scholarly journals Maximum approximate likelihood estimation of general continuous-time state-space models

2022 ◽  
pp. 1471082X2110657
Author(s):  
Sina Mews ◽  
Roland Langrock ◽  
Marius Ötting ◽  
Houda Yaqine ◽  
Jost Reinecke
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Likelihood Estimation ◽  
The State ◽  
State Space Models ◽  
State Transitions ◽  
Model Parameters ◽  
State Process ◽  
Approximate Likelihood ◽  
Non Gaussian

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

scholarly journals On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

2016 ◽  
Vol 6 (1) ◽  
pp. 13
Author(s):  
Chunlin Ji
Keyword(s):  
State Space ◽  
Blind Deconvolution ◽  
State Space Model ◽  
The State ◽  
State Space Models ◽  
Sequential Learning ◽  
Model Parameters ◽  
Learning Method ◽  
Space Model ◽  
Deconvolution Problem

Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.

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.

scholarly journals Block Method for SolvingState-Space Equations of Linear Continuous-Time Control Systems

2007 ◽  
Vol 4 (2) ◽  
pp. 318-329
Author(s):  
Baghdad Science Journal
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Mimo Systems ◽  
Multiple Input Multiple Output ◽  
Method Comparison ◽  
The State ◽  
Block Method ◽  
Single Input Single Output ◽  
Single Output ◽  
Time Control

This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different types of state-space equations using block method for conciliated the accuracy of the results of this method.

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