Bayesian Methods for Astrophysics and Particle Physics

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Declaration This dissertation is the result of work carried out in the Astrophysics Group of the Cavendish Laboratory, Cambridge, between October 2005 and September 2008. Except where explicit reference is made to the work of others, the work contained in this dissertation is my own, and is not the outcome of work done in collaboration. No part of this dissertation has been submitted for a degree, diploma or other qualification at this or any other university. The total length of this dissertation does not exceed sixty thousand words. Farhan Feroz 18th September 2008
Page 1: Bayesian Methods for Astrophysics a
Page 7: Acknowledgements I acknowledge fina
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 Improved Ellipsoidal Sampling M
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2.5.4.2 Method 2 2.5 Improved Ellip
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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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