The posterior probabilities are obtained via ABC with large formula_59 by utilizing the summary statistic (with formula_69 and formula_70) and the full data sequence (with formula_69). 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 formula_69. A much longer observed data sequence would be needed to obtain a posterior concentrated around formula_73, the true value of formula_1.