We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the var...
This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Inference.
There is not much literature on objective Bayesian analysis for binary classification problems, especially for intrinsic prior related methods. On the other hand, variational inference methods have been employed to solve classification problems using...
Variational Message Passing (VMP) provides an automatable and efficient algorithmic framework for approximating Bayesian inference in factorized probabilistic models that consist of conjugate exponential family distributions. The automation of Bayesi...
Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., image understanding, data fusion, medical diagnosis, fraud detection). This paper concerns inference in an importa...
The goal of this paper is to solve the problem of dynamic obstacle avoidance for a mobile platform using the stochastic optimal control framework to compute paths that are optimal in terms of safety and energy efficiency under constraints. We propose...
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian app...
Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures. We obtain functional data that are not only subject to noise along their y axis b...
It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the funct...
In this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with traject...
Bayesian statistical inference under unknown or hard to asses likelihood functions is a very challenging task. Currently, approximate Bayesian computation (ABC) techniques have emerged as a widely used set of likelihood-free methods. A vast number of...
12 January 2021
In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used beca...
When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are updated as...
In the past few decades, probabilistic interpretations of brain functions have become widespread in cognitive science and neuroscience. In particular, the free energy principle and active inference are increasingly popular theories of cognitive funct...
Background: Hantavirus disease in humans is rare but frequently lethal in the Neotropics. Several abundant and widely distributed Sigmodontinae rodents are the primary hosts of Orthohantavirus and, in combination with other factors, these rodents can...
The computerization of many everyday tasks generates vast amounts of data, and this has lead to the development of machine-learning methods which are capable of extracting useful information from the data so that the data can be used in future decisi...
The analysis of population-wide datasets can provide insight on the health status of large populations so that public health officials can make data-driven decisions. The analysis of such datasets often requires highly parameterized models with diffe...
Invasive woodland pests have substantial ecological, economic, and social impacts, harming biodiversity and ecosystem services. Mathematical modelling informed by Bayesian inference can deepen our understanding of the fundamental behaviours of invasi...
The reliability of Internet of Things systems is critical for industrial applications; however, operational reliability data are often heterogeneous and strongly right-skewed, exhibiting non-Gaussian behaviour, overdispersion, and production-level va...
In models with nuisance parameters, Bayesian procedures based on Markov Chain Monte Carlo (MCMC) methods have been developed to approximate the posterior distribution of the parameter of interest. Because these procedures require burdensome computati...
Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that i...
Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and assess whether using the previous...
The Hidden Markov Model (HMM) is a crucial probabilistic modeling technique for sequence data processing and statistical learning that has been extensively utilized in various engineering applications. Traditionally, the EM algorithm is employed to f...
In this study, the estimation methods of bias-corrected maximum likelihood (BCML), bootstrap BCML (B-BCML) and Bayesian using Jeffrey’s prior distribution were proposed for the inverse Gaussian distribution with small sample cases to obtain the...
This paper introduces a novel variational inference (VI) method with Bayesian and gradient descent techniques. To facilitate the approximation of the posterior distributions for the parameters of the models, the Stein method has been used in Bayesian...
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally efficient app...
Variational Bayesian Approximation (VBA) is a fast technique for approximating Bayesian computation. The main idea is to assess the joint posterior distribution of all the unknown variables with a simple expression. Mean–Field Variational Bayes...
Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas pr...
In this paper, we propose a structured additive regression (STAR) model for modeling the occurrence of a disease in fields or nurseries. The methodological approach involves a Gaussian field (GF) affected by a spatial process represented by an approx...
The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP), information theory, relative entropy and the Kullback–Leibler (KL) divergence, Fisher information and its corre...
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian discrepancy measure used in testing precise statistical hypotheses. In particular, we derive results on third-order asymptotic appr...
The increased ambition of architects coupled with advancements in structural materials, as well as the rapidly increasing pressure on civil engineering sector to reduce embodied carbon, have resulted in longer spans and more slender pedestrian struct...
Censored data are frequently found in diverse fields including environmental monitoring, medicine, economics and social sciences. Censoring occurs when observations are available only for a restricted range, e.g., due to a detection limit. Ignoring c...
This study introduces a new variational Bayesian adaptive estimator that enhances traditional interactive multiple model (IMM) frameworks for maneuvering target tracking. Conventional IMM algorithms struggle with rapid maneuvers due to model-switchin...
Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion f...
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new metho...
The loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop-cutting contribution index. Compared with t...
Generative Bayesian Computation (GBC) provides a simulation-based approach to Bayesian inference. A Quantile Neural Network (QNN) is trained to map samples from a base distribution to the posterior distribution. Our method applies equally to parametr...
To infer the introduction sources of the oriental fruit fly, Bactrocera dorsalis, we used a mitochondrial marker to reconstruct the haplotype network and 15 microsatellite loci to reveal genetic structure and relationships between the geographically...
For non-ignorable missing response variables, the mechanism of whether the response variable is missing can be modeled through logistic regression. In Bayesian computation, the lack of a conjugate prior for the logistic function poses a significant c...
Particle-based Variational Inference (ParVI) methods have been widely adopted in deep Bayesian inference tasks such as Bayesian neural networks or Gaussian Processes, owing to their efficiency in generating high-quality samples given the score of the...
Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is...
The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent G...
Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuou...
In this article, the estimation of the parameters and the reliability and hazard functions for Weibull inverted exponential (WIE) distribution is considered based on progressive first-failure censoring (PFFC) data. For non-Bayesian inference, maximum...
Groundwater vulnerability assessment (GVA) is critical for understanding contaminant migration into groundwater systems, yet conventional methods often overlook its probabilistic nature. Bayesian inference offers a robust framework using Bayes’ rule...
In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihoo...
This paper presents a comprehensive study on the estimation of multicomponent stress–strength reliability under progressively censored data, assuming the inverse Rayleigh distribution. Both maximum likelihood estimation and Bayesian estimation...
We developed Variational Laplace for Bayesian neural networks (BNNs), which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational...
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensi...
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