The Inverse Gaussian Distribution

Seshadri, V.

doi:10.1007/978-1-4612-1456-4

Cited by 168 publications

(58 citation statements)

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“…This connection allows us to apply powerful tools from stochastic calculus (Karatzas and Shreve, 1997) to understand the behavior of this model. For example, in the nonleaky case (g(t) = 0) with constant current input (I(t) = I), we may employ the "reflection principle" from the basic theory of Brownian motion to derive the so-called "inverse Gaussian" first passage time density (Gerstein and Mandelbrot, 1964;Seshadri, 1993;Iyengar and Liao, 1997;; denoting p(τ |θ) as the probability density that the next interspike interval will be of length τ , we may explicitly calculate…”

Section: The If Model As a Diffusion Processmentioning

confidence: 99%

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Statistical Models of Spike Trains

Paninski¹,

Brown²,

Iyengar³

2009

Stochastic Methods in Neuroscience

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Section: The If Model As a Diffusion Processmentioning

confidence: 99%

“…This explicit analytical formula for the spike train likelihood allows us, for example, to derive closed-form expressions for the maximum likelihood estimate of the model parameters θ here (Seshadri, 1993); thus the classical stochastic process theory makes model fitting in this simple case quite straightforward.…”

Section: The If Model As a Diffusion Processmentioning

confidence: 99%

Statistical Models of Spike Trains

Paninski¹,

Brown²,

Iyengar³

2009

Stochastic Methods in Neuroscience

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“…Following Waugh et al (2004), we further assume that the G(t) (TTDs) at a certain location can be modelled as an Inverse Gaussian function (Chhikara and Folks, 1989;Seshadri, 1999), i.e. has a broad, asymmetric distribution with a long tail, as…”

Section: Apparent Transit Time Of Pbmentioning

confidence: 99%

Evolution of anthropogenic Pb and Pb isotopes in the deep North Atlantic Ocean and the Indian Ocean

Lee¹

2013

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, in partial fulfillment of the Requirement for the degree of Doctor of PhilosophyPb and Pb isotopes in the ocean have varied on decadal to centennial time scales due to anthropogenic Pb inputs. Thus, tracing the temporal variation of Pb and Pb isotopes in the ocean provides information on the major sources of Pb and the transport of Pb from sources to the ocean surface and into the ocean interior. In this thesis study, first, a method was developed for the analysis of dissolved Pb and other trace elements in seawater using single batch nitrilotriacetate resin extraction and isotope dilution ICP-MS, which was applied in analyzing seawater Pb concentrations in the rest of the study. A -550 year history of the Pb and Pb isotopes in the deep North Atlantic Ocean is reconstructed using a deep-sea coral, showing the infiltration of anthropogenic Pb to deep sea. Comparing the results to the surface North Atlantic Ocean Pb record using a Transit Time Distribution model, the mean transit time of Pb is estimated to be -64 years. This is longer than the transit time estimate assuming simple advection from a source, showing the importance of advective-diffusive mixing in the transport of Pb to the ocean interior. The later part of the thesis investigates Pb in the Indian Ocean, where no useful Pb data have been previously reported. First, using annually-banded surface growing corals, I reconstruct variations of Pb and isotopes in the surface waters of the central and eastern Indian Oceans during the past half-century. Results of the study show the increase of Pb concentrations from the mid-1970s, and major sources of the Pb are discussed, including leaded gasoline and coal burning, based on their emission histories and Pb isotope signatures. Second, Pb concentration and isotope profiles are presented from the northern and western Indian Oceans. AcknowledgementI would like to thank all the people who made this work possible. First, I owe a big thank to my advisor Ed Boyle. He taught me a lot about trace metal techniques, guided me to find right and important scientific questions whenever I was lost, and supported all my work. Not only that, he was also supportive of me having a family, very understanding and patient, which I cannot be grateful enough.I'd like to thank my committee: Bill Jenkins, Carl Lamborg, Phoebe Lam, and Konrad Hughen. Interests they showed during committee meetings were so inspiring and encouraging. I usually had this magical experience that my work, which looked so boring beforehand, turns into the most interesting one in the world after the committee meeting.I also would like to thank Jess Adkins and Selene Eltgroth, who provided the deep-sea coral and the radiocarbon data used in Chapter 3, and shared their expertise in deep-sea coral analysis with me. My work in Chapter 4 and 5 could not be completed without these people who helped me to collect corals and seawater samples from the Indian Ocean: Miriam Pfeiffer, Aron Meltzner, Kerry Sieh, Bambang Suwargadi, Danny Natawidjaja, Toshitaka Gamo, Hajim...

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“…For this purpose, G is defined in a convenient way as an Inverse Gaussian Distribution (IG) in terms of the mean age G and the width D, used in many different fields [e.g., Chikara and Folks, 1989;Seshadri, 1999]: [34] For the parameterization of the TTD, we apply G 2 /D = 0.7 as suggested by Hall and Plumb [1994] and confirmed by Engel et al [2002]. To prove that the initial mean age field is close to reality, a comparison is made with mean age profiles, derived from balloon-born measurements of CO 2 and SF 6 performed at mid-and high latitudes [Engel et al, 2002[Engel et al, , 2006b].…”

Section: Construction Of Initial Tracer Fieldsmentioning

confidence: 99%

Model evaluation of CO₂ and SF₆ in the extratropical UT/LS region

et al. 2008

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[1] We evaluate the transport of three-dimensional chemical transport models in the upper troposphere and lower stratosphere applying observed distributions of CO 2 and SF 6 . The data consist of high-resolution in situ observations, obtained during all seasons at subtropical, middle and high latitudes over Western Europe within the SPURT (Spurenstofftransport in der Tropopausenregion) project (2001)(2002)(2003). We show that the combination of the two passive tracers SF 6 and CO 2 with their different tropospheric characteristics and the propagation of the temporal trends of these two gases into the lower stratosphere is a powerful diagnostic for evaluation of model transport. The model evaluation shows that all models are able to capture the general features in the tracer distributions including the vertical and horizontal propagation of the CO 2 seasonal cycle. However, the modeled CO 2 cycles are a few months out of phase in the lowermost stratosphere due to tropospheric mixing. Two models show a too strong Brewer-Dobson circulation causing an overestimation of the tracers in the lowermost stratosphere during winter and spring. One model displays a too strong tropical isolation leading to an underestimation of the tracers in the lowermost stratosphere during winter. All models suffer to some extend from diffusion and/or too strong mixing across the tropopause. In addition, the models show too weak vertical upward transport into the upper troposphere during the boreal summer. Sensitivity studies show that our initial conditions and boundary constraints are realistic and that a horizontal resolution higher than 2 degrees and an increase of the meteorology update frequency (from 6 to 3-hourly) have negligible impact on the modeled CO 2 and SF 6 distributions.

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The Inverse Gaussian Distribution

Cited by 168 publications

References 0 publications

Statistical Models of Spike Trains

Statistical Models of Spike Trains

Evolution of anthropogenic Pb and Pb isotopes in the deep North Atlantic Ocean and the Indian Ocean

Model evaluation of CO₂ and SF₆ in the extratropical UT/LS region

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The Inverse Gaussian Distribution

Cited by 168 publications

References 0 publications

Statistical Models of Spike Trains

Statistical Models of Spike Trains

Evolution of anthropogenic Pb and Pb isotopes in the deep North Atlantic Ocean and the Indian Ocean

Model evaluation of CO2 and SF6 in the extratropical UT/LS region

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Model evaluation of CO₂ and SF₆ in the extratropical UT/LS region