Advanced statistical computing Notes

Pre

C: speed
perl: data manipulation
R: analyses and graphics

C

C

Perl

#!/usr/bin/perl -w

w for warning

chmod +x program.pl
#!/usr/bin/perl -w
print("Hello, world!\n");

more complicated example

convert

open(IN, $mfile) or die

R

Ch 1 : Intro

Ch 2 : R

Ch 3 : random number generation

#include <R.h>
GetRNGstate();
PutRNGstate();
double unif_rand();
double norm_rand();
double exp_rand();
double r****();

/usr/local/lib/R/include/R.h
/usr/local/lib/R/include/R_ext/Mathlib.h
RHOME/src/main/RNG.c
RHOME/src/nmath/snorm.c
RHOME/src/nmath/sexp.c

Ch 4: permutation test, and bootstrap

Permutation test

Parametric Bootstrap

Nonparametric Bootstrap

Bootstarp in regression

Ch5 : Numerical Linear Algebra

Ch 6: EM

• Standard errors
• Maximizing
• Slow convergence

Ch 7: Newton-Raphson, Fisher Scoring

Ch 8: Numerical Integration

• don’t use h*f(x) in reality
• Error O(1/N^2)

Gaussian Quadrature

Ch 9 : MCMC

• burn in : drop the first M steps, Gelman, drop the first half
• keep only every kth sample: gelman, keep every sample
• want steps to be big
• don’t want to reject too often
• data augmentation (EM) can be helpful
• reject 44% when p=1, 23% when p>5

Ch 10: Remarks

• against using Fortran
• use C and perl