Description Usage Arguments Details Value See Also
Estimate \cal{H}_g hyperparameters of the gauged sites using the EM algorithm, using the staircase of the missing data to determine the default block structure.
1 2 3 
data 
data matrix, grouped by blocks each with stations having the same number of missing observations. The blocks are organized in order of decreasing number of missing observations, ie. block 1 has more missing observations than block2. Default structure:

p 
number of pollutants measured at each stations. (first p columns of y are for p pollutants from station 1, block 1). 
block 
a vector indicating the number of stations in each block  from 1 to K 
covariate 
design matrix for covariates created with 
B0 
Provided if the hyperparameter β_0 (B0) is known and not estimated 
init 
Initial values for the hyperparameters; output of this function can be used for that 
a 
When p=1, the typeII MLE's for delta's are not available. Delta's are assumed to follow a gamma distribution with parameters (a,r) 
r 
When p=1, the typeII MLE's for delta's are not available. Delta's are assumed to follow a gamma distribution with parameters (a,r) 
verbose 
flag for writing out the results at each iteration 
maxit 
the default maximum number of iterations 
tol 
the convergence level. 
The estimated model is as follows:
data \sim MVN ( z \times β , {\rm kronecker}(I, Σ) )
β \sim MVN (β_0 , {\rm kronecker}(F^{1} , Σ ) )
Σ \sim GIW (Θ , δ )
Θ is a collection of hyperparameters including ξ_0, Ω, Λ, H^{1}.
A list with following elements:
Delta 
The estimated degrees freedom for each of the blocks (list) 
Omega 
The estimated covariance matrix between pollutants 
Lambda 
The estimated conditional covariance matrix between stations in each block given data at stations in higher blocks (less missing data)  (list) 
Xi0 
The estimated slopes of regression between stations in each blocks and those in higher blocks (list). Note that τ_{0i} = {\rm kronecker}(ξ_0, diag(p))  same across stations for each pollutants. 
Beta0 
Coefficients  assumed to be the same across stations for each pollutant 
Finv 
Scale associated with β_0 
Hinv 
The estimated hyperparameters (list)  inverse of H_j 
Psi 
The estimated (marginal) covariance matrix between stations 
block 
From input 
data 
From input 
covariate 
From input 
Lambda.1K 
The inverse Bartlett decomposition (eqn 23?) 
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