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From http://scikit-learn.org/stable/modules/linear_model.html#bayesian-ridge-regression, they gave the bayesian ridge distribution as this:

$p(w|\lambda) = \mathcal{N}(w|0,\lambda^{-1}{I_{p}})$

And there is a variable $I_p$ but it's unexplained what does the $I_p$ refer to?

Also, the variable $\mathcal{N}$ is unexplained but I'm not sure whether I've guessed correctly but is that the Gaussian prior as described in the Bayesian regression section above the Bayesian Ridge?

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$\mathcal{N}$ does indeed denote a (multivariate) normal / Gaussian distribution. $I_p$ is just an identity matrix of dimension $p$. So this a matrix with $\lambda^{-1}$ along the diagonal. Read this as the covariance matrix, so this is a spherical Gaussian (0 covariance between different dimensions) where each variable has variance $\lambda^{-1}$.

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N is function and represents the Normal, or Gaussian, distribution.

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  • $\begingroup$ What does Ip refer to? $\endgroup$
    – alvas
    Commented Jul 28, 2015 at 9:44
  • $\begingroup$ I believe it's the priors, but not exactly sure what the formulation using Ip refers to. $\endgroup$
    – image_doctor
    Commented Jul 28, 2015 at 9:45

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