Correction: A Mixture of Delta-Rules Approximation to Bayesian Inference in Change-Point Problems

[This corrects the article DOI: 10.1371/journal.pcbi.1003150.].


Major issue with change-point prior in Fig 3
The Unfortunately, this error in Fig 3 was carried over into the code and we actually used this (incorrect) change-point prior in our simulations. Fortunately, however, updating the code to include the new change-point prior has a relatively small effect on most results. Thus there are only minor, quantitative changes required in Figs 1, 5 and 6. Likewise the model fitting results (Figs 10, 11 and S1 and Tables 1 and S1) are slightly changed, with the biggest change being that the 2-node, not the 3-node, model now best fits human behavior.
The one place our use of the incorrect change-point prior has a large effect is in the section "Performance of the reduced model relative to ground truth." In particular, when we use the correct change-point prior, the simplifying assumption in Eq 48 no longer holds. That is, we have This invalidates the analysis of the two-and three-node cases in Figs 8 and 9. Specifically, the results in Fig 8B, 8C, 8E and 8F and the results in Fig 9B, 9C, 9E and 9F no longer hold.
We have therefore instead computed numerical solutions to the optimization problem for the Gaussian case. As shown in the updated figures, the results are quantitatively different from the original paper, as to be expected given the problems discussed above, but are qualitatively consistent with our previous findings. Thus, the new results do not change the main conclusions, most importantly that performance of the algorithm improves substantially from 1 to 2 nodes, but only incrementally from 2 to 3 nodes.

Typos
In addition to the major error with the change-point prior, the original paper also contains a number of typos. These do not reflect how the algorithm was actually implemented. We now list these changes in detail: In Eqs 6 and 7, the sums should start from r t+1 = 0 not r t+1 = 1; i.e. they should read pðx tþ1 jr tþ1 Þpðr tþ1 jx 1:t Þ and pðr t jx 1:t Þ / pðx t jr t Þpðr t jx 1:tÀ 1 Þ pðr t jr tÀ 1 Þpðr tÀ 1 jx 1:tÀ 1 Þ

Eq 14 has sign error and should read
Eq 15 should read where the only change is that the order of arguments intoÃ have been switched. Eq 32 for the weight of the increasing node should read Eq 33 for the weight of the self node should read l jþ1 À l j À 1 l jþ1 À l j 1 À h ð Þp l j jx 1:t for l jþ1 > l j þ 1 0 otherwise Eq 34 should read Eq 38 should read pðl 1 jx 1:t Þ / pðx t jl 1 Þðpðl 1 jl 1 Þpðl 1 jx 1:tÀ 1 Þ þ pðl 1 jl 2 Þpðl 2 jx 1:tÀ 1 ÞÞ The model probability for each of the _ve models. This measure reports the estimated probability that a given subject will be best _t by each of the models. (B) The exceedance probability for each of the _ve models. This measure reports the probability that each of the models best explains the data from all subjects.