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21 Paper 4, Section I 9H Markov ChainsLet X0, ...
www.statslab.cam.ac.uk/~rrw1/markov/MarkovChainTriposQuestions.pdf17 Sep 2015: Assume p > q. Let Tj = inf{n > 1 : Xn = j} if this is finite, and Tj = otherwise. ... Let Ti = inf{n > 1 : Xn = i}. For each i 6= j letqij = P(Tj < Ti | X0 = i) and mij = E(Tj | X0 = i). -
Intersection and mixing times for reversible chains Yuval Peres∗ ...
www.statslab.cam.ac.uk/~ps422/intersection-mixing.pdf7 Jan 2015: i=0. tj=0 1(Xi = Yj). count the number of intersections up to time t. ... Qt =ti=0. tj=0. pij(x,x). Using the spectral theorem together with transitivity, we obtain. -
Sensitivity of mixing times in Eulerian digraphs Lucas Boczkowski ...
www.statslab.cam.ac.uk/~ps422/rw-directed-graphs.pdf23 Mar 2016: Sensitivity of mixing times in Eulerian digraphs. Lucas Boczkowski Yuval Peres† Perla Sousi‡. Abstract. Let X be a lazy random walk on a graph G. If G is undirected, then the mixing time isupper bounded by the maximum hitting time of the graph. -
Adaptive estimation of a distribution function and its density in…
www.statslab.cam.ac.uk/~nickl/Site/__files/BEJ239.pdf19 Nov 2010: Let T := Tj = {ti (j )} = 2j Z, j Z, be a bi-infinite sequence of equally spaced knots,ti := ti (j ). A function S is a spline of order r , or ... Nj,k,r (x) := Nk,r (2j x) = N0,r (2j x k).By the Curry–Schoenberg theorem, any S Sr (Tj ) can be uniquely -
Advanced Probability Perla Sousi∗ November 6, 2023 Contents 1 ...
www.statslab.cam.ac.uk/~ps422/mynotes.pdf6 Nov 2023: Advanced Probability. Perla Sousi. November 6, 2023. Contents. 1 Conditional expectation 3. 1.1 Discrete case. 4. 1.2 Existence and uniqueness. 5. 1.3 Product measure and Fubini’s theorem. 11. 1.4 Examples of conditional expectation. 11. 1.4.1 -
Journal of Machine Learning Research ? (????) ?-?? Submitted ...
www.statslab.cam.ac.uk/~rds37/papers/shah16.pdf9 Jun 2016: Journal of Machine Learning Research? (?)? -? Submitted 11/13; Revised 3/16; Published? /? Modelling Interactions in High-dimensional Data withBacktracking. Rajen D. Shah r.shah@statslab.cam.ac.ukStatistical Laboratory. University of Cambridge. -
10-grg.dvi
www.statslab.cam.ac.uk/~grg/books/hammfest/10-grg.pdf15 Aug 2012: n,(c) if ti = tj , then (ti, zi) / (tj , zj ) in {ti} Zd, for 0 i < j n. -
Probability J.R. Norris January 22, 2024 1 Contents 1 ...
