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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
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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
Only Yesterday… • DeMoivre/Laplace/Gauss/Normal 1733ff • 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 (GdM, RAT, JRT)
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 the 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 LeCam, I am unbothered …. because of my familiarity with computer intensive statistical methods.”
Today • “Aster” Models • Dennis Cox • Pd.D.(1980) University of Washington • Rice Systems and Synthetic Biology Group • Ken 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