## Constrained space MCMC methods for nested sampling Bayesian computations

##### Typ

Examensarbete fÃ¶r masterexamen

##### Program

Physics and astronomy (MPPAS), MSc

##### Publicerad

2020

##### FÃ¶rfattare

Olander, Jacob

##### Modellbyggare

##### Tidskriftstitel

##### ISSN

##### Volymtitel

##### Utgivare

##### Sammanfattning

Natural phenomena can in general be described using several different scientific models,
which creates a need for systematic model selection. Bayesian model comparison assigns
relative probabilities to a set of possible models using the model evidence (marginal
likelihood), obtained by an integral that in general needs to be evaluated numerically.
Nested sampling is a conceptual framework that efficiently estimates the model evidence
and, additionally, provides samples from the model parameter posterior distribution used
in Bayesian parameter estimation. A vital step of nested sampling is the likelihoodconstrained
sampling of the model parameter prior distribution, a task that has proven
particularly difficult and that is subject to ongoing research. In this thesis we implement,
evaluate and compare three methods for constrained sampling in conjunction with a nested
sampling framework. The methods are variants of Markov chain Monte Carlo algorithms:
Metropolis, Galilean Monte Carlo and the affine-invariant stretch move, respectively. The
latter is applied in the context of nested sampling for the first time in this work. The
performances of the methods are assessed by their application to a reference problem
that has a known analytical solution. The problem is inspired by effective field theories
in subatomic physics where the model parameters take the form of coefficients that are
of natural size. We conclude that the efficiency and computational accuracy of nested
sampling is strongly dependent on the choice of sampling method and the settings of its
associated hyperparameters. In certain cases, especially for high-dimensional parameter
spaces, the implementations of this work are seen to achieve better computational accuracy
than MultiNest, a state-of-the-art nested sampling implementation extensively used
in astronomy and cosmology. Generally for nested sampling, we observe that it is possible
to obtain an inaccurate result without receiving any clear warning signs indicating that
this is the case. However, we demonstrate that the validity of the computational results
can be assessed by monitoring the sampling process.

##### Beskrivning

##### Ã„mne/nyckelord

Bayesian inference , parameter estimation , model comparison , evidence , nested sampling , MCMC , Metropolis , Galilean Monte Carlo , affine-invariant sampling