Download Bayesian Spectral Line Fitting

Bayesian Spectral Line Fitting
Dr. Michelle Lochner
With Ian Harrison & Michael Brown
https://arxiv.org/abs/1704.08278
The Problem with Spectra
Radio spectra can be noisy, contaminated with RFI
and containing very faint spectral lines
SKA HI Galaxy Survey
HI emission line is one of the few spectral features
of radio galaxies
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
Continuum
selected galaxies
(not a blind HI
data cube search)
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
Model Comparison
vs.
We use Bayesian model comparison to decide if the HI line profile
(with 6 parameters) is a better fit than a completely flat line
(consistent with pure noise)
Results
SNR ~ 11
Results
SNR ~ 11
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 2)
?
B>6 evidence cut
Multimodal P(z)
P(z)
N(z)
Conclusions
We’ve developed a promising, automated, general
approach to spectral line fitting in the radio
Allows more realistic number counts for forecasts
We introduce statistical rigour into detection
The Bayesian nature of the technique allows for
correct uncertainty propagation and interesting
extentions
Go to https://arxiv.org/abs/1704.08278 to read the
paper and get the code
Email me at: [email protected]