Correction to: Nature Neuroscience https://doi.org/10.1038/10.1038/s41593-019-0533-x, published online 25 November 2019.

In the version of this article initially published in the Methods section “E-step” several variables appeared as m which should have been i. The sentence “The forward step identifies the probability \(a_m\left( t \right) = P\left( {Y_1 = y_1, \ldots ,Y_t,Z_t = m|{\mathbf{\theta }}} \right)\) of observing \(Y = y_1,y_2, \ldots ,y_t\) and, assuming there are N total states, of being in state m at time t by iteratively computing as follows:” should have read, “The forward step identifies the probability \(a_i\left( t \right) = P\left( {Y_1 = y_1, \ldots ,Y_t,Z_t = i|{\mathbf{\theta }}} \right)\) of observing \(Y = y_1,y_2, \ldots ,y_t\) and, assuming there are N total states, of being in state i at time t by iteratively computing as follows:” and errors appears in equations (8) and (9). The errors have been corrected in the PDF and HTML versions of this article.

Original:

$$a_i\left( {t + 1} \right) = \eta _{i,y_{t + 1}}\mathop {\sum}\nolimits_{j = 1}^N {a_j\left( t \right)\alpha _{j,m}}$$
(8)
$${b}_{i}(t)=P({Y}_{t+1}={y}_{t+1},...,{Y}_{T}={y}_{T}| {Z}_{t}=m,{\bf \theta} )=\sum _{j=1}^{N}{b}_{j}(t+1){\eta }_{j,{y}_{t+1}}{\alpha }_{i,j}$$
(9)

Corrected:

$$a_i\left( {t + 1} \right) = \eta _{i,y_{t + 1}}\mathop {\sum}\nolimits_{j = 1}^N {a_j\left( t \right)\alpha _{i,j}}$$
(8)
$${b}_{i}(t)=P({Y}_{t+1}={y}_{t+1},...,{Y}_{T}={y}_{T}| {Z}_{t}=i,{\bf \theta} )=\sum _{j=1}^{N}{b}_{j}(t+1){\eta }_{j,{y}_{t+1}}{\alpha }_{i,j}$$
(9)