Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations

We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function...

Bayesian inference of the multi-period optimal portfolio for an exponential utility

We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing the Jeffreys non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not...

Particle filter for aircraft mass estimation and uncertainty modeling

This article investigates the estimation of aircraft mass and thrust settings of departing aircraft using a recursive Bayesian method called particle filtering. The method is based on a nonlinear state-space system derived from aircraft point-mass performance models. Using only aircraft surveillance data, flight states such as position,...

Decompounding discrete distributions: A nonparametric Bayesian approach

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a Markov chain Monte Carlo...

Logit mixture with inter and intra-consumer heterogeneity and flexible mixing distributions

Logit mixture models have gained increasing interest among researchers and practitioners because of their ability to capture unobserved taste heterogeneity. Becker et al. (2018) proposed a Hierarchical Bayes (HB) estimator for logit mixtures with inter- and intra-consumer heterogeneity (defined as taste variations among different individuals...

Exact Network Reconstruction from Complete SIS Nodal State Infection Information Seems Infeasible

The SIS dynamics of the spread of a virus crucially depend on both the network topology and the spreading parameters. Since neither the topology nor the spreading parameters are known for the majority of applications, they have to be inferred from observations of the viral spread. We propose an inference method for both topology and spreading...

Aircraft Mass and Thrust Estimation Using Recursive Bayesian Method

This paper focuses on estimating aircraft mass and thrust setting using a recursive Bayesian method called particle filtering. The method is based on a nonlinear state-space system derived from aircraft point-mass performance models. Using solely ADS-B and Mode-S data, flight states such as position, velocity, and wind speed are collected and...

Diffusion Kurtosis Imaging with free water elimination: A Bayesian estimation approach

Purpose: Diffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the...

New Sparse-Promoting Prior for the Estimation of a Radar Scene with Weak and Strong Targets

In this paper, we consider the problem of estimating a signal of interest embedded in noise using a sparse signal representation (SSR) approach. This problem is relevant in many radar applications. In particular, estimating a radar scene consisting of targets with wide amplitude range can be challenging since the sidelobes of a strong target can...

A non-parametric Bayesian approach to decompounding from high frequency data

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density f0 of its jump sizes, as well as of its intensity λ0. We take a Bayesian approach to the problem and specify the prior on f0 as the Dirichlet location mixture of normal densities. An independent prior for λ0 is assumed to be...

Bayesian estimation for decision-directed stochastic control