I shall assume that we have some function , which takes parameters, ..., the set of which may collectively be written as the vector . We are supplied a datafile, containing a number of datapoints, each consisting of a set of values for each of the parameters, and one for the value which we are seeking to make match. I shall call of parameter values for the th datapoint , and the corresponding value which we are trying to match . The data file may contain error estimates for the values , which I shall denote . If these are not supplied, then I shall consider these quantities to be unknown, and equal to some constant .
Finally, I assume that there are coefficients within the function that we are able to vary, corresponding to those variable names listed after the via statement in the fit command. I shall call these coefficients ..., and refer to them collectively as .
I model the values in the supplied data file as being noisy Gaussian-distributed observations of the true function , and within this framework, seek to find that vector of values which is most probable, given these observations. The probability of any given is written .