Bayesian Spectral Line Fitting
Dr. Michelle Lochner
In collaboration with Dr. Ian Harrison
The Problem with Spectra
Radio spectra can be noisy, contaminated with RFI
and containing very faint spectral lines
SKA HI Galaxy Survey
HI is intrinsically faint
High SNR requirement means very few high redshift
galaxies can actually be detected with the SKA
(Yahya et al. 2014)
This limits the usefulness of HI galaxies for
cosmology
SKADS Simulations
Obreschow et al. 2009
HI Line Profile
Obreschow et al. 2009
Signal to Noise Ratio
We use the SNR definition from Yahya et al. 2015
Line Fitting Approach
We want to:
Line Fitting Approach
We want to:
Be able to tell if there is a detectable HI line
Line Fitting Approach
We want to:
Be able to tell if there is a detectable HI line
Fit this with the HI line profile to estimate the
parameters (including redshift)
Line Fitting Approach
We want to:
Be able to tell if there is a detectable HI line
Fit this with the HI line profile to estimate the
parameters (including redshift)
Get the full probability distribution for the
parameters
Bayesian Statistics to the Rescue!
Introduction to Bayesian Statistics
Bayes' theorem tells us:
Introduction to Bayesian Statistics
Bayes' theorem tells us:
Posterior
Likelihood
Bayesian Evidence
Prior
Introduction to Bayesian Statistics
Bayesian Inference:
Hard to do for N dimensions
Marginalisation requires N dimensional integrals
Fortunately you can use numerical samplers like
MCMC or Nested Sampling
Example 1d
marginalised
posterior
σ
μ
Model Selection with Bayesian Evidence
Bayesian Evidence
Likelihood
Prior
Model Selection with Bayesian Evidence
Model Priors
Bayes Factor
Ratio of Posterior Odds
Model Selection with Bayesian Evidence
Bayes Factor
Model Selection with Bayesian Evidence
Jeffreys’ Scale
Trotta 2008
Preliminary Results
SNR ~ 11
Preliminary Results
SNR ~ 11
Preliminary Results
Black true, red maximum posterior fit
P(z)
Redshift estimates (band 1)
Redshift estimates (band 1)
B>6 evidence cut
Redshift estimates (band 1)
B>6 evidence cut
Redshift estimates (band 1)
B>6 evidence cut
Redshift estimates (band 2)
B>6 evidence cut
Redshift estimates (band 2)
B>6 evidence cut
Redshift estimates (band 2)
?
B>6 evidence cut
Multimodal P(z)
Conclusions
We’ve developed a promising, general approach to
spectral line fitting in the radio
This technique should allow higher numbers of high
redshift galaxies to be detected
We introduce statistical rigour into detection
The Bayesian nature of the technique allows
interesting extentions
Email me at:
[email protected]