Related papers: Multi-Object Posterior Computation via Gibbs Sampl…
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…
If computational tractability were not an issue, multi-object estimation should integrate all measurements from multiple sensors across multiple scans. In this article, we propose an efficient numerical solution to the multi-scan…
Multi-object estimation in state-space models (SSMs) wherein the system state is represented as a finite set has attracted significant interest in recent years. In Bayesian inference, the posterior density captures all information on the…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
State space models in which the system state is a finite set--called the multi-object state--have generated considerable interest in recent years. Smoothing for state space models provides better estimation performance than filtering by…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
In multi-object inference, the multi-object probability density captures the uncertainty in the number and the states of the objects as well as the statistical dependence between the objects. Exact computation of the multi-object density is…
This paper proposes an efficient implementation of the multi-sensor generalized labeled multi-Bernoulli (GLMB) filter. The solution exploits the GLMB joint prediction and update together with a new technique for truncating the GLMB…
In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of…
We consider sparse Bayesian estimation in the classical multivariate linear regression model with $p$ regressors and $q$ response variables. In univariate Bayesian linear regression with a single response $y$, shrinkage priors which can be…
This paper considers multiple extended object tracking based on Poisson multi-Bernoulli mixture (PMBM) filtering, which gives the closed-form Bayesian solution for standard multiple extended object models with Poisson birth. To efficiently…
Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…
We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…
The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…
Multi-target state estimation refers to estimating the number of targets and their trajectories in a surveillance area using measurements contaminated with noise and clutter. In the Bayesian paradigm, the most common approach to…
P-splines provide a flexible setting for modeling nonlinear model components based on a discretized penalty structure with a relatively simple computational backbone. Under a Bayesian inferential framework based on Markov chain Monte Carlo,…