A detailed comparison of optimality and simplicity in perceptual decision-making

. Author manuscript; available in PMC: 2017 Jun 1.

Published in final edited form as: Psychol Rev. 2016 May 12;123(4):452–480. doi: 10.1037/rev0000028

MaxT2:

x_{\underset{L}{argmax} (- {\bar{x}}_{\ L}^{2})} > 0

MaxT12:

x_{\underset{L}{argmax} (- \frac{x_{L}^{2}}{2 (σ_{s}^{2} + σ^{2})} - \frac{{\bar{x}}_{\ L}^{2}}{2 (σ_{s}^{2} + \frac{σ^{2}}{N - 1})})} > 0

MaxT13:

\begin{array}{l} x_{\underset{L}{argmax} (- \frac{x_{L}^{2}}{2 (σ_{s}^{2} + σ^{2})} - \frac{N - 1}{2 σ^{2}} var x_{\ L})} > 0 \end{array}

MaxT23:

\begin{array}{l} x_{\underset{L}{argmax} (- \frac{{\bar{x}}_{\ L}^{2}}{2 (σ_{s}^{2} + \frac{σ^{2}}{N - 1})} - \frac{N - 1}{2 σ^{2}} var x_{\ L})} > 0 \end{array}

MaxT123:

\begin{array}{l} x_{\underset{L}{argmax} (- \frac{x_{L}^{2}}{2 (σ_{s}^{2} + σ^{2})} - \frac{{\bar{x}}_{\ L}^{2}}{2 (σ_{s}^{2} + \frac{σ^{2}}{N - 1})} - \frac{N - 1}{2 σ^{2}} var x_{\ L})} > 0 \end{array}