University of Minnesota

School of Statistics

February 2012

George R. Brown School of Engineering STATISTICS

“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 Soul2

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)

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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.”

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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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