Related papers: MLE-induced Likelihood for Markov Random Fields
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
We describe a Bayesian approach to estimating luminosity functions. We derive the likelihood function and posterior probability distribution for the luminosity function, given the observed data, and we compare the Bayesian approach with…
In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form $Z = \int L(x) d P(x)$, where $L$ is a target function (often a likelihood) and $P$ a finite measure. We present vertical-likelihood…
Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…
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…
Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $\Omega$ such that one is able to…
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…
The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on…
In this paper, the weak convergence of impulsive recurrent process with Markov switching in the scheme of Levy approximation is proved. For the relative compactness, a method proposed by R. Liptser for semimartingales is used with a…
The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…
We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…
We investigate the use of the Multiple Optimised Parameter Estimation and Data compression algorithm (MOPED) for data compression and faster evaluation of likelihood functions. Since MOPED only guarantees maintaining the Fisher matrix of…
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated…
This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of $\varepsilon$-perturbed bisimulation…