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Spyridon J. Hatjispyros

Publications and source records attributed to Spyridon J. Hatjispyros.

10 recordsLinked to original sources
arXiv2019

A Bayesian nonparametric approach to the approximation of the global stable manifold

We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo (MCMC) methods for unveiling the structure of the invariant global stable manifold from observed time-series data. The underlying unknown dynamical process is possibly contaminated by additive noise. We introduce the Stable Manifold Geometric Stick Breaking Reconstruction (SM-GSBR) model with which we reconstruct the unknown dynamic equations and in parallel we estimate the global structure of the perturbed stable manifold. Our method works for noninvertible maps without modifications. The stable manifold estimation procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.

stat.AP↗
arXiv2019

Joint reconstruction and prediction of random dynamical systems under borrowing of strength

We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo (MCMC) methods for the joint reconstruction and prediction of discrete time stochastic dynamical systems, based on $m$-multiple time-series data, perturbed by additive dynamical noise. We introduce the Pairwise Dependent Geometric Stick-Breaking Reconstruction (PD-GSBR) model, which relies on the construction of a $m$-variate nonparametric prior over the space of densities supported over $\mathbb{R}^m$. We are focusing in the case where at least one of the time-series has a sufficiently large sample size representation for an independent and accurate Geometric Stick-Breaking estimation, as defined in Merkatas et al. (2017). Our contention, is that whenever the dynamical error processes perturbing the underlying dynamical systems share common characteristics, underrepresented data sets can benefit in terms of model estimation accuracy. The PD-GSBR estimation and prediction procedure is demonstrated specifically in the case of maps with polynomial nonlinearities of an arbitrary degree. Simulations based on synthetic time-series are presented.

stat.ME↗
arXiv2018

A Bayesian Nonparametric Approach to Dynamical Noise Reduction

We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods (MCMC). The underlying unknown noise process (possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise Reduction Replicator (DNRR) model with which we reconstruct the unknown dynamic equations and in parallel we replicate the dynamics under reduced noise level dynamical perturbations. The dynamic noise reduction procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.

stat.ME↗
arXiv2017

A Bayesian Nonparametric approach to Reconstruction and Prediction of Random Dynamical Systems

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

stat.AP↗
arXiv2017

Dependent Mixtures of Geometric Weights Priors

A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking processes. This approach is based on a new random central masses version of the Pairwise Dependent Dirichlet Process prior mixture model (PDDP) first introduced in Hatjispyros et al. (2011). The idea is to create pairwise dependence through random measures that are location-preserving-expectations of Dirichlet random measures. Our contention is that mixture modeling with Pairwise Dependent Geometric Stick Breaking Process (PDGSBP) priors is sufficient for prediction and estimation purposes; moreover the associated Gibbs sampler is much faster and easier to implement than its Dirichlet Process based counterpart. To this respect, we provide a-priori-synchronized comparison studies under sparse $m$-scalable synthetic and real data examples.

stat.ME↗
arXiv2015

A High Accuracy Stochastic Estimation of a Nonlinear Deterministic Model

In this paper, an approach to estimating a nonlinear deterministic model is presented. We introduce a stochastic model with extremely small variances so that the deterministic and stochastic models are essentially indistinguishable from each other. This point is explained in the paper. The estimation is then carried out using stochastic optimisation based on Markov chain Monte Carlo (MCMC) methods.

stat.ME↗
arXiv2015

Dependent Random Density Functions with Common Atoms and Pairwise Dependence

The paper is concerned with constructing pairwise dependence between $m$ random density functions each of which is modeled as a mixture of Dirichlet process model. The key to this is how to create dependencies between random Dirichlet processes. The present paper adopts a plan previously used for creating pairwise dependence, with the simplification that all random Dirichlet processes share the same atoms. Our contention is that for all dependent Dirichlet process models, common atoms are sufficient. We show that by adopting common atoms, it is possible to compute the $L_p$ distances between all pairs of random probability measures.

math.ST↗
arXiv2015

Bayesian Nonparametric Density Estimation under Length Bias

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to computationally evaluate posterior quantities conditionally on length biased data were hindered by the inability to circumvent the problem of a normalizing constant. In this paper we present a novel Bayesian nonparametric approach to the length bias sampling problem which circumvents the issue of the normalizing constant. Numerical illustrations as well as a real data example are presented and the estimator is compared against its frequentist counterpart, the kernel density estimator for indirect data of Jones (1991).

math.ST↗
arXiv2007

A Fleming--Viot process and Bayesian nonparametrics

This paper provides a construction of a Fleming--Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the Chapman--Kolmogorov consistency conditions which allows a simple derivation of such a Fleming--Viot process, once a key and apparently new combinatorial result for Pólya-urn sequences has been established.

math.PR↗