C.1 Notation

I shall assume that we have some function $$f()$, which takes $n_x$ parameters, $x_0$...$x_n_x-1$, the set of which may collectively be written as the vector $x$. We are supplied a datafile, containing a number $n_d$ of datapoints, each consisting of a set of values for each of the $n_x$ parameters, and one for the value which we are seeking to make $f(x)$ match. I shall call of parameter values for the $i$th datapoint $x_i$, and the corresponding value which we are trying to match $f_i$. The data file\  may contain error estimates for the values $f_i$, which I shall denote $σ_i$. If these are not supplied, then I shall consider these quantities to be unknown, and equal to some constant $σ_data$. 

Finally, I assume that there are 

$n_u$ coefficients within the function $f()$ that we are able to vary, corresponding to those variable names listed after the {\tt via} statement in the {\tt fit} command. I shall call these coefficients $u_0$...$u_n_u-1$, and refer to them collectively as $u$. 

I model the values 

$f_i$ in the supplied data file\  as being noisy Gaussian-distributed observations of the true function $f()$, and within this framework, seek to find that vector of values $u$ which is most probable, given these observations. The probability of any given $u$ is written $P u | x_i, f_i, σ_i $. 

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