Bayesian learning in the absence of training data, by embedding model parameters into support of the likelihood: applications to astrophysics
thesisposted on 23.10.2019, 14:10 by Cedric Spire
In this thesis I introduce a method on addressing the problem of learning in the absence of training data, when information on the distribution of the system parameters and of the observable that influences such parameters are also lacking. Additionally, it can be anticipated that the relation between the system parameter and observable vector, is nonlinear. I introduce the method for a stationary dynamical system for which the temporal evolution of the state space probability density function (pdf) is known, by embedding the sought system parameters into the support of the likelihood of the state space pdf. This allows to learn (the discretised versions of) the relevant system function as well as the state space pdf, using the only available test data on the observable. Inference is carried out using a Metropolis-within-Gibbs Markov Chain Monte Carlo (MCMC) scheme. I illustrate this new method empirically, by learning the system property of the real galaxy NGC4494 – namely its gravitational mass density function – and the pdf of the galactic state space vector, where test data comprises measured values of only half of the state space coordinates of resolved particles of the galaxy. Two distinct test datasets available for two distinct types of galactic particles are used. On the basis of my work, I reject the hypothesis that the state space pdf could be modelled using a parametric density that is symmetric about any point in its support. Additionally, the results show a large gravitational mass condensation near the centre of this galaxy, but I cannot reject the hypothesis that this central mass condensation is the supermassive black hole reported by some astronomers in NGC4494. Learning in this galaxy is conditional on the assumption of a simple (isotropic) model for the galactic state space. Then in the very distant galaxy 0047-281, I investigate if invoking ancillary information (comprising analysis of gravitational lensing measurements) can identify the solution for the galactic gravitational mass density, in spite of this potentially mis-specified model. I conclude that including the ancillary information definitely introduces identifiability to the mass density parameters, even within the given mis-specified model.
- Mathematical Sciences