Impute missing data by optimizing the likelihood function
fill_data(obs, mu, sigma, p, index, lucid_model)
an observation with updated imputed value
a vector of length M
a matrix of size M x K
a matrix of size M x M x K
a vector of length K
a vector of length M, indicating whether a value is missing or not in the raw data
Specifying LUCID model, "early" for early integration, "parallel" for lucid in parallel, "serial" for lucid in serial