data is a Matlab structure that defines any number of data and the associated uncertainty/noise model.
data{1} defines the first data set (which must always be defined), and any number of additional data sets can be defined in
data{2},
data{3}, ...
This allows to consider for example seismic data in data{1}, and electromagnetic data in data{2}.
For each set of data, a Gaussian noise model (both correlated and uncorrelated) can be specified. The noise model for different data types (e.g. data{1} and data{2} are independent).
Once the noise model has been defined, the log-likelihood related to any model, m, with the corresponding forward response, d, can be computed using
[d,forward,prior,data]=sippi_forward(m,forward,prior,data) logL=sippi_likelihood(data,d)
where d is the output of sippi_forward.
The specification of the noise model can be divided into a description of the measurement noise (mandatory) and the modeling error (optional).
To define a set of observed data, [0,1,2], with an associated uncorrelated uncertainty defined by a Gaussian model with mean 0 and standard deviation 2, use
data{1}.d_obs=[0 1 2]';
data{1}.d_std=[2 2 2]';
which is equivalent to (as the noise model for each data is the same, and independent)
data{1}.d_obs=[0 1 2]';
data{1}.d_std=2;
One can also choose to define the uncertainty using a variance as opposed to the standard deviation
data{1}.d_obs=[0 1 2]';
data{1}.d_var=4;
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