Related papers: Composite Bayesian inference
We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…
Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…
A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian prior or posterior.…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
Humans rely on effective representations to learn from few examples and abstract useful information from sensory data. Inducing such representations in machine learning models has been shown to improve their performance on various…
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…
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 networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
We outline how to create a mechanism that provides an optimal way to elicit, from an arbitrary group of experts, the probability of the truth of an arbitrary logical proposition together with collective information that has an explicit form…
Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…