scholarly journals Bayesian Model Averaging with Temporal Correlation for Time Series Forecasts

2021 ◽  
Author(s):  
Kosuke Ono
Keyword(s):  
Time Series ◽  
Latent Variables ◽  
Bayesian Model ◽  
Lead Time ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Temporal Correlation ◽  
Lead Times ◽  
Probabilistic Forecasts ◽  
Interval Time Series

AbstractThis study extends Bayesian model averaging (BMA) to a form suitable for time series forecasts. BMA is applied to a three-member ensemble for temperature forecasts with a 1-h interval time series at specific stations. The results of such an application typically have a problematic characteristic. BMA weights assigned to ensemble members fluctuate widely within a few hours because BMA optimizations are independent at each lead time, which is incompatible with the spatiotemporal continuity of meteorological phenomena. To ameliorate this issue, a degree of correlation among different lead times is introduced by the extension of latent variables to lead times adjacent to the target lead time for the calculation of BMA weights and variances. This extension approach stabilizes the BMA weights, improving the performance of deterministic and probabilistic forecasts. Also, an investigation of the effects of this extension technique on the shapes of forecasted probability density functions showed that the extension approach offers advantages in bimodal cases. This extension technique may show promise in other applications to improve the performance of forecasts by BMA.

scholarly journals Using Bayesian Model Averaging (BMA) to calibrate probabilistic surface temperature forecasts over Iran

2011 ◽  
Vol 29 (7) ◽  
pp. 1295-1303 ◽  
Author(s):  
I. Soltanzadeh ◽  
M. Azadi ◽  
G. A. Vakili
Keyword(s):  
Boundary Conditions ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Training Sample ◽  
Limited Area ◽  
Probabilistic Forecasts ◽  
Rank Histogram ◽  
Initial And Boundary Conditions ◽  
Environmental Prediction

Abstract. Using Bayesian Model Averaging (BMA), an attempt was made to obtain calibrated probabilistic numerical forecasts of 2-m temperature over Iran. The ensemble employs three limited area models (WRF, MM5 and HRM), with WRF used with five different configurations. Initial and boundary conditions for MM5 and WRF are obtained from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) and for HRM the initial and boundary conditions come from analysis of Global Model Europe (GME) of the German Weather Service. The resulting ensemble of seven members was run for a period of 6 months (from December 2008 to May 2009) over Iran. The 48-h raw ensemble outputs were calibrated using BMA technique for 120 days using a 40 days training sample of forecasts and relative verification data. The calibrated probabilistic forecasts were assessed using rank histogram and attribute diagrams. Results showed that application of BMA improved the reliability of the raw ensemble. Using the weighted ensemble mean forecast as a deterministic forecast it was found that the deterministic-style BMA forecasts performed usually better than the best member's deterministic forecast.

Probabilistic Wind Vector Forecasting Using Ensembles and Bayesian Model Averaging

2013 ◽  
Vol 141 (6) ◽  
pp. 2107-2119 ◽  
Author(s):  
J. McLean Sloughter ◽  
Tilmann Gneiting ◽  
Adrian E. Raftery
Keyword(s):  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Prediction Models ◽  
Weather Prediction ◽  
Model Averaging ◽  
Wind Vector ◽  
Bivariate Distributions ◽  
Ensemble Forecasts ◽  
Probabilistic Forecasts ◽  
Wide Range

Abstract Probabilistic forecasts of wind vectors are becoming critical as interest grows in wind as a clean and renewable source of energy, in addition to a wide range of other uses, from aviation to recreational boating. Unlike other common forecasting problems, which deal with univariate quantities, statistical approaches to wind vector forecasting must be based on bivariate distributions. The prevailing paradigm in weather forecasting is to issue deterministic forecasts based on numerical weather prediction models. Uncertainty can then be assessed through ensemble forecasts, where multiple estimates of the current state of the atmosphere are used to generate a collection of deterministic predictions. Ensemble forecasts are often uncalibrated, however, and Bayesian model averaging (BMA) is a statistical way of postprocessing these forecast ensembles to create calibrated predictive probability density functions (PDFs). It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights reflect the forecasts’ relative contributions to predictive skill over a training period. In this paper the authors extend the BMA methodology to use bivariate distributions, enabling them to provide probabilistic forecasts of wind vectors. The BMA method is applied to 48-h-ahead forecasts of wind vectors over the North American Pacific Northwest in 2003 using the University of Washington mesoscale ensemble and is shown to provide better-calibrated probabilistic forecasts than the raw ensemble, which are also sharper than probabilistic forecasts derived from climatology.

scholarly journals Bayesian Model Averaging: A Unique Model Enhancing Forecasting Accuracy for Daily Streamflow Based on Different Antecedent Time Series

2020 ◽  
Vol 12 (22) ◽  
pp. 9720
Author(s):  
Sungwon Kim ◽  
Meysam Alizamir ◽  
Nam Won Kim ◽  
Ozgur Kisi
Keyword(s):  
Time Series ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Time Series Data ◽  
Model Averaging ◽  
Uncertainty Estimation ◽  
Series Data ◽  
Streamflow Forecasting ◽  
Forecasting Accuracy ◽  
Daily Streamflow

