Maximum-a-posteriori estimation of LTI state-space models via efficient Monte-Carlo sampling

2021 ◽  
pp. 1-6
Author(s):  
Manas Mejari ◽  
Dario Piga
Keyword(s):  
Monte Carlo ◽  
State Space ◽  
Posterior Distribution ◽  
Linear Time ◽  
Monte Carlo Sampling ◽  
The State ◽  
Maximum A Posteriori ◽  
Model Parameters ◽  
A Posteriori ◽  
State Sequence

Abstract This paper addresses Maximum-A-Posteriori (MAP) estimation of Linear Time-Invariant State-Space (LTI-SS) models. The joint posterior distribution of the model matrices and the unknown state sequence is approximated by using Rao-Blackwellized Monte-Carlo sampling algorithms. Specifically, the conditional distribution of the state sequence given the model parameters is derived analytically, while only the marginal posterior distribution of the model matrices is approximated using a Metropolis-Hastings Markov-Chain Monte-Carlo sampler. From the joint distribution, MAP estimates of the unknown model matrices as well as the state sequence are computed. The performance of the proposed algorithm is demonstrated on a numerical example and on a real laboratory benchmark dataset of a hair dryer process.

scholarly journals Time triggered stochastic hybrid system with nonlinear continuous dynamics

2021 ◽  
Author(s):  
Zahra Vahdat ◽  
Abhyudai Singh
Keyword(s):  
State Space ◽  
Cell Size ◽  
Time Evolution ◽  
Continuous Time ◽  
Linear Time ◽  
The State ◽  
Closed Form Expression ◽  
Model Parameters ◽  
Continuous Growth ◽  
Piecewise Deterministic Markov Processes

Time triggered stochastic hybrid systems (TTSHS) constitute a class of piecewise-deterministic Markov processes (PDMP), where continuous-time evolution of the state space is interspersed with discrete stochastic events. Whenever a stochastic event occurs, the state space is reset based on a random map. Prior work on this topic has focused on the continuous-time evolution being modeled as a linear time- invariant system, and in this contribution, we generalize these results to consider nonlinear continuous dynamics. Our approach relies on approximating the nonlinear dynamics between two successive events as a linear time-varying system and using this approximation to derive analytical solutions for the state space’s statistical moments. The TTSHS framework is used to model continuous growth in an individual cell’s size and its subsequent division into daughters. It is well known that exponential growth in cell size, together with a size- independent division rate, leads to an unbounded variance in cell size. Motivated by recent experimental findings, we consider nonlinear growth in cell size based on a Michaelis- Menten function and show that this leads to size homeostasis in the sense that the variance in cell size remains bounded. Moreover, we provide a closed-form expression for the variance in cell size as a function of model parameters and validate it by performing exact Monte Carlo simulations. In summary, our work provides an analytical approach for characterizing moments of a nonlinear stochastic dynamical system that can have broad applicability in studying random phenomena in both engineering and biology.

Parametric uncertainty quantification in the Rothermel model with randomised quasi-Monte Carlo methods

2015 ◽  
Vol 24 (3) ◽  
pp. 307 ◽  
Author(s):  
Yaning Liu ◽  
Edwin Jimenez ◽  
M. Yousuff Hussaini ◽  
Giray Ökten ◽  
Scott Goodrick
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Monte Carlo Methods ◽  
Wildland Fire ◽  
Parametric Uncertainty ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Quasi Monte Carlo ◽  
Control Variate ◽  
Fuel Model

Rothermel's wildland surface fire model is a popular model used in wildland fire management. The original model has a large number of parameters, making uncertainty quantification challenging. In this paper, we use variance-based global sensitivity analysis to reduce the number of model parameters, and apply randomised quasi-Monte Carlo methods to quantify parametric uncertainties for the reduced model. The Monte Carlo estimator used in these calculations is based on a control variate approach applied to the sensitivity derivative enhanced sampling. The chaparral fuel model, selected from Rothermel's 11 original fuel models, is studied as an example. We obtain numerical results that improve the crude Monte Carlo sampling by factors as high as three orders of magnitude.

