Author Correction: Multiplexed droplet single-cell RNA-sequencing using natural genetic variation

Correction to: Nature Biotechnology https://doi.org/10.1038/nbt.4042, published online 11 December 2017.

In this article as published, there were errors or omissions in three equations in the Methods. In paragraph 1, in the sentence “When e_cvi = 1, we assume that Pr(b_cvi|g,e_cvi) follows Supplementary Table 4,” the probability expression should be clarified by the addition of an equivalency: “we assume that

$${\mathrm{Pr}}\left( {b_{cvi}|g,e_{cvi}} \right) = \frac{{{\mathrm{Pr}}\left( {b_{cvi},e_{cvi}|g} \right)}}{{{\mathrm{Pr}}\left( {e_{cvi}} \right)}}$$

follows Supplementary Table 4.”

As published, the equation at the end of paragraph 2 reads

$$L_c\left( s \right) = \mathop {\prod}\nolimits_{v = 1}^V {\left[ {\mathop {\sum}\nolimits_{g = 0}^2 {\left\{ {\mathop {\prod}\nolimits_{i = 1}^{d_{cv}} {\left( {\mathop {\sum}\nolimits_{e = 0}^1 {{\mathrm{Pr}}\left( {b_{cvi}|g,e} \right)} } \right)P_{sv}^{\left( g \right)}} } \right\}} } \right]} $$

The correct equation is

$$L_c\left( s \right) = \mathop {\prod}\nolimits_{v = 1}^V {\left[ {\mathop {\sum}\nolimits_{g = 0}^2 {\left\{ {\mathop {\prod}\nolimits_{i = 1}^{d_{cv}} {\left( {\mathop {\sum}\nolimits_{e = 0}^1 {{\mathrm{Pr}}\left( {b_{cvi},e_{cvi}|g} \right)} } \right)P_{sv}^{\left( g \right)}} } \right\}} } \right]}$$

At the end of the first paragraph in the second section, the equation as published reads

$$\begin{array}{rcl}{L_c}\left( {s_1,s_2,} \right)\alpha &=& \mathop {\prod}\nolimits_{v = 1}^V \left[ \mathop {\sum}\nolimits_{g_1,g_2} \left\{\mathop {\prod}\nolimits_{i = 1}^{d_{cv}} \left( \mathop {\sum}\nolimits_{e = 0}^1 \left( {1 - \alpha } \right){\mathrm{Pr}}\left( {b_{cvi}|g_1,e} \right) + \alpha {\mathrm{Pr}}\left( {b_{cvi}|g_2,e} \right) \right) P_{sv}^{\left( {g_1} \right)}P_{sv}^{\left( {g_2} \right)}\right\} \right]\end{array}$$

The correct equation is

$$\begin{array}{rcl}{L_c}\left( {s_1,s_2,\alpha } \right) &=& \mathop {\prod}\nolimits_{v = 1}^V \left[ \mathop {\sum}\nolimits_{g_1,g_2} \left\{ \mathop {\prod}\nolimits_{i = 1}^{d_{cv}} \left( \mathop {\sum}\nolimits_{e = 0}^1 \left( {1 - \alpha } \right){\mathrm{Pr}}\left( {b_{cvi},e|g_1} \right) + \alpha {\mathrm{Pr}}\left( {b_{cvi},e|g_2} \right) \right) P_{sv}^{\left( {g_1} \right)}P_{sv}^{\left( {g_2} \right)} \right\} \right]\end{array}$$

The errors affect the article only, not the implementation of the tool. They have not been corrected in the original article.