Suppose I’m analyzing data sequentially using a Bayesian statistical model. The data are clustered by site, so the model includes a hierarchical component for site. In addition, suppose that some sites may take longer than others to come “on line”, so that for instance data from Site X may become available only after the i^{th} look at the data.

Are there any special considerations we need to make in this scenario, or can we just update the posterior using the full data, including the data from Site X, at the (i + 1)^{th} look at the data?