Deviderjit Singh Sivia

Bio: Deviderjit Singh Sivia is an academic researcher. The author has contributed to research in topics: Estimation theory & Nested sampling algorithm. The author has an hindex of 1, co-authored 1 publications receiving 1946 citations.

Data analysis : a Bayesian tutorial

Abstract: 1. The Basics 2. Parameter Estimation I 3. Parameter Estimation II 4. Model Selection 5. Assigning Probabilities 6. Non-parametric Estimation 7. Experimental Design 8. Least-Squares Extensions 9. Nested Sampling 10. Quantification Appendices Bibliography

Cosmological parameters from CMB and other data: A Monte Carlo approach

Abstract: We present a fast Markov chain Monte Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent cosmic microwave background ~CMB! experiments and provide parameter constraints, including s 8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae type Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass ( mn&0.3 eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendixes we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.

Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses

Abstract: In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation of our methods will be publicly released shortly.

Trigonometric parallaxes of high mass star forming regions: the structure and kinematics of the milky way

Abstract: Over 100 trigonometric parallaxes and proper motions for masers associated with young, high- mass stars have been measured with the Bar and Spiral Structure Legacy Survey, a Very Long Baseline Array key science project, the European VLBI Network, and the Japanese VLBI Exploration of Radio Astrometry project. These measurements provide strong evidence for the existence of spiral arms in the MilkyWay, accurately locating many arm segments and yielding spiral pitch angles ranging from about 7 degrees to 20 degrees. The widths of spiral arms increase with distance from the Galactic center. Fitting axially symmetric models of the MilkyWay with the three- dimensional position and velocity information and conservative priors for the solar and average source peculiar motions, we estimate the distance to the Galactic center, R-0, to be 8.34 +/- 0.16 kpc, a circular rotation speed at the Sun, Theta(0), to be 240 +/- 8 km s(-1), and a rotation curve that is nearly flat ( i. e., a slope of -0.2 +/- 0.4 km s(-1) kpc(-1)) between Galactocentric radii of approximate to 5 and 16 kpc. Assuming a " universal" spiral galaxy form for the rotation curve, we estimate the thin disk scale length to be 2.44 +/- 0.16 kpc. With this large data set, the parameters R-0 and Theta(0) are no longer highly correlated and are relatively insensitive to different forms of the rotation curve. If one adopts a theoretically motivated prior that high- mass star forming regions are in nearly circular Galactic orbits, we estimate a global solar motion component in the direction of Galactic rotation, V-circle dot = 14.6 +/- 5.0 km s(-1). While Theta(0) and V-circle dot are significantly correlated, the sum of these parameters is well constrained, Theta(0) + V circle dot = 255.2 +/- 5.1 km s(-1), as is the angular speed of the Sun in its orbit about the Galactic center, ( Theta(0) + V-circle dot)/R-0 = 30.57 +/- 0.43 km s(-1) kpc(-1). These parameters improve the accuracy of estimates of the accelerations of the Sun and the Hulse-Taylor binary pulsar in their Galactic orbits, significantly reducing the uncertainty in tests of gravitational radiation predicted by general relativity.

Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis

Abstract: In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional MCMC sampling methods. Second, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive. The nested sampling method introduced by Skilling (2004), has greatly reduced the computational expense of calculating evidences and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee et al. (2006), but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw et al. (2007), recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical datasets.

Cosmology and Fundamental Physics with the Euclid Satellite

Abstract: Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.