TABLE OF CONTENTS Our task is to infer the parameters of some model function, f, that we sample in the presence of noise. We assume that we have N data values, d i, that are related to N values of the function f i, according to
| (10.1) |  |
where e i represents an unknown error component in the measurement of f i.We assume that our knowledge (or lack thereof !) of the source of the errors is described by a Gaussian distribution for the e i. [3] For now, we assume the distribution for each e i to be independent of the values of the other errors, and that all of the error distributions have a common standard deviation, ?. We will later generalize the results to remove the restriction of equal and independent data errors.
By a linear model, we mean that f i can be written as a linear superposition of M functions, g i?, where g i? is the value of the ?th known function for the ith datum. The M functions are each completely specified (they have no parameters); it is their relative amplitudes that are unknown and to be inferred. Denoting the coefficients of the known functions by A ?, we thus have
| (10.2) |  |
Our task is to infer { A ?}, which we will sometimes denote collectively with an unadorned A, as we have...
