posterior predictive distributions - Githubissues

reichlab / lssm

Linear state space models

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posterior predictive distributions #2

Open elray1 opened 3 years ago

elray1 commented 3 years ago

function is posterior_predict
output is vector of length n with p by p + 1 matrices with smoothed mean and variance for y_t

Logic:

Smoothing will get us to a conditional distribution for alpha_t | Y_n for each t = 1, ..., n: alpha_t | Y_n ~ Normal(\hat{alpha}_t, V_t) -- Unclear exactly how to get variance V_t based on jrnold functions
Then we can get to a conditional distribution for \tilde{y}_t | Y_n where \tilde{y}_t is a hypothetical value that could have been observed at time t. \tilde{y}_t = d + Z \alpha_t + epsilon_t ~ Normal(d + Z \hat{alpha}_t, Z V_t Z' + H)