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 PCA SUPP Rev 11 18 Indd 2018-2024

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so uh We've um been talking about uh principal component analysis um I've been trying to emphasize the similarity between the sort of maths we were using um and the uh math for basian linear regression um and last time we got as far as computing being the marginal likelihood for principal component analysis so the marginal likelihood um had a particular form which was a gaussian with a mean so the marginal likelihood of the data given the Matrix and the noise and the mean oh Sor yeah that would be good thanks is independent across data points what we looked at last time was just for one data point and because we're making assumptions about uh I think I'm using Capital ends aren't I uh since we're making assumptions about independence across data points for both the likelihood and the prior the overall ra marginal likelihoods in the across data points um and it has this form which we derived last time 2 pi p over 2 where p is the dimensionality of the vector TI which is the uh I data po

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