dlm.lpl {DGM} R Documentation

## Calculate the log predictive likelihood for a specified set of parents and a fixed delta.

### Description

Calculate the log predictive likelihood for a specified set of parents and a fixed delta.

### Usage

dlm.lpl(Yt, Ft, delta, priors = priors.spec())


### Arguments

 Yt the vector of observed time series, length T. Ft the matrix of covariates, dim = number of thetas (p) x number of time points (T), usually a row of 1s to represent an intercept and the time series of the parent nodes. delta discount factor (scalar). priors list with prior hyperparameters.

### Value

 mt the vector or matrix of the posterior mean (location parameter), dim = p x T. Ct and CSt the posterior scale matrix C_{t} is C_{t} = C*_{t} x S_{t}, with dim = p x p x T, where S_{t} is a point estimate for the observation variance phi^{-1} Rt and RSt the prior scale matrix R_{t} is R_{t} = R*_{t} x S_{t-1}, with dim = p x p x T, where S_{t-1} is a point estimate for the observation variance phi^{-1} at the previous time point. nt and dt the vectors of the updated hyperparameters for the precision phi with length T. S the vector of the point estimate for the observation variance phi^{-1} with length T. ft the vector of the one-step forecast location parameter with length T. Qt the vector of the one-step forecast scale parameter with length T. ets the vector of the standardised forecast residuals with length T, \newline defined as (Y_{t} - f_{t}) / sqrt (Q_{t}). lpl the vector of the Log Predictive Likelihood with length T.

### References

West, M. & Harrison, J., 1997. Bayesian Forecasting and Dynamic Models. Springer New York.

### Examples

data("utestdata")
Yt = myts[,1]
Ft = t(cbind(1,myts[,2:5]))
m = dlm.lpl(Yt, Ft, 0.7)



[Package DGM version 1.7.4 Index]