scispace - formally typeset
Search or ask a question
Author

Petter Wiberg

Bio: Petter Wiberg is an academic researcher from Goldman Sachs. The author has contributed to research in topics: Gibbs sampling & Estimation theory. The author has an hindex of 2, co-authored 2 publications receiving 97 citations.

Papers
More filters
Journal ArticleDOI
TL;DR: In this article, a deterministic scan Gibbs sampler was used to combine missing data in the unobserved solution components, and parameters, alternating between missing data and the observed solution components.
Abstract: Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact likelihoods for the transition densities are typically not known, approximations are used that are expected to work well in the limit of small intersample times Δt and large total observation times N Δt. Hypoellipticity together with partial observation leads to ill conditioning requiring a judicious combination of approximate likelihoods for the various parameters to be estimated. We combine these in a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters. Numerical experiments illustrate asymptotic consistency of the method when applied to simulated data. The paper concludes with an application of the Gibbs sampler to molecular dynamics data.

53 citations

Posted Content
TL;DR: In this paper, a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters is used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis.
Abstract: Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact likelihoods for the transition densities are typically not known, approximations are used that are expected to work well in the limit of small inter-sample times $\Delta t$ and large total observation times $N\Delta t$. Hypoellipticity together with partial observation leads to ill-conditioning requiring a judicious combination of approximate likelihoods for the various parameters to be estimated. We combine these in a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters. Numerical experiments illustrate asymptotic consistency of the method when applied to simulated data. The paper concludes with application of the Gibbs sampler to molecular dynamics data.

49 citations


Cited by
More filters
Book ChapterDOI
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

2,446 citations

01 Jan 2009
TL;DR: This short course is devoted to a few statistical problems related to the observation of a given process on a fixed time interval, when the observations occur at regularly spaced discrete times.
Abstract: This short course is devoted to a few statistical problems related to the observation of a given process on a fixed time interval, when the observations occur at regularly spaced discrete times. This kind of observations may occur in many different contexts, but they are particularly relevant in finance: we do have now huge amounts of data on the prices of various assets, exchange rates, and so on, typically ”tick data” which are recorded at every transaction time. So we are mainly concerned with the problems which arise in this context, and the concrete applications we will give are all pertaining to finance.

128 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider time-dependent problems and introduce a fully discrete solution method, which simplifies both the analysis of the data and the numerical algorithms, and the resulting time series are identified by a NARMAX (nonlinear autoregression moving average with exogenous input).
Abstract: Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. In the present paper we consider time-dependent problems and introduce a fully discrete solution method, which simplifies both the analysis of the data and the numerical algorithms. The resulting time series are identified by a NARMAX (nonlinear autoregression moving average with exogenous input) representation familiar from engineering practice. The connections with the Mori–Zwanzig formalism of statistical physics are discussed, as well as an application to the Lorenz 96 system.

93 citations

Journal ArticleDOI
TL;DR: This paper considers stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects, etc.) and introduces diffusion-driven susceptible exposed infected retired-type models with age structure.
Abstract: Epidemics are often modeled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects, etc.). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle Markov chain Monte Carlo algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion-driven susceptible exposed infected retired-type models with age structure are also introduced.

84 citations

Book
17 May 2012
TL;DR: Pavliotis et al. as discussed by the authors proposed an estimation method for multiscale diffusion coefficient estimation based on bridge processes and unbiased Monte Carlo for diffusions using high frequency data.
Abstract: Estimating functions for diffusion-type processes, Michael Sorensen Introduction Low frequency asymptotics Martingale estimating functions The likelihood function Non-martingale estimating functions High-frequency asymptotics High-frequency asymptotics in a fixed time-interval Small-diffusion asymptotics Non-Markovian models General asymptotic results for estimating functions Optimal estimating functions: General theory The econometrics of high frequency data, Per. A. Mykland and Lan Zhang Introduction Time varying drift and volatility Behavior of estimators: Variance Asymptotic normality Microstructure Methods based on contiguity Irregularly spaced data Statistics and high frequency data, Jean Jacod Introduction What can be estimated? Wiener plus compound Poisson processes Auxiliary limit theorems A first LNN (Law of Large Numbers) Some other LNNs A first CLT CLT with discontinuous limits Estimation of the integrated volatility Testing for jumps Testing for common jumps The Blumenthal-Getoor index Importance sampling techniques for estimation of diffusion models, Omiros Papaspiliopoulos and Gareth Roberts Overview of the chapter Background IS estimators based on bridge processes IS estimators based on guided processes Unbiased Monte Carlo for diffusions Appendix: Typical problems of the projection-simulation paradigm in MC for diffusions Appendix: Gaussian change of measure Non parametric estimation of the coefficients of ergodic diffusion processes based on high frequency data, Fabienne Comte, Valentine Genon-Catalot, and Yves Rozenholc Introduction Model and assumptions Observations and asymptotic framework Estimation method Drift estimation Diffusion coefficient estimation Examples and practical implementation Bibliographical remarks Appendix. Proof of Proposition.13 Ornstein-Uhlenbeck related models driven by Levy processes, Peter J. Brockwell and Alexander Lindner Introduction Levy processes Ornstein-Uhlenbeck related models Some estimation methods Parameter estimation for multiscale diffusions: an overview, Grigorios A. Pavliotis, Yvo Pokern, and Andrew M. Stuart Introduction Illustrative examples Averaging and homogenization Subsampling Hypoelliptic diffusions Nonparametric drift estimation Conclusions and further work

79 citations