Streamflow forecasting is a vital task for hydrology and water resources engineering, and the different artificial intelligence (AI) approaches have been employed for this purposes until now. Additionally, the forecasting accuracy and uncertainty estimation are the meaningful assignments that need to be recognized. The addressed research investigates the potential of novel ensemble approach, Bayesian model averaging (BMA), in streamflow forecasting using daily time series data from two stations (i.e., Hongcheon and Jucheon), South Korea. Six categories (i.e., M1–M6) of input combination using different antecedent times were employed for streamflow forecasting. The outcomes of BMA model were compared with those of multivariate adaptive regression spline (MARS), M5 model tree (M5Tree), and Kernel extreme learning machines (KELM) models considering four assessment indexes, root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), correlation coefficient (R), and mean absolute error (MAE). The results revealed the superior accuracy of BMA model over three machine learning models in daily streamflow forecasting. Considering RMSE values among the best models during testing phase, the best BMA model (i.e., BMA2) enhanced the forecasting accuracy of MARS1, M5Tree4, and KELM3 models by 5.2%, 5.8%, and 3.4% in Hongcheon station. Additionally, the best BMA model (i.e., BMA1) improved the forecasting accuracy of MARS1, M5Tree1, and KELM1 models by 6.7%, 9.5%, and 3.7% in Jucheon station. In addition, the best BMA models in both stations allowed the uncertainty estimation, and produced higher uncertainty of peak flows compared to that of low flows. As one of the most robust and effective tools, therefore, the BMA model can be successfully employed for streamflow forecasting with different antecedent times.

scholarly journals Bayesian Model Averaging’s Problematic Treatment of Extreme Weather and a Paradigm Shift That Fixes It

2008 ◽  
Vol 136 (12) ◽  
pp. 4641-4652 ◽  
Author(s):  
Craig H. Bishop ◽  
Kevin T. Shanley
Keyword(s):  
Paradigm Shift ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Extreme Weather ◽  
Ensemble Forecasts ◽  
Stochastic Perturbations ◽  
New Approach ◽  
Weather Forecasts ◽  
Probabilistic Forecasts

Abstract Methods of ensemble postprocessing in which continuous probability density functions are constructed from ensemble forecasts by centering functions around each of the ensemble members have come to be called Bayesian model averaging (BMA) or “dressing” methods. Here idealized ensemble forecasting experiments are used to show that these methods are liable to produce systematically unreliable probability forecasts of climatologically extreme weather. It is argued that the failure of these methods is linked to an assumption that the distribution of truth given the forecast can be sampled by adding stochastic perturbations to state estimates, even when these state estimates have a realistic climate. It is shown that this assumption is incorrect, and it is argued that such dressing techniques better describe the likelihood distribution of historical ensemble-mean forecasts given the truth for certain values of the truth. This paradigm shift leads to an approach that incorporates prior climatological information into BMA ensemble postprocessing through Bayes’s theorem. This new approach is shown to cure BMA’s ill treatment of extreme weather by providing a posterior BMA distribution whose probabilistic forecasts are reliable for both extreme and nonextreme weather forecasts.

scholarly journals Locally Calibrated Probabilistic Temperature Forecasting Using Geostatistical Model Averaging and Local Bayesian Model Averaging

2011 ◽  
Vol 139 (8) ◽  
pp. 2630-2649 ◽  
Author(s):  
William Kleiber ◽  
Adrian E. Raftery ◽  
Jeffrey Baars ◽  
Tilmann Gneiting ◽  
Clifford F. Mass ◽  
...  
Keyword(s):  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Grid Point ◽  
Model Averaging ◽  
Training Data ◽  
Geostatistical Model ◽  
Local Method ◽  
Probabilistic Forecasts ◽  
Temperature Forecasting ◽  
Network Experiment

AbstractThe authors introduce two ways to produce locally calibrated grid-based probabilistic forecasts of temperature. Both start from the Global Bayesian model averaging (Global BMA) statistical postprocessing method, which has constant predictive bias and variance across the domain, and modify it to make it local. The first local method, geostatistical model averaging (GMA), computes the predictive bias and variance at observation stations and interpolates them using a geostatistical model. The second approach, Local BMA, estimates the parameters of BMA at a grid point from stations that are close to the grid point and similar to it in elevation and land use. The results of these two methods applied to the eight-member University of Washington Mesoscale Ensemble (UWME) are given for the 2006 calendar year. GMA was calibrated and sharper than Global BMA, with prediction intervals that were 8% narrower than Global BMA on average. Examples using sparse and dense training networks of stations are shown. The sparse network experiment illustrates the ability of GMA to draw information from the entire training network. The performance of Local BMA was not statistically different from Global BMA in the dense network experiment, and was superior to both GMA and Global BMA in areas with sufficient nearby training data.

scholarly journals Bayesian Model Averaging and Prior Sensitivity in Stochastic Frontier Analysis

Econometrics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 13 ◽  
Author(s):  
Kamil Makieła ◽  
Błażej Mazur
Keyword(s):  
Latent Variables ◽  
Bayesian Model ◽  
Stochastic Frontier Analysis ◽  
Bayesian Model Averaging ◽  
Scale Parameter ◽  
Stochastic Frontier ◽  
Model Averaging ◽  
Model Parameters ◽  
Frontier Analysis ◽  
Stochastic Parameters

This paper discusses Bayesian model averaging (BMA) in Stochastic Frontier Analysis and investigates inference sensitivity to prior assumptions made about the scale parameter of (in)efficiency. We turn our attention to the “standard” prior specifications for the popular normal-half-normal and normal-exponential models. To facilitate formal model comparison, we propose a model that nests both sampling models and generalizes the symmetric term of the compound error. Within this setup it is possible to develop coherent priors for model parameters in an explicit way. We analyze sensitivity of different prior specifications on the aforementioned scale parameter with respect to posterior characteristics of technology, stochastic parameters, latent variables and—especially—the models’ posterior probabilities, which are crucial for adequate inference pooling. We find that using incoherent priors on the scale parameter of inefficiency has (i) virtually no impact on the technology parameters; (ii) some impact on inference about the stochastic parameters and latent variables and (iii) substantial impact on marginal data densities, which are crucial in BMA.

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