I¡m learning Bayesian Networks and now I'm studying Decision Making.
I have the following probability table (sorry about the format, I don't know how to do it better):
________| $\psi(y,t,d)$
$+y,+t,+d$ | 7.4238
$+y,+t,\neg d$ | 4.5178
$+y,\neg t,+d$ | 0
$+y,\neg t,\neg d$ | 0
$\neg y,+t,+d$ | 79.8762
$\neg y,+t,\neg d$ | 90.307
$\neg y,\neg t,+d$ | 0
$\neg y,\neg t,\neg d$ | 0
I need to calculate the following formulas:
(1) $$\psi(y,t)=\max_d\psi(y,t,d)$$ (2) $$\pi_D^{opt}(y,t)= \underset{d}{\arg\max}\, \psi(y,t,d)$$ (3) $$\psi(t)=\sum_y\psi(y,t)$$ (4) $$UE=\max_t\psi(t)$$ (5) $$\pi_T^{opt}()= \underset{t}{\arg\max}\,\psi(t)$$
I know how to compute (1), (3) and (4); but how can I compute (2) and (5)?
I don't know what $\max_d$ means. It is a $\max$ function with an underscore $d$, I don't know what that $d$ means.