Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data

TL;DR

This paper introduces a Bayesian state space modeling approach for inverse problems in astrophysics, specifically estimating galactic mass density from incomplete kinematic data without relying on training data or Gaussian Processes.

Contribution

It develops a novel Bayesian framework that models the likelihood via state space densities and employs adaptive MCMC for inference, applicable to real and synthetic galactic data.

Findings

Effective estimation of galactic mass density from missing data

Successful application to synthetic and real galaxy datasets

Demonstrates the method's robustness without training data

Abstract

In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with situations in which training data is not available. Then we cannot model the unknown functional relationship between data and the unknown model function (or parameter vector) with a Gaussian Process of appropriate dimensionality. A Bayesian method based on state space modelling is advanced instead. Within this framework, the likelihood is expressed in terms of the probability density function ($pdf$) of the state space variable and the sought model parameter vector is embedded within the domain of this $pdf$. As the measurable vector lives only inside an identified sub-volume of the system state space, the $pdf$ of the state space variable is projected onto the space of the measurables, and it is in terms of the projected state space density that the likelihood is written; the final form of the likelihood is achieved after convolution with the distribution of measurement errors. Application motivated vague priors are invoked and the posterior probability density of the model parameter vectors, given the data is computed. Inference is performed by taking posterior samples with adaptive MCMC. The method is illustrated on synthetic as well as real galactic data.