Great question—this is a classic scenario in Bayesian modeling where we need to "borrow strength" from related data sources to regularize posteriors when our own data is sparse. When you use information about a similar but not identical parameter to build an informative prior, you're making three key, interconnected assumptions:

• 参数分布的相似性假设
  You’re assuming that your target parameter (the one you’re actually trying to estimate) and the "related but different" parameter share a common underlying distribution, or that their values are sufficiently close that the external information acts as a reasonable constraint. For example, if you’re estimating the effect of a drug in a small patient population, and you use data from a similar drug’s effect size as your prior, you’re assuming these two effect sizes come from a shared hyper-distribution (like a normal distribution with a common mean and variance), with only minor random differences between them.

• 信息的可迁移性假设
  You’re asserting that the patterns, relationships, or constraints captured by the external information are relevant to your target problem. This means the data-generating process behind the related parameter isn’t fundamentally different from your own problem’s process. If you’re using prior info from a study of urban housing prices to regularize a model for a small rural town, you’re assuming the core drivers of housing prices (like square footage, number of bedrooms) translate across these contexts—even if the absolute values differ.

• 正则化的无偏性假设
  You’re assuming that using this informative prior won’t introduce systematic bias into your posterior estimate. In other words, the external information you’re using is reliable enough that the "shrinkage" it imposes on your sparse-data posterior pulls the estimate toward a reasonable, accurate value, rather than a misleading one. If the related parameter’s data was collected with flawed methodology, this assumption breaks down.

Put simply, this approach relies on the idea that the "similar but different" parameter isn’t just arbitrarily similar—it’s similar in ways that matter for your model, and that similarity lets you use its information to stabilize your estimate when your own data is too thin to do the job alone.

内容的提问来源于stack exchange，提问作者Nay