Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

An overview of Sequential Monte Carlo methods for parameter estimation in general state-space models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, provide very good numerical approximations to the associated optimal state estimation problems. However, in many scenarios, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard SMC methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models. We discuss the advantages and limitations of these methods. © 2009 IFAC.

Real-time parameter estimation of dynamic temperature and humidity models for greenhouse adaptive climate control

A real-time parameter estimator for the climate discrete-time dynamic models of a greenhouse located at the North of Portugal are presented. The experiments showed that the second order models identified for the air temperature and humidity achieve a close agreement between simulated and experimantal data.

Real-time parameter estimation of dynamic temperature models for greenhouse environmental control

For a greenhouse located at UTAD-University, the methods used to estimate in real-time the parameters of the inside air temperature model will be described. The structure and the parameters of the climate discrete-time dynamic model were previously identified using data acquired during two different periods of the year.

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

Image registration for triggered and non-triggered DTI of the human kidney: Reduced variability of diffusion parameter estimation

BACKGROUND: To investigate if non-rigid image-registration reduces motion artifacts in triggered and non-triggered diffusion tensor imaging (DTI) of native kidneys. A secondary aim was to determine, if improvements through registration allow for omitting respiratory-triggering. METHODS: Twenty volunteers underwent coronal DTI of the kidneys with nine b-values (10-700 s/mm2 ) at 3 Tesla. Image-registration was performed using a multimodal nonrigid registration algorithm. Data processing yielded the apparent diffusion coefficient (ADC), the contribution of perfusion (FP ), and the fractional anisotropy (FA). For comparison of the data stability, the root mean square error (RMSE) of the fitting and the standard deviations within the regions of interest (SDROI ) were evaluated. RESULTS: RMSEs decreased significantly after registration for triggered and also for non-triggered scans (P < 0.05). SDROI for ADC, FA, and FP were significantly lower after registration in both medulla and cortex of triggered scans (P < 0.01). Similarly the SDROI of FA and FP decreased significantly in non-triggered scans after registration (P < 0.05). RMSEs were significantly lower in triggered than in non-triggered scans, both with and without registration (P < 0.05). CONCLUSION: Respiratory motion correction by registration of individual echo-planar images leads to clearly reduced signal variations in renal DTI for both triggered and particularly non-triggered scans. Secondarily, the results suggest that respiratory-triggering still seems advantageous.J. Magn. Reson. Imaging 2014. (c) 2014 Wiley Periodicals, Inc.

OASIS : parameter estimation system for aquifer restoration models : user's manual version 2.0 /

Mode of access: Internet.

Faster parameter estimation using risk-sensitive filters

In this paper, we propose a risk-sensitive approach to parameter estimation for hidden Markov models (HMMs). The parameter estimation approach considered exploits estimation of various functions of the state, based on model estimates. We propose certain practical suboptimal risk-sensitive filters to estimate the various functions of the state during transients, rather than optimal risk-neutral filters as in earlier studies. The estimates are asymptotically optimal, if asymptotically risk neutral, and can give significantly improved transient performance, which is a very desirable objective for certain engineering applications. To demonstrate the improvement in estimation simulation studies are presented that compare parameter estimation based on risk-sensitive filters with estimation based on risk-neutral filters.