Statistical Physics for Sparse Statistical Inference

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. There are mathematical similarities between the inference problems in statistics and statistical physics, and the viewpoint from statistical physics can help the quantitative understanding of inference problems. Over the last few years, it has been increasingly realised that ideas from statistical physics of disordered systems can help to develop new algorithms for important inference problems in different fields of application. This interdisciplinary field between statistical physics and statistics is now attracting much attention, but there is as yet no summarizing books to capture this synergy. This book will help researchers interested in the application of statistical inference and will enhance further development in statistical physics and statistics by presenting a review of the present landscape. It explains how the analytical tools of statistical physics can be exploited in the understanding wider inference problems. The authors describe how important statistical problems including maximum likelihood estimation, Bayesian inference, sparse estimation, information criterion and model selection can be mapped onto the statistical physics view and how the analytical tools of statistical physics can be used for solving such problems.

Key Features:

• First book on the topic

• Self-contained

• Mathematically accessible by grad students

• Author team of physicist and statistician