Related papers: On Parameter Estimation of Threshold Autoregressiv…
The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double…
Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two…
We derive a variational representation for the log-normalizing constant of the posterior distribution in Bayesian linear regression with a uniform spherical prior and an i.i.d. Gaussian design. We work under the "proportional" asymptotic…
The pure tone hearing threshold is usually estimated from responses to stimuli at a set of standard frequencies. This paper describes a probabilistic approach to the estimation problem in which the hearing threshold is modelled as a smooth…
In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square…
We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…
So far, various techniques have been implemented for generating discrete distributions based on continuous distributions. The characteristics and properties of this kind of probability distributions have been studied. Furthermore, the…
Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
A technique for detecting errors made by Hidden Markov Model taggers is described, based on comparing observable values of the tagging process with a threshold. The resulting approach allows the accuracy of the tagger to be improved by…
Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…
The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable…
In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector by distribution. The…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…