相关论文: Appropriate and Inappropriate Estimation Technique…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

To compare different forecasting methods on demand series we require an error measure. Many error measures have been proposed, but when demand is intermittent some become inapplicable, some give counter-intuitive results, and there is no…

The Potts model is frequently used to describe the behavior of image classes, since it allows to incorporate contextual information linking neighboring pixels in a simple way. Its isotropic version has only one real parameter beta, known as…

The Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solutions, the classical estimators such as the maximum a…

Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…

We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating relationship between a response variable and its covariates. Specifically, modal regression…

It is often desirable to summarise a probability measure on a space $X$ in terms of a mode, or MAP estimator, i.e.\ a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention. This paper presents two strategies for evaluating these subsidiary metrics under a policy that is…

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…

The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…

Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such…

We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of the system within a prescribed basis. We estimate the…

State and parameter estimation, along with fault detection, are three crucial estimation problems within the control systems community. Although different approaches have been proposed for each type of problem, the modulating function…

In practical applications, data is used to make decisions in two steps: estimation and optimization. First, a machine learning model estimates parameters for a structural model relating decisions to outcomes. Second, a decision is chosen to…