Other Statistics and Probability Commons^™

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Reference Priors For Exponential Families With Increasing Dimension, Bertrand Clarke, Subhashis Ghosal

Department of Statistics: Faculty Publications

In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual information valid when p = pm increases at a sufficiently slow rate. The second term in the asymptotic expansion is the largest term that depends on the prior and can be optimized to give Jeffrey's prior as the reference prior in …

Reference Priors For Exponential Families With Increasing Dimension, Bertrand S. Clarke, Subhashis Ghosal

Department of Statistics: Faculty Publications

In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual information valid when p = pn increases at a sufficiently slow rate. The second term in the asymptotic expansion is the largest term that depends on the prior and can be optimized to give Jeffreys’ prior as the reference prior in …