1d:T7ec,# Posterior mixture weight calculation Computes posterior updated mixture weights for a two-component normal–normal model using the standard logit-additive update. The **prior** mixing weight is either a fixed weight $w \in (0,1)$ or a dynamic mixing weight as for eNAP prior: $Z = |y_{\mathrm{dir}} - y_{\mathrm{ind}}| / s_{\mathrm{link}}$: $w_(Z) = 1/exp(a + b \log (Z+1)), \quad a<0, \; b > 0.$ ```r post_w( w, a, b, s_EC2, s_EC1, s_C2C1, y_EC2, y_EC1 = -0.5, y_C2C1 = -0.5, tau0 = 1000, mu0 = 0, eps = 1e-12 ) ``` ## Arguments - `w`: Scalar. If `w > 1`, use the ADAPTIVE branch (logistic prior on log-Z). If `0 < w < 1`, use a fixed prior weight equal to `w`. - `a, b`: Parameters used in the elastic function for dynamic mixing weight. Must satisfy `a < 0` and `b > 0`. - `s_EC2, s_EC1, s_C2C1`: Sampling variances for direct evidence (E vs. C2 trial), and edges of indirect evidence (E vs. C1 trial and C2 vs. C1 trial). - `y_EC2, y_EC1, y_C2C1`: Estimated log-HR for E vs. C2 tria, E vs. C1 trial, C2 vs. C1 trial, respectively - `mu0, tau0`: Mean and variance for the vague component. - `eps`: Numeric scalar used for small-value clipping (default `1e-12`). ## Returns A numeric vector of posterior weights in `(0,1)` reflecting realized borrowing fraction of the informative component. ## Details * Fixed prior mixing weight (Robust NMAP Prior): requires `0 \< w \< 1`. * Adaptive branch (Adaptive NMAP Prior): triggered by `w \> 1`, requires `a\<0` and `b \> 0`. This corresponds to a decreasing prior weight as the inconsistency grows. * All variance/SD arguments may be given as scalars or vectors; scalars are recycled. ## Examples ```r y_EC2 <- -0.5; y_EC1 <- -0.8; y_C2C1 <- -0.3 s_EC2 <- 0.2; s_EC1 <- 0.18; s_C2C1 <- 0.18 # Fixed mixing weight 0.5 post_w(w = 0.5, a = NA, b = NA,s_EC2,s_EC1,s_C2C1, y_EC2,y_EC1,y_C2C1) # Dynamic weight with elastic function of (a=-4.6, b=3): post_w(w = 2, a = -2.5, b = 10,s_EC2,s_EC1,s_C2C1, y_EC2,y_EC1,y_C2C1) ```

post_w function