scholarly journals Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 115
Author(s):  
Hiroaki Inoue ◽  
Koji Hukushima ◽  
Toshiaki Omori

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4112 ◽  
Author(s):  
Se-Min Lim ◽  
Hyeong-Cheol Oh ◽  
Jaein Kim ◽  
Juwon Lee ◽  
Jooyoung Park

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.


2020 ◽  
Vol 9 (1) ◽  
pp. 8
Author(s):  
FITRI ANANDA DITA SARASWITA ◽  
I WAYAN SUMARJAYA ◽  
LUH PUTU IDA HARINI

State space is an approach to model and predict together several time series data that are interconnected, and these variables have dynamic interactions. The purpose of this research is to model the number of train passengers in Java and find out the forecasting results using the state space method. The algorithm used to solve the state space model is the Kalman filter. In this research, a suitable final model is local level model with seasonal and produces MAPE value of 2%, this shows that the state space method is very accurately.


PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0245642
Author(s):  
Somaya El-Saadani ◽  
Mohamed Saleh ◽  
Sarah A. Ibrahim

The study aimed to model and quantify the health burden induced by four non-communicable diseases (NCDs) in Egypt, the first to be conducted in the context of a less developing county. The study used the State-Space model and adopted two Bayesian methods: Particle Filter and Particle Independent Metropolis-Hastings to model and estimate the NCDs’ health burden trajectories. We drew on time-series data of the International Health Metric Evaluation, the Central Agency for Public Mobilization and Statistics (CAPMAS) Annual Bulletin of Health Services Statistics, the World Bank, and WHO data. Both Bayesian methods showed that the burden trajectories are on the rise. Most of the findings agreed with our assumptions and are in line with the literature. Previous year burden strongly predicts the burden of the current year. High prevalence of the risk factors, disease prevalence, and the disease’s severity level all increase illness burden. Years of life lost due to death has high loadings in most of the diseases. Contrary to the study assumption, results found a negative relationship between disease burden and health services utilization which can be attributed to the lack of full health insurance coverage and the pattern of health care seeking behavior in Egypt. Our study highlights that Particle Independent Metropolis-Hastings is sufficient in estimating the parameters of the study model, in the case of time-constant parameters. The study recommends using state Space models with Bayesian estimation approaches with time-series data in public health and epidemiology research.


2021 ◽  
Author(s):  
Somaya Mahmoud El-Saadani ◽  
Mohamed Mostafa Saleh ◽  
Sarah Assem Ibrahim

The study aimed to model and quantify the health burden induced by four non-communicable diseases in Egypt, the first to be conducted in the context of a less developing county. The study used the State-Space model and adopted two Bayesian methods: Particle Filter and Particle Independent Metropolis-Hastings to model and estimate the NCDs' health burden trajectories. We drew on time-series data of the International Health Metric Evaluation, CAPMAS's Annual Bulletin of Health Services Statistics, the World Bank, and WHO data. Both Bayesian methods showed that the burden trajectories are on the rise. Most of the findings agreed with our assumptions and are in line with the literature. Previous year burden strongly predicts the burden of the current year. High prevalence of the risk factors, disease prevalence, and the disease's severity level all increase illness burden. Years of life lost due to death has high loadings in most of the diseases. Contrary to the study assumption, results found a negative relationship between disease burden and health services utilization which can be attributed to the lack of full health insurance coverage and the pattern of health care seeking behavior in Egypt. Our study highlights that Particle Independent Metropolis-Hastings is sufficient in estimating the parameters of the study model, in the case of time-constant parameters. The study recommends using state Space models with Bayesian estimation approaches with time-series data in public health and epidemiology research.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.


1994 ◽  
Vol 20 (2) ◽  
pp. 143-148 ◽  
Author(s):  
Siddhartha Chib ◽  
Ram C. Tiwari

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