Here's another useful way to state the Bayes' rule for conditional probability (it just expands on what the OP wrote):
Note that here (1) is just the definition, (2) is a simple application of Bayes rule that we already know, and (3), (4) are various ways to rewrite (1) using factorization rules of the type P(ABC) = P(A|BC)P(B|C)P(C). Mentally, I find the following procedure useful:
This makes sense intuitively, if you think of conditioning as procedure of renormalizing the sample space in various ways. It's reasonable that you should be able to use Bayes' rule in the same way whether or not the probability space has been renormalized by conditioning.
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Choosing a statistical test
http://imgur.com/Ctug4Dr
Aikake Information Criterion
Maximum Likelihood
$AIC = -2*logL(\theta|y) + 2k$
$k = $ total number of parameters
Least Squares
$AIC = n*log(\frac{RSS}{n}) + 2k$
$RSS = SSE = \sum(y - h(x))^2$
$ n = $ number of samples
http://www4.ncsu.edu/~shu3/Presentation/AIC.pdf
http://en.wikipedia.org/wiki/Residual_sum_of_squares
Matrix Form Pointwise Distances
$d_ij = ||x_i - y_j||^2 = ||x_i||^2 + ||y_j||^2 - 2<X_i,y_j>$
means that
$D = X + Y - 2X'Y$
Take the norm of X and Y i.e. X*X' or dot(X,X')
Normalize and calculate covariance
A * A.T (Hermitian!) / sqrt(diag(A.T * A) * diag(A.T * A).T)
http://statinfer.wordpress.com/2011/11/14/efficient-matlab-i-pairwise-distances/
Rolling stats
http://stackoverflow.com/questions/1058813/on-line-iterator-algorithms-for-estimating-statistical-median-mode-skewnes
Current Links for Stats in Python
http://r.789695.n4.nabble.com/Ornstein-Uhlenbeck-td2991060.html
http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/
http://blog.yhathq.com/posts/estimating-user-lifetimes-with-pymc.html
http://robjhyndman.com/hyndsight/crossvalidation/
https://www.leinenbock.com/tag/statsmodels/
http://nbviewer.ipython.org/urls/raw.github.com/carljv/Will_it_Python/master/MLFH/ch8/ch8.ipynb
http://nbviewer.ipython.org/urls/github.com/weecology/progbio/raw/master/ipynbs/statistics.ipynb
http://wiki.answers.com/Q/What_does_a_high_t_statistic_mean
http://stackoverflow.com/questions/13452353/multiple-correlation-in-python
http://stats.stackexchange.com/questions/4422/small-sample-linear-regression-where-to-start
http://nbviewer.ipython.org/urls/raw.github.com/carljv/Will_it_Python/master/MLFH/ch8/ch8.ipynb
http://nbviewer.ipython.org/urls/github.com/weecology/progbio/raw/master/ipynbs/statistics.ipynb
http://wiki.answers.com/Q/What_does_a_high_t_statistic_mean
http://stackoverflow.com/questions/13452353/multiple-correlation-in-python
http://stats.stackexchange.com/questions/4422/small-sample-linear-regression-where-to-start
