Nonparametric analysis of CMB Nonparametric analysis of CMB power - - PowerPoint PPT Presentation

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Nonparametric analysis of CMB Nonparametric analysis of CMB power - - PowerPoint PPT Presentation

Sep 22, 2022 34 likes •257 views

Nonparametric analysis of CMB Nonparametric analysis of CMB power spectrum data and consistency power spectrum data and consistency test of cosmological models test of cosmological models Amir Aghamousa Asia Pacific Center for Theoretical

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Nonparametric analysis of CMB Nonparametric analysis of CMB power spectrum data and consistency power spectrum data and consistency test of cosmological models test of cosmological models

Amir Aghamousa

All models are false, some are useful. (George E. P. Box)

2nd APCTP-TUS workshop on Dark Energy August 03 ~ 05, 2015, Tokyo University of Science

Asia Pacific Center for Theoretical Physics, Pohang, South Korea

Bull pictures courtesy of “Pablo Picasso”

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I will talk about:

  • Model-independent estimation of CMB angular power spectrum

(with Arman Shafieloo, Mihir Arjunwadkar, Tarun Souradeep).

  • Nonparametric test of consistency between cosmological models

and CMB data (with Arman Shafieloo).

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Model-independent estimation of CMB angular power spectrum

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Timeline of the Universe

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CMB Anisotropies and the Power Spectrum

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WMAP 1/3/5/7: Power Spectrum Data

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Regression Problems

Data:

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Parametric regression

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Frequentist vs Bayesian

  • Frequentist

It defjnes a probability as the limit of its relative frequency in a large number of trials.

  • Bayesian

It defjnes a probability as a degree of belief. likelihood prior posterior

How to sample a high dimensional probability distribution?

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REACT: nonparametric regression

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(Aghamousa, Shafieloo, Arjunwadkar and Souradeep, JCAP, 2015)

Planck: Power Spectrum Data

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(Aghamousa, Shafieloo, Arjunwadkar and Souradeep, JCAP, 2015)

Planck 2013 power spectrum estimation

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Nonparametric fit

= = 95%

Confidence set in Function space

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(Aghamousa, Shafieloo, Arjunwadkar and Souradeep, JCAP, 2015)

Picks and dips

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(Aghamousa, Shafieloo, Arjunwadkar and Souradeep, JCAP, 2015)

Other results

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Nonparametric test of consistency between cosmological models and CMB data

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Nonparametric fit

= 95 % = = = ? %

Parametric fit

Best fit LCDM at 36%

Validating Cosmological Models

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Nonparametric fit

= = 95%

Calibrating Confidence distances

= 95% =

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Calibrating Confidence distances

(Aghamousa, Shafieloo, JCAP, 2015)

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Best fit LCDM at 95%

Bias control

(Aghamousa, Shafieloo, JCAP, 2015)

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Bias control

Best fit LCDM at 70%

(Aghamousa, Shafieloo, JCAP, 2015)

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Thank you