bmdl.eta: Calculate BMDL for a Given Changepoint Model

In yingboli/BayesMDL: Bayesian MDL for Multiple Changepoint Detection

Description

For mean shifts detection in a univariate time series. These functions can handle metadata.

Usage

bmdl.eta(X, month, eta, meta, p, fit, penalty, nu, a, b1, b2, period)

Arguments

X	A vector of length N, observed time series data.
month	A vector of length N, month indicators. Takes value in 1, 2, ..., 12 for monthly data, or 1 for annual data.
eta	A 0-1 indicator vector of length N, changepoint model. The first p elemenet are always 0.
meta	A 0-1 indicator vector of length N, metadata indicator. The first p elemenet are always 0.
p	The order of the AR process.
fit	For likelihood calculation, 'marlik' for marginal likelihood, or 'lik' for likelihood. Note that the 'lik' option already includes the two-part MDL of mu.
penalty	For penalty function calculation, 'bmdl' for Beta-Binomial prior, or 'mdl' for MDL.
nu	Prior variance scale of mu; only used if fit == 'marlik'.
a	The first and second parameters in the Beta-Binomial prior; only used if penalty == 'bmdl'.
b1	The b parameter in the Beta-Binomial prior of η, for un-documented times (i.e., times not in metadata). Default value is 239 for monthly data, and 19 for annual data.
b2	The b parameter in the Beta-Binomial prior of η, for documented times (i.e., times in metadata). Default value is 47 for monthly data, and 3 for annual data.
period	Period of the seasonal cycle, 12 for monthly data, or 1 for annual data.

Details

• To compute BMDL, use fit = 'marlik' and penalty = 'bmdl'.

• To compute automatic MDL, use fit = 'lik' and penalty = 'mdl'.

• To compute BIC, use penalty = 'BIC' (the fit argument does not matter in this case).

• Note, the marginal likelihood fit = 'marlik' can also be combined with penalty = 'uniform', which assigns uniform prior on the model space.

Value

mdl	The Bayesian MDL score for the changepoint model eta.
phi	A vector of length p, the Yule-Walker estimator of the autocorrelation parameter phi.
sigmasq	The EB estimator of the white noise variance sigmasq.
mu	A vector of length sum(eta); the conditional posterior mean of regime-wise means mu.
s	A vector of length period, the EB estimator of the monthly means s.

yingboli/BayesMDL documentation built on May 29, 2019, 12:18 p.m.