Construct changepoint penalties — cpt

Helper to construct standard penalty values for use with changepoint detection methods. Returns a numeric penalty value.

Usage

cpt_penalty(type, n = NULL, k = 1, value = NULL, alpha = 1.01)

type: Penalty type: "None", "BIC" (or "SIC"), "MBIC", "AIC", "Hannan-Quinn", "sSIC", or "Manual".
n: Series length. Required for BIC, MBIC, AIC, Hannan-Quinn, sSIC.
k: Number of parameters per changepoint (typically 2 for mean+variance, 1 for mean-only). Defaults to 1. The "MBIC" penalty additionally reads k as the number of changepoints being placed, in its \(\log{n \choose k}\) term.
value: Numeric value for Manual type.
alpha: Exponent of the strengthened SIC ("sSIC") penalty \(k (\log n)^\alpha\); must exceed 1. Defaults to 1.01 (Fryzlewicz, 2014).

A numeric penalty value.

The same penalty name may be interpreted differently by different engines:

changepoint-based methods (PELT, BinSeg, SegNeigh, AMOC): accept character penalties ("MBIC", "BIC", "AIC", "Hannan-Quinn", "None") and pass them to the upstream changepoint package. These methods do not accept raw numeric penalty values.
Functional-pruning methods (fpop, cpop, decafs): accept numeric penalties only. When a character penalty is supplied via cpt_detect(), it is resolved to a numeric value using cpt_penalty() before dispatch.
Search-based methods (WBS, WBS2, NOT, MOSUM, IDetect, TGUH): use internal model-selection criteria (e.g., sSIC, threshold) and generally ignore the penalty argument. Specify thresholds via the wrapper's own arguments.
Inference/Bayesian methods (smuce, bcp, bocpd, beast, cpm, sn): are tuned by a significance level, posterior-probability threshold, hazard, or average run length rather than a penalty; see each wrapper.
MBIC in cpt_penalty() is a BIC-type penalty that adds a combinatorial term for the number of ways k changepoints can be placed in n observations, \(0.5(k+1)\log n + \log{n \choose k}\). It is deliberately stronger than "BIC". It is not the modified BIC of Zhang and Siegmund (2007), whose penalty \(1.5 k \log n + 0.5 \sum_i \log(l_i / n)\) depends on the segment lengths \(l_i\) and so cannot be expressed by a function of n and k alone. Use the character "MBIC" with changepoint-based methods to get the engine's native MBIC.

cpt_penalty("BIC", n = 100)
#> [1] 4.60517
cpt_penalty("AIC", n = 100)
#> [1] 2
cpt_penalty("Manual", value = 5)
#> [1] 5