Bayesian Inference of Normal Distribution Parameters with Aggregate Data
Rémi Cuingnet · HAL (Le Centre pour la Communication Scientifique Directe) · 2021
This note extends standard Bayesian inference of normal distribution parameters to aggregate observed data points. It considers the case where data points cannot be observed directly but only through sum or average. As a result, the posterior and predictive posterior distributions can be derived by simply adapting the sample variance to aggregate data. Thus, the posterior follows a normal-gamma distribution while the posterior predictive has a non-standardized Student's t-distribution.