Stat E

18 The Exponential Family and Statistical Applications

e ¡2 3 • (x1¡„)2 2 + (x2¡„)2 2 2(x1 „)(2) ‚ I x 1;x22R = 1 2 p 3… e • 2 3 „(x1+x2)¡2 3 „ 2 ‚ e¡ x2 1+x 2 2¡4 x1 2 3 I x 1;x22R: This is in the form of a one parameter Exponential family with the natural su–cient statistic T(X)=T(X1;X2)=X1 +X2. Example 18.5. (Gamma Distribution). Suppose X has the Gamma density e¡ x ...

Abstract arXiv:1607.06450v1 [stat.ML] 21 Jul 2016

Geoffrey E. Hinton University of Toronto and Google Inc. hinton@cs.toronto.edu Abstract Training state-of-the-art, deep neural networks is computationally expensive. One way to reduce the training time is to normalize the activities of the neurons. A recently introduced technique called batch normalization uses the distribution of

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Logistic Regression - Pennsylvania State University

Logistic Regression I The Newton-Raphson step is βnew = βold +(XTWX)−1XT(y −p) = (XTWX)−1XTW(Xβold +W−1(y −p)) = (XTWX)−1XTWz , where z , Xβold +W−1(y −p). I If z is viewed as a response and X is the input matrix, βnew is the solution to a weighted least square problem: βnew ←argmin β (z−Xβ)TW(z−Xβ) . I Recall that linear regression by least square is …

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Importance Sampling - U-M LSA

E(X) where you can’t even generate from the distribution of X, importance sampling is necessary. The final, and most crucial, situation where importance sampling is useful is when you want to generate from a density you only know up to a multiplicative constant.

Factor Analysis - University of Minnesota

˙jj is the variance of Xj (i.e., the j-th diagonal of ) h2 j = (LL 0) jj = ‘2 j1 + ‘ 2 j2 + + ‘ 2 jm is the communality of Xj j is the specific variance (or uniqueness) of Xj Note that the communality h2 j is the sum of squared loadings for Xj. Nathaniel E. Helwig (U of Minnesota) Factor Analysis Updated 16-Mar-2017 : Slide 11

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Linear Mixed-Effects Regression - University of Minnesota

Nathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects Regression Updated 04-Jan-2017 : Slide 17. One-Way Repeated Measures ANOVA Model Form and Assumptions Note on Compound Symmetry and Sphericity Assumption of compound symmetry is …

Fuji Duo SC-E Series Contactors - AutomationDirect

2. AC1 non-inductive or slightly inductive loads. Typically resistive loads (i.e. furnaces, ovens, etc.) SC-E2S SC-E7 Features • 5 to 100 hp at 480VAC • cULus and CSA approval, CE mark, meets JIS and IEC standards. • Models SC-E02-xxx to SC-E4-xxx have 3-pole main circuits and come in three sizes with widths of 43mm, 54mm, and 67mm.

Posterior Predictive Distribution - University of South ...

Posterior Predictive Distribution I Recall that for a fixed value of θ, our data X follow the distribution p(X|θ). I However, the true value of θ is uncertain, so we should average over the possible values of θ to get a better idea of the distribution of X. I Before taking the sample, the uncertainty in θ is represented by the prior distribution p(θ).

Post Hoc Power: Tables and Commentary - University of Iowa

There is substantial literature, much of it outside of the social sciences (e.g., Goodman and Berlin, 1994; Zumbo and Hubley, 1998; Levine and Ensom, 2001; Hoenig and Heisey, 2001), that takes an opposing view to PHP practices. Lenth (2001) points out that PHP is simply a function of the P value of the test, and thus adds no new information.

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Yeo-Johnson Power Transformations - University of …

E 9 E D c. Figure 1: Comparison of Box-Cox and Yeo-Johnson power transformations for % . The Box-Cox transformations (and simple power transformations) behave very differently for values of cloase to zero than do the Yeo-Johnsontransformations. 3.4 Default family A setting in the Settings menu for *transformation-default-family*can

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