Study on the data treatment using the Kalman filter technique and the Bayesian approach

1986 ◽  
Vol 14 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Joo-Young Park ◽  
Soon Heung Chang
Keyword(s):  
Kalman Filter ◽  
Bayesian Approach ◽  
Filter Technique ◽  
Data Treatment ◽  
The Bayesian Approach

scholarly journals Optimizing the performance of Kalman filter based statistical time-varying air quality models

2013 ◽  
Vol 12 (1) ◽  
pp. 27-39
Keyword(s):  
Kalman Filter ◽  
Bayesian Approach ◽  
Autoregressive Model ◽  
Prediction Models ◽  
Mean Squared Error ◽  
Model Performance ◽  
Time Varying ◽  
Squared Prediction Error ◽  
Statistical Time ◽  
The Bayesian Approach

In this study, the Bayesian approach is proposed to estimate the noise variances of Kalman filter based statistical models for predicting the daily averaged PM10 concentrations of a typical coastal city, Macau, with Latitude 22°10’N and Longitude 113°34’E. By using the measurements in 2001 and 2002, the Bayesian approach is capable to estimate the most probable values of the noise variances in the Kalman filter based prediction models. It turns out that the estimated process noise variance of the time-varying autoregressive model with exogenous inputs, TVAREX, is significantly (~76%) less than that of the time-varying autoregressive model of order 1, TVAR(1), since the TVAREX model incorporates important mechanisms which govern the daily averaged PM10 concentrations in Macau. By further using data between 2003 and 2005, the choice of the noise variances is shown to affect the model performance, measured by the root-mean-squared error, of the TVAR(p) model and the TVAREX model. In addition, the optimal estimates of noise variances obtained by Bayesian approach for both models are located in the region where the model performance is insensitive to the choice of noise variances. Furthermore, the Bayesian approach will be demonstrated to provide more reasonable estimates of noise variances compared to the noise variances found by simply minimizing the root-mean-squared prediction error of the model. By comparing the optimized TVAREX model and the TVAR(p) models in predicting the daily averaged PM10 concentrations between 2003 and 2005, it is found that the TVAREX model outperforms the TVAR(p) models in terms of the general performance and the episode capturing capability.

scholarly journals The Bayesian Approach and the Results of the ISAR-REACT 5 Trial

2021 ◽  
Vol 14 (2) ◽  
pp. 231-232
Author(s):  
Adnan Kastrati ◽  
Alexander Hapfelmeier
Keyword(s):  
Bayesian Approach ◽  
The Bayesian Approach

A new Bayesian approach for QTL mapping of family data

2021 ◽  
Author(s):  
Daiane Aparecida Zuanetti ◽  
Luis Aparecido Milan
Keyword(s):  
Qtl Mapping ◽  
Random Effects ◽  
Bayesian Approach ◽  
Variance Component ◽  
Mendelian Inheritance ◽  
Family Data ◽  
Data Sets ◽  
Mendelian Segregation ◽  
Gaw17 Data ◽  
The Bayesian Approach

In this paper, we propose a new Bayesian approach for QTL mapping of family data. The main purpose is to model a phenotype as a function of QTLs’ effects. The model considers the detailed familiar dependence and it does not rely on random effects. It combines the probability for Mendelian inheritance of parents’ genotype and the correlation between flanking markers and QTLs. This is an advance when compared with models which use only Mendelian segregation or only the correlation between markers and QTLs to estimate transmission probabilities. We use the Bayesian approach to estimate the number of QTLs, their location and the additive and dominance effects. We compare the performance of the proposed method with variance component and LASSO models using simulated and GAW17 data sets. Under tested conditions, the proposed method outperforms other methods in aspects such as estimating the number of QTLs, the accuracy of the QTLs’ position and the estimate of their effects. The results of the application of the proposed method to data sets exceeded all of our expectations.

scholarly journals Experience Rating of ARIMA Processes by the Kalman Filter

1986 ◽  
Vol 16 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Jukka Rantala
Keyword(s):  
Kalman Filter ◽  
Time Delay ◽  
State Space ◽  
Theoretical Approach ◽  
Space Form ◽  
The State ◽  
Experience Rating ◽  
Filter Technique ◽  
Main Emphasis ◽  
Arima Processes

AbstractThis paper deals with experience rating of claims processes of ARIMA structures. By experience rating we mean that future premiums should be only a function of past values of the claims process. The main emphasis is on demonstrating the usefulness of the control-theoretical approach in the search for optimal rating rules. Optimality is here defined to mean as smooth a flow of premiums as possible when the variation in the accumulated profit is restricted to a certain amount. First it is shown how the underlying model in its simplest form can be transformed into the state-space form. Then the Kalman filter technique is used to find the optimal rules. Also a time delay in information is taken into account. The optimal rules are illustrated by examples.

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