Point process-based Monte Carlo estimation

Point process-based Monte Carlo estimation

This paper addresses the issue of estimating the expectation of a real-valued random variable of the form X = g(U) where g is a deterministic function and U can be a random finiteor infinite-dimensional vector. Using recent results on rare event simulation, we propose a unified framework for dealing with both probability and mean estimation for such random variables, i.e. linking algorithms suc...

Sequential Monte Carlo Point-Process Estimation of Kinematics from Neural Spiking Activity for Brain-Machine Interfaces

Many decoding algorithms for brain machine interfaces' (BMIs) estimate hand movement from binned spike rates, which do not fully exploit the resolution contained in spike timing and may exclude rich neural dynamics from the modeling. More recently, an adaptive filtering method based on a Bayesian approach to reconstruct the neural state from the observed spike times has been proposed. However, ...

Point Process Monte Carlo Filtering for Brain Machine Interfaces

Integration by parts for point processes and Monte Carlo estimation

We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation and to the construction of a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard kernel estimators. Simulations are pres...

Estimation of k-Factor GIGARCH Process: A Monte Carlo Study

In this paper, we discuss the parameter estimation for a k-factor generalized long memory process with conditionally heteroskedastic noise. Two estimation methods are proposed. The rst method is based on the conditional distribution of the process and the second is obtained as an extension of Whittle's estimation approach. For comparison purposes, Monte Carlo simulations are used to evaluate th...