complexityPrior

maximum number of change-points (default = 20).

Lmax

positive real number, corresponding to \(\alpha\).

gammaParameter

positive integer denoting the total number of time-points.

nTime

This function computes the complexity prior distribution on the number of change-points, defined as \(f(\ell) = P(\ell_n = \ell)\propto e^{-\alpha\ell\log(bT/\ell)}, a, b &gt; 0; \ell = 0,1,2,\ldots\). Note that this distribution has exponential decrease (Castillo and van der Vaart, 2012) when \(b&gt;1+e\), so we set \(b=3.72\).

Assume that a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. The package infers the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters per time-series by MCMC sampling. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence, but also available is the Poisson distribution. See Papastamoulis et al (2017) <arXiv:1709.06111> for a detailed presentation of the method.

complexityPrior: Complexity prior distribution

Description

Usage

Arguments

Value

References