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The posterior probabilities are obtained via ABC with large <math>n</math> by utilizing the summary statistic (with <math>\epsilon = 0 </math> and <math>\epsilon = 2 </math>) and the full data sequence (with <math>\epsilon = 0 </math>). These are compared with the true posterior, which can be computed exactly and efficiently using the [[Viterbi algorithm]]. The summary statistic utilized in this example is not sufficient, as the deviation from the theoretical posterior is significant even under the stringent requirement of <math>\epsilon = 0 </math>. A much longer observed data sequence would be needed to obtain a posterior concentrated around <math>\theta = 0.25</math>, the true value of <math>\theta</math>.
This example application of ABC uses simplifications for illustrative purposes. More realistic applications of ABC are available in a growing number of peer-reviewed articles.<ref name="Beaumont2010" /><ref name="Bertorelle" /><ref name="Csillery" /><ref name="Marin11" /><ref>{{cite book |first=Christian P. |last=Robert |chapter=Approximate Bayesian Computation: A Survey on Recent Results |year=2016 |editor-last=Cools |editor-first=R. |editor2-last=Nuyens |editor2-first=D. |title=Monte Carlo and Quasi-Monte Carlo Methods |pages=185–205 |series=Springer Proceedings in Mathematics & Statistics |volume=163 |isbn=978-3-319-33505-6 |doi=10.1007/978-3-319-33507-0_7 }}</ref>
==Model comparison with ABC==
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