# Tag Info

15

Roman gave you the best advice possible. In addition, I'll take a shot at it. But remember : Learning statistics is like learning any other thing : There. Are. No. Shortcuts. 1) know what you are talking about. It's no use to ask questions about concepts you don't know. So indeed, reading a book and -even better- following some courses to get a thorough ...

15

I do not have a number of examples, only one (see below), but know some paper you should cite from Psychology/Cognitive Sciences. The most important one is definitely: Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390–412. ...

14

Neural networks have been around for a while, and they've changed dramatically over the years. If you only poke around on the web, you might end up with the impression that "neural network" means multi-layer feedforward network trained with back-propagation. Or, you might come across any of the dozens of rarely used, bizarrely named models and conclude that ...

14

There is no minimum sample size for the t test to be valid. Validity requires that the assumptions for the test statistic hold approximately. Those assumptions are in the one sample case that the data are iid normal (or approximately normal) with mean 0 under the null hypothesis and a variance that is unknown but estimated from the sample. In the two ...

13

Here's a place to start: ftp://selab.janelia.org/pub/publications/Eddy-ATG3/Eddy-ATG3-reprint.pdf http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/ http://yudkowsky.net/rational/bayes http://www.math.umass.edu/~lavine/whatisbayes.pdf http://en.wikipedia.org/wiki/Bayesian_inference http://en.wikipedia.org/wiki/Bayesian_probability ...

12

Stanford (Ng) and Caltech (Abu-Mostafa) have put machine learning classes on YouTube. You don't get to see the assignments, but the lectures don't rely on those. I recommend trying to watch those first, as those will help you to find out what math you need to learn. I believe a very similar class with assignments is taught by Andrew Ng on Coursera, which Ng ...

11

Try Morgan and Winship (2007) for a social science take or Hernan and Robins (forthcoming) for an epidemiological take. Although still in progress, this looks like it's going to be very good. Morgan and Winship is particularly good on what must be assumed for causal interpretations of regression-type models. Pearl (2000) is in no sense introductory, ...

10

With all deference to him, he doesn't know what he's talking about. The t-test was designed for working with small samples. There isn't really a minimum (maybe you could say a minimum of 3 for a one-sample t-test, IDK), but you do have a concern regarding adequate power with small samples. You may be interested in reading about the ideas behind compromise ...

10

You can prove Popoviciu's inequality as follows. Use the notation $m=\inf X$ and $M=\sup X$. Define a function $g$ by $$g(t)=\mathbb{E}\left[\left(X-t\right)^2\right] \, .$$ Computing the derivative $g'$, and solving $$g'(t) = -2\mathbb{E}[X] +2t=0 \, ,$$ we find that $g$ achieves its minimum at $t=\mathbb{E}[X]$ (note that $g''>0$). (Actually, ...

9

I found Programming Collective Intelligence the easiest book for beginners, since the author Toby Segaran is is focused on allowing the median software developer to get his/her hands dirty with data hacking as fast as possible. Typical chapter: The data problem is clearly described, followed by a rough explanation how the algorithm works and finally shows ...

9

Springer textbook solution manuals can be downloaded by instructors. The signup page for an instructor account is at http://www.springer.com/instructors?SGWID=0-115-12-333200-0 If you're looking for some Bayesian practice problems with solutions, consider the online course materials from Newcastle University at: ...

9

People use all sorts of functions to keep their data between 0 and 1. The log-odds fall out naturally from the math when you derive the model (it's called the "canonical link function"), but you're absolutely free to experiment with other alternatives. As Macro alluded to in his comment on your question, one common choice is a probit model, which uses the ...

8

A good thorough review of bootstrap theory and applications is Davison and Hinkley, 1997. It's more up to date than your reference, goes a bit more gently, and has a lot of example (some of them in R). If that still looks too much, Mooney and Duval, 1993 is a simpler shorter introduction, and very good place to start. Davison and Hinkley have a discussion ...

8

It is not clear if this will suit your needs for a definitive reference, but this question comes up in the exercises of Casella and Berger: (page 364, exercise 7.45 b): With reference to exercise 5b that provides another variant, in which $\Theta_2$ and $\Theta_4$ are the second and fourth moments ($\sigma^2$ and $\kappa$), respectively: These are ...

8

Source: Introduction to the Theory of Statistics, Mood, Graybill, Boes, 3rd Edition, 1974, p. 229. Derivation: Note that in the OP's Wikipedia link, $\kappa$ is not the kurtosis but the excess kurtosis, which is the "regular" kurtosis - 3. To get back to the "regular" kurtosis we have to add 3 in the appropriate place in the Wikipedia formula. We have, ...

8

Yes the Handbook of MCMC is a very up-to-date collection of papers on MCMC, Also the book by Robert and Casella is a more current account than Markov Chain Monte Carlo in Practice. But I think MCMC in Practice is really a good place to start learning the subject. Here are amazon links to descriptions of the books I mentioned above. Introducing Monte Carlo ...

8

No book is going to tell you which variable to include and which to exclude. You should have done necessary background research before doing your fieldwork to get an idea of which variables to measure. You could have based those variables on the species life history and/or previous research. Once variables were selected, it is good practice to do a lot of ...

8

Yes it is. Look for example at this page for the wonderful headless RServe R server instance (by R Core member Simon Urbanek) which lists these deployments: Some projects using Rserve: The Dataverse Network Project Phenyx "J" interface Nexus BPM Taverna Bio7 INTAMAP ...

7

Are you looking for the theory, or something practical? If you are looking for books, here are some that I found helpful: F.R. Hampel, E.M. Ronchetti, P.J.Rousseeuw, W.A. Stahel, Robust Statistics: The Approach Based on In fluence Functions, John Wiley & Sons, 1986. P.J. Huber, Robust Statistics, John Wiley & Sons, 1981. P.J. Rousseeuw, A.M. ...

7

I bought, but have not yet read, S. Marsland, Machine Learning: An Algorithmic Perspective, Chapman & Hall, 2009. However, the reviews are favorable and state that it is more suitable for beginners than other ML books that have more depth. Flipping through the pages, it looks to me to be good for me because I have little math background.

7

For a really short introduction (seven page pdf), there's also this, intended to allow you to follow papers that use a bit of measure theory : A Measure Theory Tutorial (Measure Theory for Dummies). Maya R. Gupta. Dept of Electrical Engineering, University of Washington, 2006. He gives some refs at the end and says "one of the friendliest books is ...

7

Estimation of the covariance matrix with given restrictions on the inverse covariance matrix is of course a well studied problem. Restricting some entries to be 0 is an example of a linear restriction in the cone of positive semidefinite matrices. If the distribution is multivariate normal, the inverse covariance matrix is the canonical parameter in the ...

7

Both panel data and mixed effect model data deal with double indexed random variables $y_{ij}$. First index is for group, the second is for individuals within the group. For the panel data the second index is usually time, and it is assumed that we observe individuals over time. When time is second index for mixed effect model the models are called ...

7

I believe that the first use of the concept of profile likelihoods is in Fisher's own work, as explained here. The relevant quote from that link to the book by D. A. Sprott is: Profile likelihoods have existed for a long time in the form of likelihood ratio tests. But these are not used as likelihood functions to produce likelihood inferences. The ...

7

I have very high expectations for Austin Nichols' forthcoming book Causal Inference: Measuring the Effect of x on y. The expected publication date is 2013. In the mean time, his handout and paper provide a nice overview of panel methods, instrumental variables, propensity score matching/reweighting, and regression discontinuity. The comparisons between all ...

7

Whatever software you used was evidently reporting coefficients to 3 d.p. So 0.000 just meant <0.0005. It makes perfect sense to use units of measurement that yield coefficients that aren't inconveniently large or small. No statistical principle is violated thereby. You don't need a reference or authority to back this up: it is fine to choose (e.g.) mm ...

6

After some research, I ended up buying this when I thought I needed to know something about measure-theoretic probability: Jeffrey Rosenthal. A First Look at Rigorous Probability Theory. World Scientific 2007. ISBN 9789812703712. I haven't read much of it, however, as my personal experience is in accord with Stephen Senn's quip.

6

Introduction to Machine Learning, by E. Alpaydin (MIT Press, 2010, 2nd ed.), covers a lot of topics with nice illustrations (much like Bishop's Pattern Recognition and Machine Learning). In addition, Andrew W. Moore has some nice tutorials on Statistical Data Mining.

6

This is a highly-cited paper on mixed models for ecology and evolution: Bolker et al. (2009) Generalized linear mixed models: a practical guide for ecology and evolution Trends in Ecology & Evolution Vol. 24 pp127-135 (PDF) (from ScienceDirect with links to Supplementary Content).

6

I highly recommend watching these lectures and use this as reading material. These lectures are on machine learning in general by Andrew Ng talks in length about neural networks and does try hard to make it accessible for beginners.

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