Related papers: What we talk about when we talk about fields
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function.…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…
We introduce NIFTY, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
We are interested in creating an automated or semi-automated system with the capability of taking a set of radar imagery, collection parameters and a priori map and other tactical data, and producing likely interpretations of the possible…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
Regression for spatially dependent outcomes poses many challenges, for inference and for computation. Non-spatial models and traditional spatial mixed-effects models each have their advantages and disadvantages, making it difficult for…
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
Reconstructing cosmological initial conditions (ICs) from late-time observations is a difficult task, which relies on the use of computationally expensive simulators alongside sophisticated statistical methods to navigate multi-million…
This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…
We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…
We discuss non-parametric density estimation and regression for astrophysics problems. In particular, we show how to compute non-parametric confidence intervals for the location and size of peaks of a function. We illustrate these ideas…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…