www.statslab.cam.ac.uk/~james/Lectures/p.pdf22 Jan 2024: f(t) =k. j=0. f(j)(0). j!tj. t0. f(k1)(s). k!(t s)kds. For j = 0,1,. -
A survey of Markov decision models for control of networks of queues
www.statslab.cam.ac.uk/~rrw1/publications/Stidham%20-%20Weber%201993%20A%20survey%20of%20Markov%20decision%20models%20for%20control%20of%20networks%20of%20queues.pdf15 Sep 2011: N o t e that A is symmetric in i and j , since the operators Ti and Tj commute. -
Tutorial Bandit Processes and Index Policies Richard Weber,…
www.statslab.cam.ac.uk/~rrw1/talks/YETQweber2013.pdf14 Nov 2013: Tutorial. Bandit Processes and Index Policies. Richard Weber, University of Cambridge. Young European Queueing Theorists (YEQT VII) workshop on. Scheduling and priorities in queueing systems,. Eindhoven, November 4–5–6, 2013. 1 / 52. 2 / 52. 3 / -
pcm_proof
www.statslab.cam.ac.uk/~frank/PAPERS/PRINCETON/pcm0052.pdf1 May 2006: Tj (yj ) = yj D′j (yj ). Then µj is the generalized cost of using link j, definedas the sum of the toll and the delay, and λs is theminimum generalized cost -
CHOICE OF NEIGHBOUR ORDER FOR NEAREST-NEIGHBOUR CLASSIFICATION RULE…
www.statslab.cam.ac.uk/~rjs57/HPSLV.pdf28 Aug 2007: 2/d , then, with v defined by. (4.8), and tj = νj1 {ν/k2(ν)}. -
crit6.dvi
www.statslab.cam.ac.uk/~grg/papers/UScrit6.pdf15 Aug 2012: t0,x0,. ,xr1, tr) for some r 0 with xi Z2{O}, ti T, and tj 6= R for. ... iii) r = s 1, xi = yi for i r 1, tj = uj for j r, ys O and us = R. -
Advanced Probability Perla Sousi∗ December 17, 2011 Contents 1 ...
www.statslab.cam.ac.uk/~ps422/notes-2011.pdf10 Oct 2013: Advanced Probability. Perla Sousi. December 17, 2011. Contents. 1 Conditional expectation 3. 1.1 Discrete case. 4. 1.2 Existence and uniqueness. 5. 1.3 Product measure and Fubini’s theorem. 11. 1.4 Examples of conditional expectation. 11. 1.4.1 -
Statistical modellingRajen D. Shah r.shah@statslab.cam.ac.uk Course…
www.statslab.cam.ac.uk/~rds37/teaching/statistical_modelling/notes.pdf14 Feb 2019: and (Xj )TXj = X. Tj (I Pj)Xj = ‖(I Pj)Xj‖2. -
Asymptotics and optimal bandwidth selection for highest density…
www.statslab.cam.ac.uk/~rjs57/Samworth10.pdf21 Apr 2010: tn, tj tn], where D4 = 12 μ2(K)f ′′(xj ) D1;. • ... tn = o(n1/6).Then. P(f̂h(x. tj ) < f̂h,τ. ) ( tf ′(xj ) D4n1/2h5/2{R(K)fτ 2D3,j D2}1/2). -
Three theorems in discrete random geometry
www.statslab.cam.ac.uk/~grg/papers/PS_2011_185-rev.pdf27 Jan 2012: The outcome is a decomposition ofγ into an ordered set of bridges with vertical displacements written T0 > T1 > > Tj. ... Therefore,. Z(x) 2. Ti<<T1T0>>Tj. j. k=i. ζxTk = 2. T =1. -
Mathematics of Operational Research Contents Table of Contents i ...
www.statslab.cam.ac.uk/~rrw1/mor/morweber.pdf15 Mar 2016: Mathematics of Operational Research. Contents. Table of Contents i. Schedules v. 1 Lagrangian Methods 11.1 Lagrangian methods. 11.2 The Lagrange dual. 31.3 Supporting hyperplanes. 3. 2 Convex and Linear Optimization 62.1 Convexity and strong duality. -
41 Paper 1, Section I 7H StatisticsSuppose that X1, ...
www.statslab.cam.ac.uk/~rrw1/stats/StatisticsTriposQuestions.pdf17 Sep 2015: for j 6= i. Prove that the random vectors Yj AjX are independent, and thatY (Y T1 ,. , Y TJ )T has a multivariate normal distribution.[ Hint: Random vectors are independent if -
Cluster detection in networks using percolation
www.statslab.cam.ac.uk/~grg/papers/BEJ412.pdf14 Mar 2013: Patil and Taillie [42]argued that this can be done faster by using the tree structure of Qm, where the root is the entirenetwork Vm and a cluster K Km(tj ) ... is the parent of any cluster L Km(tj 1) such that L K ,where t1 < < tM denote the distinct
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