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From the Wikipedia article on Bayesian Linear Regression:

Model complexity is already taken into account by the model evidence, because it marginalizes out the parameters by integrating $p(\mathbf{y},\boldsymbol\beta,\sigma|\mathbf{X})$ over all possible values of $\boldsymbol\beta$ and $\sigma$.

$$p(\mathbf{y}|m)=\int p(\mathbf{y}|\mathbf{X},\boldsymbol\beta,\sigma)\, p(\boldsymbol\beta,\sigma)\, d\boldsymbol\beta\, d\sigma$$

Should there be two integrals instead of just one? Why or why not?

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There are two integrals there just aren't two integral signs. Notice the $d\beta d\sigma$ at the end. It is common in multivariable calculus to represent and multiple integral with one integral sign, often with a subscript denoting the region of integration, when it is not clear.

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  • $\begingroup$ I did notice the two differentials. That is why I asked the question :P Thanks jlimahaverford $\endgroup$
    – BCLC
    Commented Sep 13, 2015 at 15:45

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