Related papers: Nested Sampling Methods
In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae…
I describe an approach to fitting and comparison of radio spectra based on Bayesian analysis and realised using a new implementation of the nested sampling algorithm. Such an approach improves on the commonly used maximum-likelihood fitting…
Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
As data size and computing power increase, the architectures of deep neural networks (DNNs) have been getting more complex and huge, and thus there is a growing need to simplify such complex and huge DNNs. In this paper, we propose a novel…
Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the…
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…
Nested sampling is often used in Bayesian statistics problems in astronomy. It operates with a set of live points, iteratively replacing the point with the lowest likelihood with a new point of higher likelihood. Each iteration reduces the…
Two commonly arising computational tasks in Bayesian learning are Optimization (Maximum A Posteriori estimation) and Sampling (from the posterior distribution). In the convex case these two problems are efficiently reducible to each other.…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches…
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…
Score-based algorithms that learn the structure of Bayesian networks can be used for both exact and approximate solutions. While approximate learning scales better with the number of variables, it can be computationally expensive in the…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…