Probability Decomposition--please help

[caryover]

Can someone help me please to solve the following equation?

(θ,I)=arg max p(r|θ,d,I)p(θ)Πp(I_k|d_k)

where, r_k=c₀d_kh_k+Σd_lh_lc_{(l-k)mod N}+η_k

the limit of sum is l=0,1...N-1 but l≠k

where can I find this type of probability decomposition equation?

Thanks in advance..