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linear regression via maximum likelihood and some simple assumptions about the system.

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We wish to establish the parameters for a set of gaussian distributions that can straddle a linear function. These distributions should be centred (have means) equal to the estimated function, and a constant variance independent of 

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. The linear parameters (weights) and constant variance should maximise the likelihood for a given set of data points.

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Mathematically, this can be stated as saying that for any 

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 the corresponding optimal 

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 is a guassian distributed variable around a linear function with weights 

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:

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