EBIC: Bayesian Information Criterion (BIC) for a partition.

In SCEM: Splitting-Coalescence-Estimation Method

Description

This function calculates an extended version of BIC, which is computed using a particular weighted average of the total residual sum of squares and the number of clusters.

SCEM uses the following equation for the BIC of each partition:

\loadmathjax \mjdeqn

BIC(P) = (np)\log \left\lbrace\fracRSS(P)np\right\rbrace + |P|(B_n^-1-1) \log(nB_n),ASCII representation

where \mjeqnRSS(P) = \sum_q=1^Q RSS(S_q)ASCII representation.

The sample size of each individual time series (i.e. the number of observations) is denoted by n, but in dealing with archaeological data, not all the time series in a data set will have the same number of observations.

In order to have a reasonable representative value for the sample size, we have chosen to use the natural arithmetic mean \mjeqnn=(n_1+...+n_p)/pASCII representation.

\mjeqn

(B_n^-1-1)\log(nB_n)ASCII representation is the tuning parameter that places the penalty on the number of clusters (also note that the term \mjeqnnB_nASCII representation). Using a different tuning parameter \mjeqn\gamma_nASCII representation in place of \mjeqn(B_n^-1-1)\log(nB_n)ASCII representation allows stronger or weaker penalties on the number of clusters.

Usage

EBIC(paths, partition, bandwidth)

Arguments

paths	A list of data frames, where each frame contains the data for one individual. Every data frame should have two columns with names 'distance' and 'oxygen'.
partition	A list of vectors. Each element in the list is a vector of integers, corresponding to individuals considered in one group.
bandwidth	Denotes the order of the bandwidth that should be used in the estimation process. bandwidth = k will mean that the bandwidth is n^k.

Value

Value of the extended BIC function for the partition.

Examples

armenia_split = split(armenia,f = armenia$ID)
band = -0.33
p = length(armenia_split)
EBIC(armenia_split,1:p,band)

SCEM documentation built on Sept. 5, 2021, 5:50 p.m.