Related papers: Error Estimation in Approximate Bayesian Belief Ne…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…
Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…
We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
The willingness to trust predictions formulated by automatic algorithms is key in a vast number of domains. However, a vast number of deep architectures are only able to formulate predictions without an associated uncertainty. In this…
This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to…