documentclass[12pt,a4paper,oneside]{book}
usepackage[utf8]{inputenc}
usepackage{textgreek}
usepackage{amsmath,amssymb,amsthm}
usepackage{mathtools}
begin{document}

begin{equation*}
begin{aligned}
theta_1^*(t) ~ P(theta_1| Y_1^obs, Y_2^(t-1),…,Y_p^(t-1))\
Y_1^*(t) ~ P(Y_1| Y_1^obs, Y_2^(t-1),…,Y_p^(t-1), theta_1^*(t)) %<----stops here
end{aligned}
end{equation*}
end{document}