关于CausalImpact/bsts纳入先验概率及M参数设置的技术问询

Great question! Let's unpack how this works in the CausalImpact package:

Where is the M/J prior selection logic implemented? #

The core logic for covariate selection with the M/J prior lives in two key parts of the package:

1. Internal model-building functions: When you call CausalImpact(), it uses helper functions (like buildModel()—you can inspect this in R with getAnywhere(buildModel)) to calculate the prior probability for covariate inclusion. This probability is exactly the M/J value referenced in the paper, where J is your total number of covariates.
2. Underlying Stan model code: The actual prior distribution is defined in the package's Stan model file. You can locate this file on your system with this R command:

   system.file("stan", "causalimpact.stan", package = "CausalImpact")
   

   Inside the file, you’ll find code for the inclusion indicator variables (typically named gamma) that uses a Bernoulli prior tied to the prior_inclusion_prob parameter. This parameter is the computed M/J value.

If you don’t specify M, the package uses a default (often a 50% inclusion rate, i.e., M = J/2) when no explicit guidance is given.

Can you set a custom M? #

There’s no direct M parameter exposed in the CausalImpact() function, but you can achieve this indirectly by calculating the corresponding inclusion probability and passing it via the model.args parameter:

1. Calculate the target probability: prob = M / J (replace M with your expected model size and J with your total number of covariates)
2. Pass this probability when initializing your CausalImpact object:

   ci <- CausalImpact(data, pre.period, post.period,
                      model.args = list(prior.inclusion.prob = prob))
   

This lets you explicitly control the expected model size M by aligning the prior inclusion probability with your desired M/J ratio.

内容的提问来源于stack exchange，提问作者Booley