model {
for (i in 1:nsearch) { # search for "just
pr.sd[i] <- start + i*step # significant" prior
pr.mean[i] <- 0
}
pr.mean[nsearch+1] <- -0.26
pr.sd[nsearch+1] <- 0.13 # clinical prior
pr.mean[nsearch+2] <- 0
pr.sd[nsearch+2] <- 0.35 # sceptical prior
# replicate data for each prior and specify likelihood...
for (i in 1:(nsearch+3)) {
for (j in 1:2) {
r.rep[i,j] <- r[j]
n.rep[i,j] <- n[j]
r.rep[i,j] ~ dbin(pi[i,j], n.rep[i,j])
}
}
delta.mle <- -0.753
delta.mle ~ dnorm(delta[nsearch+4], 7.40)
# define priors and link to log-odds...
for (i in 1:(nsearch+2)) {
logit(pi[i,1]) <- alpha[i] + delta[i]/2
logit(pi[i,2]) <- alpha[i] - delta[i]/2
alpha[i] ~ dnorm(0, 0.0001)
delta[i] ~ dnorm(pr.mean[i], pr.prec[i])
pr.prec[i] <- 1/pow(pr.sd[i], 2)
}
pi[nsearch+3,1] ~ dbeta(0.5, 0.5)
pi[nsearch+3,2] ~ dbeta(0.5, 0.5) # Jeffreys prior
delta[nsearch+3] <- logit(pi[nsearch+3,1])
- logit(pi[nsearch+3,2])
delta[nsearch+4] ~ dunif(-10, 10) # locally uniform prior
delta.plot[1] <- delta[25]
delta.plot[2] <- delta[41]
delta.plot[3] <- delta[42]
delta.plot[4] <- delta[43]
delta.plot[5] <- delta[44]
prior.plot[1] ~ dnorm(pr.mean[25], pr.prec[25])
prior.plot[2] ~ dnorm(pr.mean[41], pr.prec[41])
prior.plot[3] ~ dnorm(pr.mean[42], pr.prec[42])
}
Data:
list(r = c(13, 23), n = c(163, 148),
start = 0.8, step = 0.005, nsearch = 40)
node mean sd MC error 2.5% median 97.5% start sample
delta[1] -0.6351 0.3342 4.823E-4 -1.3 -0.6326 0.01388 1001 500000
delta[2] -0.6362 0.3347 4.86E-4 -1.301 -0.633 0.01206 1001 500000
delta[3] -0.6377 0.3349 4.731E-4 -1.303 -0.6351 0.01166 1001 500000
delta[4] -0.6392 0.3352 5.097E-4 -1.304 -0.6361 0.01176 1001 500000
delta[5] -0.6391 0.3353 5.101E-4 -1.305 -0.6364 0.01028 1001 500000
delta[6] -0.6412 0.3359 5.034E-4 -1.308 -0.6381 0.008304 1001 500000
delta[7] -0.6424 0.3358 4.924E-4 -1.309 -0.6396 0.007906 1001 500000
delta[8] -0.6433 0.3368 4.899E-4 -1.311 -0.6402 0.00849 1001 500000
delta[9] -0.6446 0.3364 4.899E-4 -1.312 -0.6418 0.007047 1001 500000
delta[10] -0.6456 0.3374 4.779E-4 -1.316 -0.6433 0.009481 1001 500000
delta[11] -0.6472 0.338 4.869E-4 -1.32 -0.6436 0.009341 1001 500000
delta[12] -0.6476 0.3387 4.852E-4 -1.321 -0.6451 0.008901 1001 500000
delta[13] -0.65 0.3385 4.826E-4 -1.322 -0.6471 0.007652 1001 500000
delta[14] -0.6503 0.3393 5.042E-4 -1.323 -0.6474 0.007114 1001 500000
delta[15] -0.6526 0.339 5.023E-4 -1.326 -0.6498 0.004507 1001 500000
delta[16] -0.6528 0.3393 4.813E-4 -1.328 -0.6498 0.005786 1001 500000
delta[17] -0.6544 0.3393 4.955E-4 -1.33 -0.6511 8.954E-4 1001 500000
delta[18] -0.6552 0.3403 4.917E-4 -1.332 -0.6521 0.002135 1001 500000
delta[19] -0.6555 0.3397 4.9E-4 -1.331 -0.6523 0.001753 1001 500000
delta[20] -0.6567 0.3402 4.801E-4 -1.334 -0.6534 0.001299 1001 500000
delta[21] -0.6581 0.3412 4.793E-4 -1.339 -0.6543 0.001263 1001 500000
delta[22] -0.6591 0.3412 5.083E-4 -1.338 -0.6555 4.645E-4 1001 500000
delta[23] -0.66 0.3417 5.323E-4 -1.34 -0.6572 0.00112 1001 500000
delta[24] -0.6619 0.3418 4.832E-4 -1.341 -0.6589 1.396E-4 1001 500000
delta[25] -0.6635 0.3423 5.075E-4 -1.343 -0.6609 3.598E-4 1001 500000
delta[26] -0.6633 0.342 5.054E-4 -1.344 -0.6601 -0.001383 1001 500000
delta[27] -0.6641 0.3422 5.069E-4 -1.344 -0.6613 -4.922E-4 1001 500000
delta[28] -0.6655 0.3426 5.223E-4 -1.347 -0.6628 -0.001396 1001 500000
delta[29] -0.6662 0.3435 5.198E-4 -1.349 -0.6626 -0.002746 1001 500000
delta[30] -0.6676 0.3439 5.213E-4 -1.352 -0.6641 -0.002247 1001 500000
delta[31] -0.6684 0.3436 5.134E-4 -1.352 -0.6654 -0.002408 1001 500000
delta[32] -0.6684 0.344 5.066E-4 -1.352 -0.6655 -0.00158 1001 500000
delta[33] -0.6696 0.3443 4.926E-4 -1.352 -0.6664 -0.003633 1001 500000
delta[34] -0.6705 0.345 4.966E-4 -1.357 -0.668 -0.002591 1001 500000
delta[35] -0.6717 0.3444 5.075E-4 -1.356 -0.6688 -0.005456 1001 500000
delta[36] -0.6737 0.3454 5.048E-4 -1.36 -0.6708 -0.004817 1001 500000
delta[37] -0.6748 0.345 4.986E-4 -1.361 -0.6714 -0.006334 1001 500000
delta[38] -0.6743 0.3459 5.109E-4 -1.36 -0.6713 -0.004526 1001 500000
delta[39] -0.6752 0.3456 5.119E-4 -1.362 -0.6717 -0.005816 1001 500000
delta[40] -0.6756 0.3454 5.074E-4 -1.364 -0.6715 -0.008499 1001 500000
delta[41] -0.317 0.1223 1.741E-4 -0.5562 -0.317 -0.07745 1001 500000
delta[42] -0.3664 0.2509 3.497E-4 -0.8608 -0.366 0.1245 1001 500000
delta[43] -0.7523 0.367 5.342E-4 -1.487 -0.7479 -0.04719 1001 500000
delta[44] -0.7534 0.3673 5.432E-4 -1.475 -0.7529 -0.0334 1001 500000
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