Fast Automatic Bayesian Cubature Using Matching Kernels and Designs

Automatic cubatures approximate integrals to user-specified error tolerances. For high dimensional problems, it is difficult to adaptively change the sampling pattern to focus on peaks because peaks can hide more easily in high dimensional space. But, one can automatically determine the sample size, $n$, given a reasonable, fixed sampling pattern. This approach is pursued in Jagadeeswaran and Hickernell, Stat.\ Comput., 29:1214-1229, 2019, where a Bayesian perspective is used to construct a credible interval for the integral, and the computation is terminated when the half-width of the interval is no greater than the required error tolerance. Our earlier work employs integration lattice sampling, and the computations are expedited by the fast Fourier transform because the covariance kernels for the Gaussian process prior on the integrand are chosen to be shift-invariant. In this chapter, we extend our fast automatic Bayesian cubature to digital net sampling via \emph{digitally} shift-invariant covariance kernels and fast Walsh transforms. Our algorithm is implemented in the MATLAB Guaranteed Automatic Integration Library (GAIL) and the QMCPy Python library.Comment: PhD thesi

Implementation of Digital Filters Using Fermat Number Transform On TMS320C30 Digital Signal Processor

Precise systems design, equipment standardization, and stability of performance characteristics are among the many advantages digital techniques can offer in signal processing. Earlier research in this field of study has contributed much to many of the modern day conveniences. Many of these contributions focus on improving computational efficiency of discrete Fourier transform (DFT) calculation. However, there are many shortcomings; therefore number theoretic transform (NTT) is proposed. This study implements three digital filters using one of the NTT, namely the Fermat number transform (FNT), and DFT. It compares the execution time, number of operation, and memory requirement for both implementations. Implementation of both types of filters employs the radix-2 fast Fourier transform (FFT) . This study proposes a modified diminished-one number system in implementing FNT. The number system was originally proposed by Leibowitz. I would like to take this opportunity to thank my major advisor, Dr. Lu, for the encouragement she has offered over the years. Her patience and constructive guidance has been very helpful. Also, I would like to thank Dr. Teague for his kindness in giving me access to his digital signal processing laboratory, where most of the work in this study was done. My appreciation also goes to my parents for their continuous supportComputer Scienc

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

FAST AUTOMATIC BAYESIAN CUBATURE USING MATCHING KERNELS AND DESIGNS

Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. In many real-world integration problems, the analytical solution is either unavailable or difficult to compute. To overcome this, one can use numerical algorithms that approximately estimate the value of the integral. For high dimensional integrals, quasi-Monte Carlo (QMC) methods are very popular. QMC methods are equal-weight quadrature rules where the quadrature points are chosen deterministically, unlike Monte Carlo (MC) methods where the points are chosen randomly. The families of integration lattice nodes and digital nets are the most popular quadrature points used. These methods consider the integrand to be a deterministic function. An alternate approach, called Bayesian cubature, postulates the integrand to be an instance of a Gaussian stochastic process

Computer Science Principles with Java

This textbook is intended to be used for a first course in computer science, such as the College Board’s Advanced Placement course known as AP Computer Science Principles (CSP). This book includes all the topics on the CSP exam, plus some additional topics. It takes a breadth-first approach, with an emphasis on the principles which form the foundation for hardware and software. No prior experience with programming should be required to use this book. This version of the book uses the Java programming language.https://rdw.rowan.edu/oer/1018/thumbnail.jp

Execution model and optimizing compilation for execution migration

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 137-141).Although systems with hardware support for fine-grained execution migration are becoming a reality, no concrete execution model or compiler exist for these machines. This limits the complexity of software that can be written for these machines, and therefore also the scope of studies for which these machines can be used. In this thesis, we define a productive programming model for an execution migration platform by exposing migration as a set of interfaces usable with the C programming language via a custom optimizing compiler. We employ hardware-software co-design to describe a stack core architecture with support for partial context migration in order to simplify the compiler problem and improve compiler efficiency. We also consider instruction encoding in abstract terms to establish a baseline comparison of encoded instruction density to an ideal upper bound. The stack-based execution migration platform offers a new and unexplored cost model, which leads us to reevaluate the trade-offs associated with compilation for these architectures, and to explore novel algorithms, or novel applications of existing optimizations. Throughout this work, we attempt to gain a deep understanding of the costs and benefits of execution migration by aggressive design space exploration. We use the insight gained to better inform the the problem of compiling to this unorthodox architecture, and design the compiler, a library of optimized parallel primitives, and a set of compiler optimization passes to best reflect and utilize the underlying hardware.by Ilia Andreevich Lebedev.S.M

Developments in Demographic Forecasting

This open access book presents new developments in the field of demographic forecasting, covering both mortality, fertility and migration. For each component emerging methods to forecast them are presented. Moreover, instruments for forecasting evaluation are provided. Bayesian models, nonparametric models, cohort approaches, elicitation of expert opinion, evaluation of probabilistic forecasts are some of the topics covered in the book. In addition, the book is accompanied by complementary material on the web allowing readers to practice with some of the ideas exposed in the book. Readers are encouraged to use this material to apply the new methods to their own data. The book is an important read for demographers, applied statisticians, as well as other social scientists interested or active in the field of population forecasting. Professional population forecasters in statistical agencies will find useful new ideas in various chapters