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lecture_16 - BIOS 735: Statistical Computing Michael Wu...

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BIOS 735: Statistical Computing Michael Wu Lecture 16: Computer Arithmetic October 11, 2011 Michael Wu (Lecture 16) BIOS 735 October 11, 2011 1 / 13

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Onward to Computational Statistics Thus far, we have focused heavily on R programming: I R programming – getting R code to work I Some advanced programming – getting R to be fast I Enhancing Usability – making your R code helpful for others Next: classical computational statistics I Emphasis on ideas, though implementation is important I Code and algorithms are written for ease of understanding computational principles more than for good R programming practice. Michael Wu (Lecture 16) BIOS 735 October 11, 2011 2 / 13
What to Expect Next 1 Computer Arithmetic 2 Numerical Linear Algebra 3 Optimization and Nonlinear Equations 4 EM Algorithm 5 Laplace Approximations 6 Quadrature Methods 7 Basic Simulation Methods 8 Bootstrap and Permutation The notes will borrow heavily from Dr. Bob Gray’s notes for Harvard’s computing class. Michael Wu (Lecture 16) BIOS 735 October 11, 2011 3 / 13

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Computer Arithmetic Computers are limited in terms of binary storage: cannot store exact repreentations for most numbers or do exact computations Commonly: I Integer or Single Precision Float: 32 bits I Double Precision Float: 64 bits Accordingly, their are consequences to the individually slight imprecisions. Michael Wu (Lecture 16) BIOS 735 October 11, 2011 4 / 13
Computer Arithmetic: Integers Integers are stored as binary numbers by the computer based on 32 bits: 00000000000000000000000000011011 is the number 32. The individual bits are essentially the binary coefﬁcients x i ( x i ∈ { 0 , 1 } ) in the representation: u = 32 X i = 1 x i 2 i - 1 - 2 31 Maximum integer = 32 i = 1 2 i - 1 - 2 31 = 31 i = 1 2 i - 1 = 2 , 147 , 836 , 747 Minimum integer = 0 - 2 - 31 = - 2 , 147 , 483 , 648

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This note was uploaded on 11/18/2011 for the course BIOS 735 taught by Professor Staff during the Spring '10 term at UNC.

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lecture_16 - BIOS 735: Statistical Computing Michael Wu...

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