Σεμινάριο: "Bayesian Methods for the Integration of Historical Data"

ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ 2023-2024

Ομιλητής: Roberto Macrì Demartino, Department of Statistical Sciences University of Padua (IT)

Bayesian Methods for the Integration of Historical Data

Αίθουσα Τ107

ΠΕΡΙΛΗΨΗ

In recent years, there has been an increasing interest and acceptance in utilizing and integrating historical data. Given the inherent nature of sequential information updating, Bayesian methods are natural for this purpose. Moreover, the process of informative prior elicitation is widely recognized as a complex and multifaceted task.

Within this context, the concept of power priors (Chen and Ibrahim, 2000) has emerged as a popular approach for incorporating historical data into the prior distribution. The power prior methodology heavily relies on a power parameter, ranging between 0 and 1, that is a crucial factor in determining the degree to which the historical data influences the prior distribution. The optimal prior distribution for the power parameter should balance the aims of encouraging borrowing when the data are compatible and limiting borrowing when they are in conflict. Consequently, the ability to effectively elicit an optimal initial prior for this parameter is a crucial step not fully investigated. We explore the use of a Simulation-based Calibrated Bayes Factor, employing hypothetical replications generated from the posterior predictive distribution, to discriminate between competing initial Beta prior specifications for the power parameter.

Additionally, analyzing replication studies involves per definition the use of historical data. Notably, power priors (Pawel et al., 2023) and hierarchical models (Bayarri and Mayoral 2002; Pawel and Held 2020) are two leading approaches in this domain. However, the development of mixture models for analyzing replication studies is still an unexplored field. We propose a novel and conceptually intuitive Bayesian approach for quantifying replication success based on the use of mixture priors.