t J_{f} (boldm; θ) true|

where p ( m ) is the prior distribution of model m , and

J_{f} (boldm; θ) = \frac{\partial f (boldm; θ)}{\partial boldm}

is the Jacobian of the forward transform embodied in the network (Devore & Berk, 2012). Given those expressions, the training loss function

scriptL

can be expressed as:

scriptL = {falsefalse}_{\sum}^{i = 1} (‖‖ {boldd}^{i} - f false({boldm}^{i}; θ false)) + α normalM normalM normalD [q (d^{i}, z^{i}; θ), p (d^{i}) p (z^{i})]

where each model vector corresponds to a single data vector and a single latent vector.…”

Section: Methodsmentioning

confidence: 99%

“…is the Jacobian of the forward transform embodied in the network (Devore & Berk, 2012). Given those expressions, the training loss function  can be expressed as:…”

Section: Solving Inverse Problems Using Innsmentioning

confidence: 99%

Bayesian Geophysical Inversion Using Invertible Neural Networks

Zhang

Curtis

2021

JGR Solid Earth

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Geoscientists build models of the subsurface to understand properties and processes in the Earth's interior. The models are usually parameterized in some way, so to constrain the models, we must solve a parameter estimation problem. Data are recorded which provide constraints, together with prior knowledge. However, since the physical relationships between parameters and data usually predict data given the parameters (known as the forward calculation) but not the reverse, the solution must be found using inverse theory.Geophysical inverse problems usually have nonunique solutions due to noise in the data, to nonlinearity of the physical relationships between model parameters and data, and to fundamentally unconstrained combinations of parameters. Uncertainties in parameter estimates must therefore be quantified to interpret inversion results correctly. Unfortunately, estimating uncertainty in nonlinear inverse problems can be computationally expensive, and the cost increases both with the number of parameters, and with the computational cost of the forward calculation. In this study, we therefore solve two different types of seismic tomography problems which each have fewer than 100 parameters, and have relatively rapid forward functions (each evaluation takes on the order of seconds). This allows us to evaluate solutions sufficiently accurately to thoroughly test a new method of Geophysical inversion.Geophysical inverse problems are traditionally solved by linearizing (approximating) the nonlinear physics, and using optimization methods which seek a model that minimizes the misfit between observed and predicted data (Aki & Lee, 1976;Dziewonski & Woodhouse, 1987;Iyer & Hirahara, 1993). However, despite their wide applications, linearized procedures cannot produce accurate estimates of uncertainty because data uncertainty distributions can deviate substantially from analytic forms of probability such as Gaussians or Uniform distributions that can be propagated through linearized methods efficiently, and since the distribution of possible models post inversion can be strongly affected by nonlinearity in the physics (Bo-

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“…This leads to the second observation noted from Figure 5-1. A characteristic of a Poisson type distribution is that the variance is equal to the mean which is the case for a point process exhibiting complete spatial randomness (Devore and Berk, 2012). The deviation is suspected to be due to the increasing variance that is characteristic of a more clustered point process as illustrated by the simulated point patterns given in Figure 3-17.…”

Section: Degree Of Clusteringmentioning

confidence: 96%

The influence of fibre spatial characteristics on the flexural performance of SFRC

Bosman

Kearsley

2019

Mater Struct

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The addition of discontinuous discrete fibres to concrete has repeatedly been shown as an effective method to overcome the inherently brittle nature of concrete. The resulting composite has enhanced toughness and impact resistance and is broadly referred to as Fibre-Reinforced Concrete (FRC).Although the benefits of implementing FRC are evident, the high variability associated with FRC has frequently been cited as a characteristic stunting vast structural application of the material. This research is focussed on the spatial distribution of fibres and the way it affects flexural performance. A thorough understanding of the influence of fibre spatial distribution on composite performance is the first step in incorporating fibre distribution into material and structural design procedures and aids the pursuit of effective and optimal implementation of FRC in practice.

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Modern Mathematical Statistics with Applications

Cited by 51 publications

References 0 publications

Seasonal Differences and Variability of Concentrations, Chemical Composition, and Cloud Condensation Nuclei of Marine Aerosol Over the North Atlantic

Seasonal Differences and Variability of Concentrations, Chemical Composition, and Cloud Condensation Nuclei of Marine Aerosol Over the North Atlantic

Bayesian Geophysical Inversion Using Invertible Neural Networks

The influence of fibre spatial characteristics on the flexural performance of SFRC

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