fit_eta: Fit an individual changepoint model 'eta'
In yingboli/BayesMDL: Bayesian MDL for Multiple Changepoint Detection

Compute the objective function of the model, i.e., log of posterior proablity for BMDL, or log MDL, and estimate model parameters.

1 2	fit_eta(x, A, eta, xi, p = 2, fit = "marlik", penalty = "bmdl", nu = 5, kappa = 3, a = 1, b = 1, scale_trend_design = 0.05, weights = NULL)

`x`	The time series data, a numeric vector of length `n`.
`A`	The design matrix for the nuisance coefficients in the linear model. It is usually the matrix of seasonal indicators, or the design matrix for harmonic regression with a column of all 1 for intercept.
`eta`	A multiple changepoint configuration, i.e., model. It is a 0/1 indicator vector of length `n`, with the first `p` elemenets always being 0.
`xi`	Outliers indicator, a 0/1 vector of length `n`.
`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'`.
`kappa`	Prior variance scale of outliers.
`a, b`	The first and second parameters in the Beta-Binomial prior; only used if `penalty == 'bmdl'`.
`scale_trend_design`	The factor multiplied to the design matrix of trend. Default is 1/50.
`weights`	A numeric vector of observation weights, defined the same as the `weights` argument in the function `lm`.

`bmdl`	BMDL or MDL.
`s`	Estimates of nuisance coefficients in the linear model. It usually contains the seasonal means or coefficients of harmonic regression (with intercept).
`mu`	Estimates of regime-wise coefficients in the linear model. It usually contains the regime means and regime trends.
`sigmasq`	Estimate of σ^2 in the AR(p) process.
`phi`	Yule-Walker estimates of the AR(p) coefficients.