## Bayesian methods for gravitational waves and neural networks

##### View / Open Files

##### Authors

Graff, Philip B.

##### Advisors

Lasenby, Anthony N.

Hobson, Michael P.

##### Date

2012-10-09##### Awarding Institution

University of Cambridge

##### Author Affiliation

Department of Physics

##### Qualification

PhD

##### Language

English

##### Type

Thesis

##### Metadata

Show full item record##### Citation

Graff, P. B. (2012). Bayesian methods for gravitational waves and neural networks (doctoral thesis).

##### Abstract

Einstein’s general theory of relativity has withstood 100 years of testing
and will soon be facing one of its toughest challenges. In a few years
we expect to be entering the era of the first direct observations of gravitational
waves. These are tiny perturbations of space-time that are generated
by accelerating matter and affect the measured distances between
two points. Observations of these using the laser interferometers, which
are the most sensitive length-measuring devices in the world, will allow
us to test models of interactions in the strong field regime of gravity and
eventually general relativity itself.
I apply the tools of Bayesian inference for the examination of gravitational
wave data from the LIGO and Virgo detectors. This is used for signal
detection and estimation of the source parameters. I quantify the ability
of a network of ground-based detectors to localise a source position
on the sky for electromagnetic follow-up. Bayesian criteria are also applied
to separating real signals from glitches in the detectors. These same
tools and lessons can also be applied to the type of data expected from
planned space-based detectors. Using simulations from the Mock LISA
Data Challenges, I analyse our ability to detect and characterise both burst
and continuous signals. The two seemingly different signal types will be
overlapping and confused with one another for a space-based detector; my
analysis shows that we will be able to separate and identify many signals
present.
Data sets and astrophysical models are continuously increasing in complexity.
This will create an additional computational burden for performing
Bayesian inference and other types of data analysis. I investigate the
application of the MOPED algorithm for faster parameter estimation and
data compression. I find that its shortcomings make it a less favourable
candidate for further implementation.
The framework of an artificial neural network is a simple model for the
structure of a brain which can “learn” functional relationships between sets
of inputs and outputs. I describe an algorithm developed for the training of
feed-forward networks on pre-calculated data sets. The trained networks
can then be used for fast prediction of outputs for new sets of inputs. After
demonstrating capabilities on toy data sets, I apply the ability of the
network to classifying handwritten digits from the MNIST database and
measuring ellipticities of galaxies in the Mapping Dark Matter challenge.
The power of neural networks for learning and rapid prediction is also
useful in Bayesian inference where the likelihood function is computationally
expensive. The new BAMBI algorithm is detailed, in which our
network training algorithm is combined with the nested sampling algorithm
MULTINEST to provide rapid Bayesian inference. Using samples
from the normal inference, a network is trained on the likelihood function
and eventually used in its place. This is able to provide significant increase
in the speed of Bayesian inference while returning identical results. The
trained networks can then be used for extremely rapid follow-up analyses
with different priors, obtaining orders of magnitude of speed increase.
Learning how to apply the tools of Bayesian inference for the optimal
recovery of gravitational wave signals will provide the most scientific information
when the first detections are made. Complementary to this, the
improvement of our analysis algorithms to provide the best results in less
time will make analysis of larger and more complicated models and data
sets practical.

##### Keywords

Bayesian inference, Gravitational waves, Machine learning

##### Identifiers

This record's URL: http://www.dspace.cam.ac.uk/handle/1810/244270

##### Rights

Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales

Licence URL: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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