Related papers: Nested Sampling with Normalising Flows for Gravita…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…
We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…
Understanding the properties of transient gravitational waves and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astro-physical measurement in transient gravitational-wave…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…
We propose a novel method for computing $p$-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS…
We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a…
We describe an application of the MultiNest algorithm to gravitational wave data analysis. MultiNest is a multimodal nested sampling algorithm designed to efficiently evaluate the Bayesian evidence and return posterior probability densities…
The present operation of the ground-based network of gravitational-wave laser interferometers in "enhanced" configuration brings the search for gravitational waves into a regime where detection is highly plausible. The development of…
Iterative Gaussianization is a fixed-point iteration procedure that can transform any continuous random vector into a Gaussian one. Based on iterative Gaussianization, we propose a new type of normalizing flow model that enables both…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…