Search Results: 'Bayesian statistics'
Probabilistic Interpretation of Data
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This book is a physicists approach to interpretation of data using Markov Chain Monte Carlo (MCMC). The concepts are derived from first principles using a style of mathematics that quickly... More > elucidates the basic ideas, sometimes with the aid of examples. Probabilistic data interpretation is a straightforward problem involving conditional probability. A prior probability distribution is essential, and examples are given. In this small book (200 pages) the reader is led from the most basic concepts of mathematical probability all the way to parallel processing algorithms for Markov Chain Monte Carlo. Fortran source code (for eigenvalue analysis of finite discrete Markov Chains, for MCMC, and for nonlinear least squares) is included with the supplementary material for this book (available online).< Less
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Axioms is "the last book on metaphysical philosophy you'll ever need to read". It uses the latest methods of bayesian analysis to prove that philosophy is bullshit. Instead of being the... More > end of all reason, this proves to be the proper beginning. It establishes once and for all that the most important free choice any human makes is their choice of what to believe, their axioms. Axioms are, in fact, the basis of all understanding, all knowing, but themselves cannot be known, only believed. The book connects these conclusions of western mathematical philosophy with the heart eastern philosophy in the form of Zen Buddhism, with axiomatic set theory, with Hume's skepticism, and more. It is written to be fun to read and accessible, even as it presents its core arguments fairly rigorously.< Less
Traceable S-Parameter Measurements in Coaxial Transmission Lines up to 70GHz
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This thesis describes the computational process from dimensions and material parameters of coaxial standards to traceable S-parameters. Standards contain coaxial connectors and sections of... More > transmission line. Several models of the slotted coaxial connector and of rough coaxial transmission lines are discussed. The S-parameters of the standards are used to calibrate a vector network analyzer. For this purpose an overdetermined Bayesian calibration algorithm, which is described in this thesis, can be used. The calibration algorithm assumes imperfections in the definitions of the standards and in the calibration model of the vector network analyzer. Highly accurate and robust calibration is the result of the underlying statistical model. Finally, a technique to measure S-parameters in nonstandard coaxial connectors is described. It relies on the characterization of beadless adapters.< Less
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