/methodology/index.html Statistical framing for the default Bayesian model. Pages Statistical Model Hugo en-gb /methodology/statistical-model/index.html Mon, 01 Jan 0001 00:00:00 +0000 /methodology/statistical-model/index.html For study (i = 1,\ldots,k), the default model is a normal-normal Bayesian random-effects model. The likelihood is marginalised over the latent study effects for more stable small-(k) sampling: [ y_i \sim \mathrm{Normal}\left(\mu, \sqrt{s_i2 + \tau2}\right), \qquad \mu \sim \mathrm{Normal}(0, \sigma_\mu), \qquad \tau \sim \mathrm{HalfNormal}(\sigma_\tau). ] Here (y_i) is the observed model-scale effect and (s_i) is its known standard error. The pooled mean is (\mu), and (\tau) is between-study heterogeneity. Posterior study-level (\theta_i) draws are exposed as derived quantities using the Normal conditional distribution implied by (y_i), (\mu), (\tau), and (s_i).