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Applied Probability 1, Lent Term 2020 grg@statslab.cam.ac.uk Example…
www.statslab.cam.ac.uk/~grg/teaching/app-prob2020-1.pdf20 Jan 2020: random variables, independent of N. Show that if g(s,x) is a function and Tj are the. ... E. expθ. Ntj=1. g(Tj,Xj). = exp {λ t. 0. [E(eθg(s,X)) 1. -
RANDOM PLANAR GEOMETRY, LENT 2020, EXAMPLE SHEET 1 Please ...
www.statslab.cam.ac.uk/~jpm205/teaching/lent2020/example_sheet1.pdf4 Feb 2020: RANDOM PLANAR GEOMETRY, LENT 2020, EXAMPLE SHEET 1. Please send corrections to jpmiller@statslab.cam.ac.uk. Problem 1. (i) Show that the cardinality of the set Tk of plane trees with k edges is the kth Catalan number. Ck =1. k 1. (2kk. ). [Hint: -
CORRECTIONS for ‘Mathematical foundations of infinite-dimensional…
www.statslab.cam.ac.uk/~nickl/Site/__files/CORRECTIONS.pdf19 Dec 2020: p.53, line after (2.55), replace second ‘|λi|’ by ‘|µi|’.p.57, line -8 to -2: it should read i) ‘d(ti, tj) ε’ (missing comma), then ii) ‘= ε2/2 ... d2X(ti, tj)’. -
Random Planar Geometry
www.statslab.cam.ac.uk/~jpm205/teaching/lent2020/rpg_notes.pdf11 Mar 2020: RANDOM PLANAR GEOMETRY. JASON MILLER. Contents. Preface 1. 1. Introduction 1. 2. Plane trees 4. 3. The Brownian excursion 6. 4. Real trees and the Gromov-Hausdorff distance 7. 5. Convergence of discrete trees to the continuum random tree 10. 6. -
Mathematical Foundations of Infinite-Dimensional Statistical Models
www.statslab.cam.ac.uk/~nickl/Site/__files/FULLPDF.pdf25 Feb 2020: Mathematical Foundations of Infinite-DimensionalStatistical Models. In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood and Bayesianposterior inference does
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