Related papers: Error structures and parameter estimation
A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending L\^e's theory in \cite{Le2020} to include weakly $C^k$-diffeological…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
We deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. Previous works by several authors have shown that the error structure of the method is characterized by…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
Estimating errors is a crucial part of any scientific analysis. Whenever a parameter is estimated (model-based or not), an error estimate is necessary. Any parameter estimate that is given without an error estimate is meaningless.…
We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data…
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $\alpha$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…