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This paper proposes approaches for the analysis of multiple changepointmodels when dependency in the data is modelled through a hierarchical GaussianMarkov random field. Integrated nested Laplace approximations are used toapproximate data quantities, and an approximate filtering recursions approachis proposed for savings in compuational cost when detecting changepoints. Allof these methods are simulation free. Analysis of real data demonstrates theusefulness of the approach in general. The new models which allow for datadependence are compared with conventional models where data within segments isassumed independent.

Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments