Likelihood based inference for observed and partially observed diffusions
نویسندگان
چکیده
This paper provides methods for carrying out likelihood based inference on non-linear observed and partially observed non-linear diffusions. The diffusions can potentially be non-stationary. The methods are based on innovative Markov chain Monte Carlo methods combined with an augmentation strategy. We study the performance of the methods as the degree of augmentation goes to infinity and find that the methods are robust. Various extensions to the modelling framework are provided, while we also discuss issues of model choice, model checking and filtering.
منابع مشابه
Exact and computationally efficient likelihood–based estimation for discretely observed diffusion processes
The objective of this paper is to present a novel methodology for likelihood-based inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation.
متن کاملInference for the Type-II Generalized Logistic Distribution with Progressive Hybrid Censoring
This article presents the analysis of the Type-II hybrid progressively censored data when the lifetime distributions of the items follow Type-II generalized logistic distribution. Maximum likelihood estimators (MLEs) are investigated for estimating the location and scale parameters. It is observed that the MLEs can not be obtained in explicit forms. We provide the approximate maximum likelihood...
متن کاملLikelihood based inference for correlated diffusions
We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observe...
متن کاملSimple simulation of diffusion bridges with application to likelihood inference for diffusions
With a view to likelihood inference for discretely observed diffusion type models, we propose a simple method of simulating approximations to diffusion bridges. The method is applicable to all one-dimensional diffusion processes and has the advantage that simple simulation methods like the Euler scheme can be applied to bridge simulation. Another advantage over other bridge simulation methods i...
متن کاملEstimation in discretely observed diffusions killed at a threshold
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modeled as discretely observed diffusions which are killed when the threshold is reached. Statisti...
متن کامل