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 Can Cattle Basis Forecasts Be Improved? A Bayesian Model Averaging Approach

2019 ◽  
Vol 51 (02) ◽  
pp. 249-266
Author(s):  
Nicholas D. Payne ◽  
Berna Karali ◽  
Jeffrey H. Dorfman
Keyword(s):  
Bayesian Approach ◽  
Model Uncertainty ◽  
Bayesian Model Averaging ◽  
Model Performance ◽  
Model Averaging ◽  
Forecasting Model ◽  
Forecast Errors ◽  
Forecast Horizon ◽  
Combining Forecasts ◽  
The Bayesian Approach

AbstractBasis forecasting is important for producers and consumers of agricultural commodities in their risk management decisions. However, the best performing forecasting model found in previous studies varies substantially. Given this inconsistency, we take a Bayesian approach, which addresses model uncertainty by combining forecasts from different models. Results show model performance differs by location and forecast horizon, but the forecast from the Bayesian approach often performs favorably. In some cases, however, the simple moving averages have lower forecast errors. Besides the nearby basis, we also examine basis in a specific month and find that regression-based models outperform others in longer horizons.

A Theoretical Framework for Estimating Swarm Success Probability Using Scouts

2012 ◽  
pp. 277-307
Author(s):  
Antons Rebguns ◽  
Diana F. Spears ◽  
Richard Anderson-Sprecher ◽  
Aleksey Kletsov
Keyword(s):  
Bayesian Approach ◽  
Mean Squared Error ◽  
Success Probability ◽  
Ground Truth ◽  
Theoretical Framework ◽  
Experimental Results ◽  
Squared Error ◽  
The Mean ◽  
The Bayesian Approach ◽  
Bayesian Formula

This paper presents a novel theoretical framework for swarms of agents. Before deploying a swarm for a task, it is advantageous to predict whether a desired percentage of the swarm will succeed. The authors present a framework that uses a small group of expendable “scout” agents to predict the success probability of the entire swarm, thereby preventing many agent losses. The scouts apply one of two formulas to predict – the standard Bernoulli trials formula or the new Bayesian formula. For experimental evaluation, the framework is applied to simulated agents navigating around obstacles to reach a goal location. Extensive experimental results compare the mean-squared error of the predictions of both formulas with ground truth, under varying circumstances. Results indicate the accuracy and robustness of the Bayesian approach. The framework also yields an intriguing result, namely, that both formulas usually predict better in the presence of (Lennard-Jones) inter-agent forces than when their independence assumptions hold.

scholarly journals Kalman filter model, as a tool for short-term forecasting of solar potential: case of the Dakar site

2018 ◽  
Vol 57 ◽  
pp. 01004
Author(s):  
A. Mbaye ◽  
J. Ndong ◽  
M.L. NDiaye ◽  
M. Sylla ◽  
M.C. Aidara ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Solar Radiation ◽  
Mean Squared Error ◽  
Model Performance ◽  
Global Solar Radiation ◽  
Plant Production ◽  
Bias Error ◽  
Short Term ◽  
Filter Model ◽  
Short Term Forecasting

The prediction of solar potential is an important step toward the evaluation of PV plant production for the best energy planning. In this study, the discrete Kalman filter model was implemented for short-term solar resource forecasting one the Dakar site in Senegal. The model input parameters are constituted at a time t of the air temperature, the relative humidity and the global solar radiation. The expected output at time t+T is the global solar radiation. The model performance is evaluated with the square root of the normalized mean squared error (NRMSE), the absolute mean of the normalized error (NMAE), the average bias error (NMBE). The model Validation is carried out by means of the data measured within the Polytechnic Higher School of Dakar for one year. The simulation results following the 20 minute horizon show a good correlation between the prediction and the measurement with an NRMSE of 4.8%, an NMAE of 0.27% and an NMBE of 0.04%. This model could contribute to help photovoltaic based energy providers to better plan the production of solar photovoltaic plants in Sahelian environments.

How a Bayesian Might Estimate the Distribution of Cronbach’s Alpha From Ordinal-Dynamic Scaled Data

Methodology ◽  
2010 ◽  
Vol 6 (2) ◽  
pp. 71-82 ◽  
Author(s):  
Byron J. Gajewski ◽  
Diane K. Boyle ◽  
Sarah Thompson
Keyword(s):  
Confidence Intervals ◽  
Bayesian Approach ◽  
Mean Squared Error ◽  
Cronbach’S Alpha ◽  
Interval Estimates ◽  
Response Options ◽  
Practical Advice ◽  
Cronbach's Alpha ◽  
Squared Error ◽  
The Bayesian Approach

We demonstrate the utility of a Bayesian-based approach for calculating intervals of Cronbach’s alpha from a psychological instrument having ordinal responses with a dynamic scale. A small number of response options on an instrument will cause traditional-based interval estimates to be biased. Ordinal-based solutions are problematic because there is no clear mechanism for handling the dynamic scale. One way to remedy the bias is to adjust with a Bayesian approach. The Bayesian approach adjusts the bias and allows theoretically simple calculations of Cronbach’s alpha and intervals. We demonstrate the calculations of the Bayesian approach while at the same time offer a comparison to more traditional-based methods using both credible (or confidence) intervals and mean squared error. Practical advice is offered.

