Related papers: Approximated maximum likelihood estimation in mult…
We introduce tools for inference in the multifractal random walk introduced by Bacry et al. (2001). These tools include formulas for smoothing, filtering and volatility forecasting. In addition, we present methods for computing conditional…
This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…
Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…
We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…
We obtain an exact formula for the first-passage time probability distribution for random walks on complex networks using inverse Laplace transform. We write the formula as the summation of finitely many terms with different frequencies…
The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter $\theta$ to be estimated identified…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the environment parameters based on a single observation of the path till the…
We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions…
Let $X$ be the constrained random walk on $\mathbb{Z}_+^d$ $d >2$, having increments $e_1$, $-e_i+e_{i+1}$ $i=1,2,3,...,d-1$ and $-e_d$ with probabilities $\lambda$, $\mu_1$, $\mu_2$,...,$\mu_d$, where $\{e_1,e_2,..,e_d\}$ are the standard…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with…
Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function…
We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…
Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In…