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Relabelling Algorithm, Boys & Henderson (2002)

boys_henderson_2002.Rd

Relabelling algorithm detailed in paper "On determining the order of Markov dependence of an observed process" (Boys & Henderson, 2002).

Usage

boys_henderson_2002(z, start = 2, z_max = max(z))

Arguments

z

bmoe_array. Component allocation output from bmoe_fit.

start

integer. Required starting point for this algorithm.

z_max

integer. Maximum possible value of z.

Value

See Permutations section in apply_relabelling().

Details

Read paper for full details; aim is to minimise 'disagreement',

\( D = - \sum_{i = 1}^n \mathbb{I} \left( \nu_m(z_i^{(m)}) = \hat{z}_i^{(m - 1)} \right) \)

where

  • \(\nu_m\) is a candidate permutation to be chosen;

  • \(\hat{z}\) is the marginal posterior mode of all MCMC iterations up to that point.

  • relabelling is applied per MCMC iterations, \(m = m_0, \dots, M\) where the user defines \(m_0\) using the start argument.

References

Boys, R. J. & Henderson, D. A. 2002 On determining the order of markov dependence of an observed process governed by a hidden markov model. Scientific Programming 10 (3), 241–251.