Exact(60)
Patients were divided into two groups by optical coherence tomography findings: 11 patients who had cystoid macular edema (CME) with SRD (SRD group) and 10 patients who had CME without SRD (SRD group).
Substituting (31) back into (30) yields the function ln p r RD, p, ĥ SRD ( N SRD ), N SRD ; the value of N SRD which maximizes this function cannot be obtained in closed form.
Similarly, during the SAGE iterations, we ignore in (12) the a priori distribution of ( h SRD, N SRD ) and perform the maximization over N SRD with h SRD fixed to Ä¥ SRD ( i ), yielding N Ì‚ SRD ( i ) = max | r RD âˆ' γ Ä¥ SRD ( i ) μ ( i ) | 2 + γ 2 | Ä¥ SRD ( i ) | 2 σ ( i ) âˆ' | μ ( i ) | 2 K, N RD, (24).
Then, p ( h SRD, N SRD ) is obtained by averaging p ( h SRD | h RD ) p ( N SRD | h RD ) over h RD, which is ZMCSCG distributed with variance h RD.
The density p ( h SRD, N SRD ) is expressed as p ( h SRD, N SRD ) = E p ( h SRD | h RD ) p ( N SRD | h RD ), where the averaging is w.r.t.
Therefore, we classified the subjects into a CME without SRD group (SRD group) and a CME with SRD group (SRD group).
Taking into account (7) and (2), we have (within terms not depending on ( h SRD, N SRD ) ) ln p r RD, p, h SRD, N SRD = âˆ' | r RD, p âˆ' γ h SRD c p | 2 N SRD âˆ' K p ln N SRD âˆ' ln N SRD âˆ' N RD âˆ' B | h SRD | 2 N SRD âˆ' N RD âˆ' A N SRD âˆ' N RD.
where ln p ( h SRD, N SRD ) follows from (7).
In order to obtain the pilot-based MAP estimate of ( h SRD, N SRD ), based on the observation r RD, p only, we have to jointly maximize ln p ( r RD, p, h SRD, N SRD ) = ln p ( r RD, p | h SRD, N SRD ) + ln p ( h SRD, N SRD ).
Using (1) and (2), it follows from (10) that h SD and ( h SRD, N SRD ) can be estimated independently Ä¥ SD ( i ) = arg max h SD E ln p ( r SD | h SD, c ) p ( h SD ) | r, ν Ì‚ ( i âˆ' 1 ) (11). and Ä¥ SRD ( i ), N Ì‚ SRD ( i ) is given by arg max h SRD, N SRD E ln p ( r RD h SRD, N SRD, c ) p ( h SRD, N SRD ) r, ν Ì‚ ( i âˆ' 1 ).
Finally, we maximize ln p r RD, p, h SRD, N Ì‚ SRD ( 0 ) over h SRD ; according to (31) in Appendix 2, this yields the closed-form expression Ä¥ SRD ( 0 ) = | c p | 2 H SR N Ì‚ SRD ( 0 ) âˆ' N RD | c p | 2 H SR N Ì‚ SRD ( 0 ) âˆ' N RD + N Ì‚ SRD ( 0 ) N SR Ä¥ SRD, ML ( 0 ).
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