Martingale Posterior Distributions for Time-Series Models
Blake Moya, Stephen Graham Walker · Statistical Science · 2025
The paper considers the analysis of time-series data from a future missing data perspective. Using predictive models with random multistep, updating of the parameters is equivalent to an iterative ensemble approach where initial conditions are randomized. The output is a sample from a posterior distribution equivalent in structure to the martingale posterior distribution. Specifically, the paper provides a posterior distribution of the parameters of a time-series model by forward sampling from the data using a predictive model based on iteratively sampling and updating the model until the sequence of parameter estimators has converged. Repetition of this produces independent samples from the posterior. Illustrative and real data examples are provided.