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Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
We develop an extension of the classical Zellner's g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
We study a class of $\Z^{d}$-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and even…
We study two generalizations of the gamma-expansion of Eulerian polynomials from the viewpoint of the decompositions of statistics. We first present an expansion formula of the trivariate Eulerian polynomials, which are the enumerators for…
Time Series forecasting (univariate and multivariate) is a problem of high complexity due the different patterns that have to be detected in the input, ranging from high to low frequencies ones. In this paper we propose a new model for…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
In this paper, first we give the cohomologies of an $n$-Hom-Lie algebra and introduce the notion of a derivation of an $n$-Hom-Lie algebra. We show that a derivation of an $n$-Hom-Lie algebra is a $1$-cocycle with the coefficient in the…
Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among…
We consider the Heath-Jarrow-Morton model of forward rates processes with linear volatility. The noise is either a Wiener or a pure jump Leevy process. We provide formulae for the forward rate processes, and discus the problem of their…
Machine learning traditionally assumes that the training and testing data are distributed independently and identically. However, in many real-world settings, the data distribution can shift over time, leading to poor generalization of…
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess…
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this…
In this study, we develop a latent factor model for analysing high-dimensional binary data. Specifically, a standard probit model is used to describe the regression relationship between the observed binary data and the continuous latent…
A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In…
In this paper we study universal central extensions and non-abelian tensor product of hom-Lie-Rinehart algebras. We discuss about universal $\alpha$- central extensions, and, lifting of automorphisms and $\alpha$-derivations to central…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $\alpha^k$-derivations and provide a classification in low dimension. We…