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University of Minnesota School of Statistics February 2012

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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University of Minnesota School of Statistics February 2012

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

  2. “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

  3. 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)

  4. 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.”

  5. 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

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