Bayesian Methods for Astrophysics and Particle Physics

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Acknowledgements I acknowledge financial support in the form of research studentships from the Cambridge Commonwealth Trust, Isaac Newton Trust and the Pakistan Higher Education Commission. I am extremely grateful to Mike Hobson for his tireless help and en- couragement over the past three years and showing me how research is done. I would also like to thank Keith Grainge and Richard Saun- ders for their help and explanations about matters concerning exper- imental astrophysics. I would like to thank all the students and postdocs in the Astrophysics group who helped me in various things. I would like to especially mention Jon Zwart for his ever willingness to help in anything and Michael Bridges for helping me see the funny side of things. I also thank David Titterington for his help with local computing issues and Victor Travieso, Andrey Kaliazin and Stuart Ranking for their help with COSMOS and Darwin supercomputing facilities. I am grateful to Mike Hobson, Richard Saunders and Jon Zwart for proof reading various parts of this thesis and giving useful feedback.
Page 1: Bayesian Methods for Astrophysics a
Page 5: I would like to dedicate this thesi
Page 10 and 11: The impending start-up of the Large
Page 12 and 13: CONTENTS 2.4.2 Recursive Clustering
Page 14 and 15: CONTENTS 5 Bayesian Analysis of Mul
Page 16 and 17: LIST OF FIGURES 2.2 Cartoon of elli
Page 18 and 19: LIST OF FIGURES 3.6 1-D Marginalize
Page 20 and 21: LIST OF FIGURES 5.1 Spectral index
Page 23 and 24: Chapter 1 Bayesian Inference This f
Page 25 and 26: Since, Pr(f|D) = = = Pr(f,Θ|D)d
Page 27 and 28: 1.4 Combining Data-Sets While for p
Page 29 and 30: 1.5 Comparing Data-Sets would point
Page 31 and 32: 1.5 Comparing Data-Sets are consist
Page 33 and 34: 1.6 Numerical Methods 1.6 Numerical
Page 35 and 36: 1.6 Numerical Methods posterior pro
Page 37 and 38: 1.6 Numerical Methods posterior are
Page 39 and 40: Chapter 2 Multimodal Nested Samplin
Page 41 and 42: 2.2 Introduction as a multivariate
Page 43 and 44: (a) (b) 2.3 Nested Sampling Figure
Page 45 and 46: 2.3 Nested Sampling could, however,
Page 47 and 48: the probability of the vector t = (
Page 49 and 50: 2.4.2 Recursive Clustering 2.4 Elli
Page 51 and 52: 2.5 Improved Ellipsoidal Sampling M
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2.5.4.2 Method 2 2.5 Improved Ellip
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2.5 Improved Ellipsoidal Sampling M
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2.6 Metropolis Nested Sampling wher
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2.7 Applications Figure 2.5: Toy Mo
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2.7 Applications points, switched o
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Toy model 1b Real Value Method 2 Me
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Likelihood 5 4 3 2 1 -6 0 -4 -2 2 0
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2.8 Bayesian Object Detection Apply
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y (pixels) 200 150 100 50 0 0 50 10
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2.8 Bayesian Object Detection full
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2.8.4 Results 2.8 Bayesian Object D
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2.9 Discussion and Conclusions real
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2.9 Discussion and Conclusions The
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Chapter 3 MultiNest: An Efficient &
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3.3 The MultiNest Algorithm in the
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3.3 The MultiNest Algorithm We now
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3.3 The MultiNest Algorithm Algorit
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3.3 The MultiNest Algorithm discuss
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3.3 The MultiNest Algorithm algorit
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3.3 The MultiNest Algorithm If, how
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3.3 The MultiNest Algorithm this il
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It is easy to check that the prescr
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3.4 Applications Owing to the highl
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Analytical MultiNest 3.4 Applicatio
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3.5 Cosmological Model Selection Th
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H 0 100 90 80 70 60 50 3.5 Cosmolog
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3.6 Comparison of MultiNest and MCM
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MCMC(3200) MCMC(48000) MultiNest 0.
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3.7 Discussion and Conclusions Appe
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Chapter 4 Cluster Detection in Weak
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4.3 Methodology astrophysical under
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Σcrit = c2 4πG Ds DlDls 4.3 Metho
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as: 4.3 Methodology If one assumes
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4.4 Application to Mock Data: 4.4 A
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4.4 Application to Mock Data: Recov
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True Positive Rate 1 0.8 0.6 0.4 0.
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x/arcsec 1000 500 0 -500 -1000 1 2
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4.5 Application to Mock Data: Wide-
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1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0
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x/arcsec z x/arcsec z 6000 4000 200
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∆z ∆z 1 0.5 0 -0.5 4.5 Applicat
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4.6 Conclusions the importance of t
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5.2 Introduction Bayesian evidence,
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5.3 The Arcminute Microkelvin Image
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5.4 Cluster Modelling through the S
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5.5 Application to Simulated SZ Obs
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y 0 /arcsec r core /h −1 kpc β M
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Parameters Priors x0, y0 Mgas 5.6 A
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5.7 Conclusions 5.7 Conclusions We
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6.2 Introduction such as superpartn
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6.2 Introduction have used Markov C
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6.3 The Analysis SM parameters Mean
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and 6.3 The Analysis χ 2 = (ci −
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6.3 The Analysis also included by t
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L/Lmax 1 0.75 0.5 0.25 constraint p
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6.4 Results Prior “2 TeV” “4
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6.4 Results fits. In the left-hand
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P/Pmax P/Pmax 1 0.75 0.5 0.25 0 1 0
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µ > 0 µ < 0 Parameter 68% region
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6.4 Results These results can be se
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We evaluate 6.5 Summary and Conclus
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Chapter 7 Future Work In this final
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References Alfano, S. & Greer, M. (
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REFERENCES Baer, H. & Balázs, C. (
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REFERENCES Bridges, M., Lasenby, A.
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REFERENCES Pooley, G., Rajguru, N.,
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REFERENCES Feroz, F., Hobson, M.P.
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REFERENCES Hennawi, J.F. & Spergel,
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REFERENCES Korolev, V.A., Sunyaev,
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REFERENCES Marshall, P. (2006). Phy
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REFERENCES Passera, M. (2007). Prec
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REFERENCES Sievers, J. et al. (2007
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REFERENCES The LEP Collaborations,
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REFERENCES Zwart, J.T.L. et al. (20
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