Marginalization with Moment Generating Functions with Applications in Astrostatistics
Abstract Number:
2009
Submission Type:
Contributed Abstract
Contributed Abstract Type:
Speed
Participants:
Siyang Li (1), David van Dyk (2), Maximilian Autenrieth (1)
Institutions:
(1) N/A, N/A, (2) Imperial College London, N/A
Co-Author(s):
Speaker:
Abstract Text:
We present a new analytical method to derive a likelihood function that is marginalised over a population. This method can be used for computational advantage in the context of Bayesian hierarchical models and marginal likelihood calculations in Bayesian models. The key innovation is the specification of the necessary integrals in terms of high-order (sometimes fractional) derivatives of the population prior moment-generating function, if particular existence and differentiability conditions hold.
We confine our attention to Poisson and gamma likelihood functions. Under Poisson likelihoods, the observed Poisson count determines the order of the derivative. Under gamma likelihoods, the shape parameter, which is assumed to be known, determines the order of the fractional derivative.
We also present examples validating this new analytical method. In some of the examples, the new method is the only known analytical method to calculate the integral, giving instantaneous and accurate calculations.
Keywords:
model evidences|fractional derivatives|moment-generating function|integration|Bayesian modeling|
Sponsors:
International Society for Bayesian Analysis (ISBA)
Tracks:
Miscellaneous
Can this be considered for alternate subtype?
Yes
Are you interested in volunteering to serve as a session chair?
Yes
I have read and understand that JSM participants must abide by the Participant Guidelines.
Yes
I understand that JSM participants must register and pay the appropriate registration fee by June 1, 2026. The registration fee is non-refundable.
I understand
You have unsaved changes.