Related papers: Computing the Dirichlet-Multinomial Log-Likelihood…
The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson--Dirichlet process $\operatorname {PD}(\alpha,\theta)$. We obtain distributional results yielding exact forms…
Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…
Density Functional Theory (DFT) is a widely used computational method for estimating the energy and behavior of molecules. Machine Learning Interatomic Potentials (MLIPs) are models trained to approximate DFT-level energies and forces at…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
Geosteering of wells requires fast interpretation of geophysical logs, which is a non-unique inverse problem. Current work presents a proof-of-concept approach to multi-modal probabilistic inversion of logs using a single evaluation of an…
For prediction of clustered time-to-event data, we propose a new deep neural network based gamma frailty model (DNN-FM). An advantage of the proposed model is that the joint maximization of the new h-likelihood provides maximum likelihood…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
Generative Artificial Intelligence (GenAI) models, with their powerful feature learning capabilities, have been applied in many fields. In mobile wireless communications, GenAI can dynamically optimize the network to enhance the user…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
The Postnikov character formula is used to express large portions of a Dirichlet character sum in terms of quadratic exponential sums. The quadratic sums are then computed using an analytic algorithm previously derived by the author. This…
We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finance. The method…
The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the…
In many applications (in particular information systems, such as pattern recognition, machine learning, cheminformatics, bioinformatics to name but a few) the assessment of uncertainty is essential - i.e., the estimation of the underlying…
Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY…
Normal mean-variance mixture distributions are widely applied to simplify a model's implementation and improve their computational efficiency under the Maximum Likelihood (ML) approach. Especially for distributions with normal mean-variance…
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,…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…