NEURAL NETWORK-BASED DIGITAL REDESIGN APPROACH FOR CONTROL OF UNKNOWN CONTINUOUS-TIME CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2433-2455
Author(s):  
JOSE I. CANELON ◽  
LEANG S. SHIEH ◽  
SHU M. GUO ◽  
HEIDAR A. MALKI
Keyword(s):  
Neural Network ◽  
State Space ◽  
Continuous Time ◽  
Digital Control ◽  
Chaotic Systems ◽  
Linear Time ◽  
The State ◽  
Control Law ◽  
Analog Control ◽  
Digital Redesign

This paper presents a neural network-based digital redesign approach for digital control of continuous-time chaotic systems with unknown structures and parameters. Important features of the method are that: (i) it generalizes the existing optimal linearization approach for the class of state-space models which are nonlinear in the state but linear in the input, to models which are nonlinear in both the state and the input; (ii) it develops a neural network-based universal optimal linear state-space model for unknown chaotic systems; (iii) it develops an anti-digital redesign approach for indirectly estimating an analog control law from a fast-rate digital control law without utilizing the analog models. The estimated analog control law is then converted to a slow-rate digital control law via the prediction-based digital redesign method; (iv) it develops a linear time-varying piecewise-constant low-gain tracker which can be implemented using microprocessors. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology.

scholarly journals Score-Based Measurement Invariance Checks for Bayesian Maximum-a-Posteriori Estimates in Item Response Theory

2020 ◽  
Author(s):  
Rudolf Debelak ◽  
Samuel Pawel ◽  
Carolin Strobl ◽  
Edgar C. Merkle
Keyword(s):  
Maximum Likelihood ◽  
Item Response Theory ◽  
Item Response ◽  
Statistical Tests ◽  
Maximum A Posteriori ◽  
Model Parameters ◽  
A Posteriori ◽  
Response Theory ◽  
Simulation Based ◽  
A Posteriori Estimates

A family of score-based tests has been proposed in the past years for assessing the invariance of model parameters in several models of item response theory. These tests were originally developed in a maximum likelihood framework. This study aims to extend the theoretical framework of these tests to Bayesian maximum-a-posteriori estimates and to multiple group IRT models. We propose two families of statistical tests, which are based on a) an approximation using a pooled variance method, or b) a simulation-based approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be practically useful with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

scholarly journals On the two-filter approximations of marginal smoothing distributions in general state-space models

2018 ◽  
Vol 50 (01) ◽  
pp. 154-177 ◽  
Author(s):  
Thi Ngoc Minh Nguyen ◽  
Sylvain Le Corff ◽  
Eric Moulines
Keyword(s):  
State Space ◽  
Posterior Distribution ◽  
The State ◽  
State Space Models ◽  
General State ◽  
Rigorous Analysis ◽  
The Past ◽  
Information Filter ◽  
General State Space ◽  
Filter Algorithms

AbstractA prevalent problem in general state-space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state, given future observations.

Hydraulic-seasonal-time-based state space model for displacement monitoring of high concrete dams

2021 ◽  
pp. 014233122110183
Author(s):  
Shaowei Wang ◽  
Cong Xu ◽  
Chongshi Gu ◽  
Huaizhi Su ◽  
Bangbin Wu
Keyword(s):  
State Space ◽  
Elastic Deformation ◽  
State Space Model ◽  
State Equation ◽  
Time Effect ◽  
The State ◽  
Arch Dam ◽  
Model Parameters ◽  
Concrete Dams ◽  
Space Model

Displacement is the most intuitive reflection of the comprehensive behavior of concrete dams, especially the time effect displacement, which is a key index for the evaluation of the structural behavior and health status of a dam in long-term service. The main purpose of this paper is to establish a state space model for separating causal components from the measured dam displacement. This approach is conducted by initially proposing two equations, which are the state and observation equations, and model parameters are then optimized by the Kalman filter algorithm. The state equation is derived according to the creep deformation of dam concrete and foundation rock and is used to preliminarily predict the dam time effect displacement. Considering the generally recognized three components of dam displacement, the hydraulic-seasonal-time (HST) model is used to establish the observation equation, which is used to update the time effect displacement. The efficiency and rationality of the established state space model is verified by an engineering example. The results show that the hydraulic component separated by the state space model only contains the instantaneous elastic hydraulic deformation, while the hysteretic elastic hydraulic deformation is divided into the time effect component. The inverted elastic modulus of dam body concrete is an instantaneous value for the state space model but a comprehensive reflection of the instantaneous and hysteretic elastic deformation ability for the HST model, where the hysteretic elastic deformation is a part of the hydraulic component. For the Xiaowan arch dam, the inverted values are 42.9 and 36.7 GPa for the state space model and HST model, respectively. The proposed state space model is useful to improve the interpretation ability of the separated displacement components of concrete dams.

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