Related papers: Variance Reduction Methods for Dirichlet Expectati…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…
The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. This study shows that ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has…
Recent work in variational inference (VI) uses ideas from Monte Carlo estimation to tighten the lower bounds on the log-likelihood that are used as objectives. However, there is no systematic understanding of how optimizing different…
Random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors…
Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
Meta-analyses of two-group studies that report median differences typically rely on methods that require, in addition to the median difference and sample size, summary measures of dispersion such as quartiles or ranges. Studies that do not…
This paper explores test-agnostic long-tail recognition, a challenging long-tail task where the test label distributions are unknown and arbitrarily imbalanced. We argue that the variation in these distributions can be broken down…
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong…
This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…
Precise estimation of uncertainty in predictions for AI systems is a critical factor in ensuring trust and safety. Deep neural networks trained with a conventional method are prone to over-confident predictions. In contrast to Bayesian…
In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…
We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that…
Simplex-valued data appear throughout statistics and machine learning, for example in the context of transfer learning and compression of deep networks. Existing models for this class of data rely on the Dirichlet distribution or other…
E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
We present unbiased, finite--variance estimators of energy derivatives for real--space diffusion Monte Carlo calculations within the fixed--node approximation. The derivative $d_\lambda E$ is fully consistent with the dependence…