Lecture 3 The linear symplectic category.
Outline The language of category theory, Sets and relations. Categorical “points”. Reductions, coreductions, etc. The linear sym Lecture 3 The linear symplectic category. Shlomo Sternberg September 8, 2011 Shlomo Sternberg Lecture 3 The linear symplectic category. Outline The language of category theory, Sets and relations. Categorical “points”. Reductions, coreductions, etc. The linear sym The p
http://isites.harvard.edu/fs/docs/icb.topic1481633.files/studentized%20bootstrap%20example.R
# Example of Studentized Bootstrap M = 100 R = 1000 # Data y = rexp( 30, 5 ) # our parameter 5 # our point estimate t = 1/mean(y) t # estimating V reps = replicate( M, { smp = sample( y, replace=TRUE ) 1/mean(smp) } ) v = sd( reps ) v # now we need quantiles of distribution of Z=(T-\theta)/V(F-hat)^1/2 zs = replicate( R, { ystar = sample( y, replace=TRUE ) tstar = 1/mean(ystar) # estimating V-star
Textbooks for Quantum Field Theory Required text: Quantum Field Theory in a Nutshell by A. Zee — I think that students should own and read this text because it is well-written and thought-provoking. Tony Zee tries to go beyond the formulas and explain
Textbooks for Quantum Field Theory Required text: Quantum Field Theory in a Nutshell by A. Zee — I think that students should own and read this text because it is well-written and thought-provoking. Tony Zee tries to go beyond the formulas and explain what is really going on. It is not quite suitable as a stand-along text, and I will supplement it with notes when necessary. Can you get along with
Physics 287a Solution Set 2 1. (Polchinski 1.5) Extend the sum ∞ n=1 n → −1/12 to the ’twisted’ case ∞ n=1 (n − θ) (1) with θ a constant. That is, kσ = (n−θ)π/l. (We have chosen l to be π in class.) You should find that the cutoff
Physics 287a Solution Set 2 1. (Polchinski 1.5) Extend the sum ∞ n=1 n → −1/12 to the ’twisted’ case ∞ n=1 (n − θ) (1) with θ a constant. That is, kσ = (n−θ)π/l. (We have chosen l to be π in class.) You should find that the cutoff-dependent term is independent of θ. Solution: We can regularize this sum by introducing a factor e− (n−θ) : ∞ n=1 (n − θ)e− (n−θ) = − e θ (−θ − e + θe ) (e − 1)2 (2) = 1
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Stat 111 Lecture 16: Score and Wald Tests 1 Lecture Outline • Score Tests • Wald Tests • Comparison of the 3 Likelihood Tests 2 The Score Function • Let L(θ) be the likelihood, and l(θ) = log[L(θ)] be the log-likelihood. • In order to calculate the MLEs, what do we need to calculate? • The score function, U(θ), is the derivative of the log- likelihood w.r.t. θ: • We’ve been using the score functi
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212a0810 Daniell's integration theory.
The Daniell Integral Monotone class theorems. Measure. H¨older, Minkowski , Lp and Lq . The Radon-Nikodym Theorem. 212a0810 Daniell’s integration theory. Shlomo Sternberg October 30, 2008 Shlomo Sternberg 212a0810Daniell’s integration theory. The Daniell Integral Monotone class theorems. Measure. H¨older, Minkowski , Lp and Lq . The Radon-Nikodym Theorem. Daniell’s idea was to take the axiomatic
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http://isites.harvard.edu/fs/docs/icb.topic138287.files/Lesson20_-_Finding_Eigenvectors_slides.pdf
http://isites.harvard.edu/icb/icb.do?keyword=k20350&pageid=icb.page101192