Weakly informative priors in meta-analysis

General
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Is anyone aware of published meta-analyses where weakly informative priors were placed on treatment effect estimates? I am familiar with studies that suggest informative priors on heterogeneity terms, which are otherwise typically specified as:

sd ~ dunif(0,5) # vague prior for between-trial SD

But, for example in standard winBUGS code used for the basic parameters (t vs t[ref]) network meta-analysis is

d[k] ~ dnorm(0,.0001)

My field is dominated by small RCTs so it seems that priors that carry more information should help avoid errors of magnitude, but people in the field generally seem loathe to touch priors on treatment effects. I imagine the statistical literature is more open to the idea?

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A couple of my colleagues wrote this about weakly informative priors for bivariate metanalysis, it might have references that help https://arxiv.org/pdf/1512.06217.pdf It also comes with quite a nice Shiny interface iirc

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