On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations*

Hurn, Stan; Lindsay, K. A.; Martin, Vance L.

doi:10.1111/1467-9892.00292

“…• Define the Fokker-Planck equation for the precipitation model given by the equations (20) and (2).…”

Section: Parallelized Ensemble Kalman Filter (Penkf)mentioning

confidence: 99%

“…There exist a variety of methods in the literature including the estimation by maximum likelihood ( [35], and [20]); the Monte Carlo Markov Chain techniques (MCMC) ( [26], [34], [42], [43]); and the sequential Monte Carlo algorithms (SMC). Examples of the latter are the Kalman filter, the extended Kalman filter (EKF), the particle filter (PF) and the unscented particle filter (UPF) (see [2], [22], [16], [23], [24], [4], [44], [18], [25], [29], [9], [30], [36], [41], [14], [8], [15], [17], [28], [39], [40], [6], [21], [3] and [38]).…”

Section: Introductionmentioning

confidence: 99%

Polynomial Chaos based on the parallelized ensemble Kalman filter to estimate precipitation states

Sánchez

¹

,

Infante²,

Marcano³

et al. 2015

Stat., optim. inf. comput.

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This article develops a methodology combining methods of numerical analysis and stochastic differential equations with computational algorithms to treat problems which have complex nonlinear dynamics in high dimensions. A method to estimate parameters and states of a dynamic system is proposed inspired by the parallelized ensemble Kalman filter (PEnKF) and the polynomial chaos theory of Wiener-Askey. The main advantage of the proposal is in providing a precise efficient algorithm with low computational cost. For the analysed data, the methods provide good predictions, spatially and temporally, for the unknown precipitation states for the first 24 hours. Two goodness of fit measures provide confidence in the quality of the model predictions. The performance of the parallel algorithm, measured by the acceleration and efficiency factors, shows an increase of 7% in speed with respect to the sequential version and is most efficient for P = 2 threads.

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“…The expansion of the polynomial chaos of order n p in terms of the solution of the equation given in (20), p np (x t , t, ξ) can be expressed as…”

Section: Ensemble Kalman Filter Based On the Polynomial Chaosmentioning

confidence: 99%

Polynomial Chaos based on the parallelized ensemble Kalman filter to estimate precipitation states

Sánchez

¹

,

Infante²,

Marcano³

et al. 2015

Stat., optim. inf. comput.

0

View full text Add to dashboard Cite

This article develops a methodology combining methods of numerical analysis and stochastic differential equations with computational algorithms to treat problems which have complex nonlinear dynamics in high dimensions. A method to estimate parameters and states of a dynamic system is proposed inspired by the parallelized ensemble Kalman filter (PEnKF) and the polynomial chaos theory of Wiener-Askey. The main advantage of the proposal is in providing a precise efficient algorithm with low computational cost. For the analysed data, the methods provide good predictions, spatially and temporally, for the unknown precipitation states for the first 24 hours. Two goodness of fit measures provide confidence in the quality of the model predictions. The performance of the parallel algorithm, measured by the acceleration and efficiency factors, shows an increase of 7% in speed with respect to the sequential version and is most efficient for P = 2 threads.

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“…Moreover, kernel density estimates based on numerical integration of the associated stochastic differential equation can be applied, that are described in greater detail in [14]. The data under consideration can be reduced significantly by a suitable discretization of data space in several bins.…”

Section: Minimization Procedures For Drift-/diffusion-processesmentioning

confidence: 99%

“…For a recent study on the preferences of current methods we refer to [14]. The intention of the present note is to derive a maximum likelihood estimator for parameters of the parametrized drift vector and diffusion matrix, that purely is based on the conditional and joint transition pdfs of the dataset under consideration.…”

mentioning

confidence: 99%