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I am looking for an introductory book that helps building some skills in working with multivariate distributions.

For example, I want to be able to work with multivariate normal easily, something between an introductory stats course that talks about distributions and a serious robotics course that talks about Kalman filtering.

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    $\begingroup$ Is the question aimed at multivariate distributions or multivariate statistics? I.e. do you need more on probability or on data analysis? $\endgroup$ – Momo Apr 12 '12 at 18:50
  • $\begingroup$ What sort of things are you looking to learn? "Work with MVN" is pretty vague, and the space you describe is capacious. $\endgroup$ – Dimitriy V. Masterov Apr 12 '12 at 19:01
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    $\begingroup$ Mark, if you are looking for continued help on CV, consider accepting some of the answers that people have provided you in the past by clicking the check mark next to one for any given question. People will be more likely to help if you aren't perceived as ungrateful. $\endgroup$ – gung Apr 12 '12 at 19:29
  • $\begingroup$ Shouldn't this be Community Wiki? $\endgroup$ – Carlos Accioly Apr 13 '12 at 3:47
  • $\begingroup$ Johnson and Wichern is also a good reference. $\endgroup$ – user10525 Apr 13 '12 at 10:42
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I compiled a list of multivariate books when I was preparing multivariate statistics classes (an elective for Ph.D. students, and an intro for senior undergrads).

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  • $\begingroup$ Do you have one with lots of examples that you like? In the style of Gelman and Hill, but with a bit more rigor. $\endgroup$ – Dimitriy V. Masterov Apr 12 '12 at 21:16
  • $\begingroup$ The best examples are in Rencher, although it is a somewhat lower level, more applied book. For you personally, Izenman will likely be the best fit. $\endgroup$ – StasK Apr 13 '12 at 13:19
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I recommend Pattern Classification by Duda, Hart, and Stork. It's good because it is front-loaded with a lot of classical results on multivariate Gaussians, and discusses things like Fisher linear discriminant analysis, maximum likelihood, etc. The other sections of the book allow you to develop an understanding of how this connects with machine learning, which is important.

A lot of statistical texts do not make clear the overlap between classical statistics (e.g. likelihood models, logistic fitting, regression) and more modern machine learning (support vector machines, decision trees). While Duda et. al. is not a great encyclopedic source for all things statistics, I think it's a good first book. It's readable and bridges gaps, which is usually the early priority before needing to chase down lots of specifics to become an expert.

Another book that might be helpful in a similar way is: Data Analysis Using Regression and Multilevel/Hierarchical Models by Gelman and Hill.

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If your concern is 'working with the multivariate normal', I'd suggest Casella's Statistical Inference as a start.

Two classic applied first-year PhD econometrics texts are Greene's Econometric Analysis as well as Woolridge's Econometric Analysis of Cross Section and Panel Data. These provide an overview of the theory; Woolridge's undergraduate text also includes many worked through examples with code available online. I used Lattin in my first regression class after introductory statistics; it is filled with examples, though the code and output uses SAS.

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I can warmly recommend Michael Greeenacre's books. Biplots in Practice provides a very easy to understand overview of all kinds of biplots (concentrating on multivariate). This book is available as a collection of pdfs for free. Correspondence analysis in Practice gives a good introduction to methods such as PCA, CA and CCA. Both books contain practical explanations and codes for doing it in R.

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For the Bayesian side of things there is a really outstanding book called Bayesian Core (amazon page) with an emphasis on practice.

It begins with an introduction of grad level basics like normal distributions and quickly moves to more advanced topics like linear model, regression, mixture models etc with a lot of programming listings in R or Matlab that help grab the essential feeling of the course.

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For econometrics I used "A Guide to Modern Econometrics" by Marno Verbeek which is fairly technical but without examples.

For more applied work I sometimes use "Multivariate Data Analysis" by Hair et al. which is very practical with thorough practical examples and outputs (it lacks code for a statistical package though) including multivariate regressions, logit models, factor/cluster analysis etcetera. This one may be a little too applied for you I think and I think it's certainly an undergraduate book.

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As of 2/21/2013 there is some discussion of this topic on Andrew Gelman's blog.

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If you have a market research background and use SPSS/SAS, you can try market research by Naresh Malhotra. It has example of code too.

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