Related papers: On Parameter Estimation of Threshold Autoregressiv…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian…
We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…
The conditional autoregressive (CAR) model, simultaneous autoregressive (SAR) model, and its variants have become the predominant strategies for modeling regional or areal-referenced spatial data. The overwhelming wide-use of the CAR/SAR…
Empirical Bayes inference is based on estimation of the parameters of an a priori distribution from the observed data. The estimation technique of the parameters of the prior, called hyperparameters, is based on the marginal distribution…
Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning…
A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We…
A standard assumption in the Bayesian estimation of linear regression models is that the regressors are exogenous in the sense that they are uncorrelated with the model error term. In practice, however, this assumption can be invalid. In…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…
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…
In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed…
We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…