## S3 method for class 'lgcpPredict':
expectation(obj, fun, maxit, ...)?dump2dir and ?setoutput. This function computes the
Monte Carlo Average of a function where data from a run of lgcpPredict has been dumped to disk.A Monte Carlo Average is computed as:
$$E_{\pi(Y_{t_1:t_2}|X_{t_1:t_2})}[g(Y_{t_1:t_2})] \approx \frac1n\sum_{i=1}^n g(Y_{t_1:t_2}^{(i)})$$
where $g$ is a function of interest, $Y_{t_1:t_2}^{(i)}$ is the $i$th retained sample from the target
and $n$ is the total number of retained iterations. For example, to compute the mean of $Y_{t_1:t_2}$ set,
$$g(Y_{t_1:t_2}) = Y_{t_1:t_2},$$
the output from such a Monte Carlo average would be a set of $t_2-t_1$ grids, each cell of which
being equal to the mean over all retained iterations of the algorithm (NOTE: this is just an example computation, in
practice, there is no need to compute the mean on line explicitly, as this is already done by default in lgcpPredict).