scholarly journals Adaptive Kalman Filter for Linear Systems with Additive and Multiplicative Noises

2021 ◽  
Author(s):  
Xingkai Yu
Keyword(s):  
Kalman Filter ◽  
Linear Systems ◽  
Bayesian Approach ◽  
Multiplicative Noise ◽  
Measurement Noise ◽  
Time Varying ◽  
Projection Formula ◽  
Adaptive Kalman Filter ◽  
Technical Issue ◽  
Multiplicative Noises

This manuscript investigates adaptive Kalman filter problem of of linear systems with multiplicative and additive noises. The main contributions are stated in two aspects. Firstly, compared with the estimation problem of linear systems with additive noises, we propose an algorithm that is applicable to the linear systems with both additive and multiplicative noises. To solve the technical issue raised by the multiplicative noise, a variational Bayesian approach is proposed. Moreover, the proposed approach is capable of estimating the multiplicative and additive measurement noise covariances as a whole, while the existing algorithms often operate in a separate way. Secondly, in contrast with existing literature, where the covariance of the multiplicative noise is assumed to be fixed and known, we focus on the situation that the covariances of both additive and multiplicative noises are time-varying and unknown. Towards this end, a novel adaptive Kalman filter is proposed to jointly estimate the covariances of multiplicative and additive noises based on projection formula and a VB approach.

scholarly journals Adaptive Kalman Filter for Linear Systems with Additive and Multiplicative Noises

2021 ◽  
Author(s):  
Xingkai Yu
Keyword(s):  
Kalman Filter ◽  
Linear Systems ◽  
Bayesian Approach ◽  
Multiplicative Noise ◽  
Measurement Noise ◽  
Time Varying ◽  
Projection Formula ◽  
Adaptive Kalman Filter ◽  
Technical Issue ◽  
Multiplicative Noises

This manuscript investigates adaptive Kalman filter problem of of linear systems with multiplicative and additive noises. The main contributions are stated in two aspects. Firstly, compared with the estimation problem of linear systems with additive noises, we propose an algorithm that is applicable to the linear systems with both additive and multiplicative noises. To solve the technical issue raised by the multiplicative noise, a variational Bayesian approach is proposed. Moreover, the proposed approach is capable of estimating the multiplicative and additive measurement noise covariances as a whole, while the existing algorithms often operate in a separate way. Secondly, in contrast with existing literature, where the covariance of the multiplicative noise is assumed to be fixed and known, we focus on the situation that the covariances of both additive and multiplicative noises are time-varying and unknown. Towards this end, a novel adaptive Kalman filter is proposed to jointly estimate the covariances of multiplicative and additive noises based on projection formula and a VB approach.

scholarly journals Bayesian back-calculation and nowcasting for line list data during the COVID-19 pandemic

2020 ◽  
Author(s):  
Tenglong Li ◽  
Laura F. White
Keyword(s):  
Bayesian Approach ◽  
Missing Values ◽  
Control Measures ◽  
Reproductive Number ◽  
Time Varying ◽  
Line List ◽  
Epidemic Curve ◽  
Back Calculation ◽  
Reporting Delays ◽  
The Bayesian Approach

AbstractSurveillance is the key of controling the COVID-19 pandemic, and it typically suffers from reporting delays and thus can be misleading. Previous methods for adjusting reporting delays are not particularly appropriate for line list data, which usually have lots of missing values that are non-ignorable for modeling reporting delays. In this paper, we develop a Bayesian approach that dynamically integrates imputation and estimation for line list data. We show this Bayesian approach lead to accurate estimates of the epidemic curve and time-varying reproductive numbers and is robust to deviations from model assumptions. We apply the Bayesian approach to a COVID-19 line list data in Massachusetts and find the reproductive number estimates correspond more closely to the control measures than the ones based on the reported curve.

scholarly journals Inverted Weibull Regression Models and Their Applications

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 269-290
Author(s):  
Sarah R. Al-Dawsari ◽  
Khalaf S. Sultan
Keyword(s):  
Regression Model ◽  
Bayesian Approach ◽  
Regression Models ◽  
Mean Squared Error ◽  
Information Criterion ◽  
Bayesian Regression ◽  
Loss Functions ◽  
Performance Criteria ◽  
Weibull Regression ◽  
The Bayesian Approach

In this paper, we propose the classical and Bayesian regression models for use in conjunction with the inverted Weibull (IW) distribution; there are the inverted Weibull Regression model (IW-Reg) and inverted Weibull Bayesian regression model (IW-BReg). In the proposed models, we suggest the logarithm and identity link functions, while in the Bayesian approach, we use a gamma prior and two loss functions, namely zero-one and modified general entropy (MGE) loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey’s bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IW-Reg and IW-BReg using some performance criteria, such as Akaike’s information criterion (AIC), deviance (D), and mean squared error (MSE). Finally, we apply the some real datasets collected from Saudi Arabia with the corresponding explanatory variables to the theoretical findings. The Bayesian approach shows better performance compare to the classical approach in terms of the considered performance criteria.

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