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Mendelian randomization: From genetic association to epidemiological…
www.statslab.cam.ac.uk/~qz280/publication/mr-partially-bayes/slides.pdf29 Apr 2024: Robust adjusted profile score (RAPS). I Define standardized residual: tj (β,τ2) =. Γ̂j βγ̂j(σ2Yj τ. 2) β2σ2Xj. I For some robust loss function ρ, the RAPS are. ... ψ(ρ)1 (β,τ. 2) =. pj=1. ρ′(tj ). βtj,. ψ(ρ)2 (β,τ. 2) =. pj=1. -
Confounder Adjustment in Multiple Hypothesis Testing
www.statslab.cam.ac.uk/~qz280/publication/cate/slides.pdf29 Apr 2024: p. tj =. nβ̂j. σ̂j. 1 ‖α̂‖2, Pj = 2(1 Φ(|tj|)). -
Confounder adjustment in large-scale linear structural models
www.statslab.cam.ac.uk/~qz280/publication/cate-mutual-fund/slides.pdf29 Apr 2024: Confounder adjustment in large-scale linearstructural models. Qingyuan Zhao. Department of Statistics, The Wharton School, University of Pennsylvania. June 19 2018, EcoStat. Based on. I Wang, J., Zhao, Q., Hastie, T., & Owen, A. B. Confounder -
Total variation cutoff in a tree Yuval Peres∗ Perla ...
www.statslab.cam.ac.uk/~ps422/tree-cutoff.pdf10 Jul 2013: We abusenotation and denote by nj the root of Tj and by 0 the root of T0. ... Using Claim 4.2 for the function (h(x) h(nj)) restricted to x Tj we obtainvTj. -
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. -
Applied Probability Nathanaël Berestycki and Perla Sousi∗ March 6,…
www.statslab.cam.ac.uk/~ps422/notes-new.pdf17 Mar 2017: and the holding times are. T1 = Si1 (s Ji) and Tj = Sij, j 2,. ... Moreover, the times Tj for j 2 are independentand independent of Sk for k i, and hence independent of (Xr)rs. -
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 -
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 -
Minkowski dimension of Brownian motion with drift Philippe H. ...
www.statslab.cam.ac.uk/~ps422/minkowski.pdf3 Aug 2012: the ball B(f(tj),ε) is contained in B(f(ti), (2k1 1)ε). ... S(k) = {j : |ti tj| < 2ε and |f(ti) f(tj)| [2kε, 2k1ε)},. -
The Isolation Time of Poisson Brownian Motions Yuval Peres∗ ...
www.statslab.cam.ac.uk/~ps422/isolation.pdf14 Mar 2012: 9. Define inductively. Tj1 = inf{m Tj 1 : i = 2,. ... E. κj=1. 1(x1 ξ1(Tj) U1Tj ). . By the independence of the motions of the nodes 1,.
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