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Bayesian Analysis of Stellar Evolution. Team Members: Steve DeGennaro (UT) Elizabeth Jeffery (STScI) Bill Jefferys (UT, UVM) Nathan Stein (Harvard) David van Dyk (UC, Irvine) PI: Ted von Hippel (Siena, UT). EuroWD2010, Tubingen August 16-20, 2010. from Hugh Harris: - PowerPoint PPT Presentation
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EuroWD2010, Tubingen August 16-20, 2010
Bayesian Analysis of Bayesian Analysis of Stellar EvolutionStellar Evolution
Team Members:Steve DeGennaro (UT)Elizabeth Jeffery (STScI)Bill Jefferys (UT, UVM)Nathan Stein (Harvard)David van Dyk (UC, Irvine)PI: Ted von Hippel (Siena, UT)
from Hugh Harris:“160 WDs with new or improved USNO parallaxes that will be in our next paper (Dahn et al AJ 2011, almost completed)”
Bayesian Approach
• Write Bayes equation for this problem, cannot analytically integrate it
• Simulate star clusters, binaries, single white dwarfs using isochrones, IFMR, WD cooling and atmosphere models, then recover input parameters using MCMC
• Markov chain Monte Carlo constructs a draw from the posterior distributions that are used to infer the quantities of interest (stellar masses, ages)
dist
[Fe/H]
dust
0.9
0.5
? ?
MWD crystal
MWD cooling
precursor ages
star A
star BA+B
Das Ende
Bayesian Inference
posterior distribution α likelihood * priororp(model|data) = p(data|model) * p(model) / p(data)
with Θ = model or model parameters
p(data) = ∫ p(data| Θ) p(Θ) d Θ
→ Markov Chain Monte Carlo
Theory: Ingredients
1. IMF (e.g., Miller & Scalo 1979)
2. pre-WD evolution (e.g., Girardi et al. 2000)
3. Initial-Final Mass Relation (e.g., Weidemann 2000)
4. WD cooling time scales (e.g., Wood 1992)
5. WD atmosphere colors (e.g., Bergeron et al. 1995)
6. binaries, non-DA/DA ratio, Mwd,up
7. other variants on the above
Sarajedini et al. 1999
NGC 188
0.30.8
1.0
An Example