# dlm.lpl: Calculate the log predictive likelihood for a specified set... In schw4b/DGM: Dynamical Graphical Models

## Description

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

## Usage

 `1` ```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.

schw4b/DGM documentation built on May 7, 2019, 3:16 p.m.