George R Brown School of Engineering STATISTICS Charles

George R. Brown School of Engineering STATISTICS Charles Geyer University of Minnesota School of Statistics February 2012

“David Lane” of Math Stat • Applications of MCMC – Complicated (hierarchical) Bayesian models; Spatial statistics; Markov (but non-Poisson) spatial point processes; Spatial lattice processes (Ising models, Potts models, Bayesian image reconstruction); Statistical genetics; monte Carlo maximum likelihood and Monte Carlo EM; Bayesian decision theory. • MCMC methodology – Regeneration in MCMC; simulated tempering, parallel tempering, umbrella sampling; MCMC so-called diagnostics; Samplers: slice, independence, random walk, MALA, hit and run, Gibbs; Kinda-sorta MCMC: Griddy gibbs, Langevin diffusion, others. • A Helpful Soul 2

Only Yesterday… • De. Moivre/Laplace/Gauss/Normal 1733 ff • 1930’s: d. f. , r. v. , SLLN, CLT, cumulant, LIL – Covariance, Cauchy & unif distribs, Martingale • 40’s: “p-value, ” , p. d. f. , asymp. eff. • 50’s: Bayesian, Bayes estimate (Wald); – Geom. distrib. , superefficiency, dec. theory, completeness, EV distrib, cusum, Gauss. Markov, K-S, K-L • 60’s: p. m. f. , Dirichlet (SSW), shrinkage (JRT) • 70’s: Boxplot, Bootstrap, penalized likelihood (Gd. M, RAT, JRT) 3

Off the Beaten Track • Le Cam: ℓ(θ)-quadratic θMLE~N( , I 1 ) – No IID, no LLN, no CLT, no N>k (I. e. , N=1) • Radically Elementary Probability (Nelson, ‘ 87) – There is no spoon, nor continuum – Infinitesimals exist and are rigorous a. s. • Teaching Paradigms – “The beauty of theory is hidden by the mess” – “We. . . start with Kolmo’s axioms and. . . just when the students are thoroughly confused, [we] drop the whole subject. . . ” – “Unlike Le. Cam, I am unbothered …. because of my 4 familiarity with computer intensive statistical methods. ”

Today • “Aster” Models • Dennis Cox – Pd. D. (1980) University of Washington – Rice Systems and Synthetic Biology Group – Kennedy Institute for Information Technology – Editor/Assoc Editor(s) • Journal of Probability and Statistics • Scandinavian Journal of Statistics • Statistical Computing. Encyclopedia of Environmentrics • Bayesian Analysis 5