scholarly journals Bayesian Model Averaging and Weighted Average Least Squares: Equivariance, Stability, and Numerical Issues

2011 ◽  
Author(s):  
Giuseppe De Luca ◽  
J.R. Magnus
Keyword(s):  
Least Squares ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average

scholarly journals Bayesian Model Averaging and Weighted-Average Least Squares: Equivariance, Stability, and Numerical Issues

2011 ◽  
Vol 11 (4) ◽  
pp. 518-544 ◽  
Author(s):  
Giuseppe De Luca ◽  
Jan R. Magnus
Keyword(s):  
Least Squares ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Simulated Data ◽  
Linear Regression Models ◽  
Explanatory Variables ◽  
Memory Problems ◽  
Regression Parameters

In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to several practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed, and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model-averaging estimation.

scholarly journals A Regional Blended Precipitation Dataset over Pakistan Based on Regional Selection of Blending Satellite Precipitation Datasets and the Dynamic Weighted Average Least Squares Algorithm

2020 ◽  
Vol 12 (24) ◽  
pp. 4009
Author(s):  
Khalil Ur Rahman ◽  
Songhao Shang
Keyword(s):  
Least Squares ◽  
Bayesian Model ◽  
Arid Regions ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Satellite Precipitation ◽  
Post Monsoon ◽  
Skill Scores ◽  
Higher Weights

Substantial uncertainties are associated with satellite precipitation datasets (SPDs), which are further amplified over complex terrain and diverse climate regions. The current study develops a regional blended precipitation dataset (RBPD) over Pakistan from selected SPDs in different regions using a dynamic weighted average least squares (WALS) algorithm from 2007 to 2018 with 0.25° spatial resolution and one-day temporal resolution. Several SPDs, including Global Precipitation Measurement (GPM)-based Integrated Multi-Satellite Retrievals for GPM (IMERG), Tropical Rainfall Measurement Mission (TRMM) Multi-Satellite Precipitation Analysis (TMPA) 3B42-v7, Precipitation Estimates from Remotely Sensed Information Using Artificial Neural Networks-Climate Data Record (PERSIANN-CDR), ERA-Interim (reanalysis dataset), SM2RAIN-CCI, and SM2RAIN-ASCAT are evaluated to select appropriate blending SPDs in different climate regions. Six statistical indices, including mean bias (MB), mean absolute error (MAE), unbiased root mean square error (ubRMSE), correlation coefficient (R), Kling–Gupta efficiency (KGE), and Theil’s U coefficient, are used to assess the WALS-RBPD performance over 102 rain gauges (RGs) in Pakistan. The results showed that WALS-RBPD had assigned higher weights to IMERG in the glacial, humid, and arid regions, while SM2RAIN-ASCAT had higher weights across the hyper-arid region. The average weights of IMERG (SM2RAIN-ASCAT) are 29.03% (23.90%), 30.12% (24.19%), 31.30% (27.84%), and 27.65% (32.02%) across glacial, humid, arid, and hyper-arid regions, respectively. IMERG dominated monsoon and pre-monsoon seasons with average weights of 34.87% and 31.70%, while SM2RAIN-ASCAT depicted high performance during post-monsoon and winter seasons with average weights of 37.03% and 38.69%, respectively. Spatial scale evaluation of WALS-RPBD resulted in relatively poorer performance at high altitudes (glacial and humid regions), whereas better performance in plain areas (arid and hyper-arid regions). Moreover, temporal scale performance assessment depicted poorer performance during intense precipitation seasons (monsoon and pre-monsoon) as compared with post-monsoon and winter seasons. Skill scores are used to quantify the improvements of WALS-RBPD against previously developed blended precipitation datasets (BPDs) based on WALS (WALS-BPD), dynamic clustered Bayesian model averaging (DCBA-BPD), and dynamic Bayesian model averaging (DBMA-BPD). On the one hand, skill scores show relatively low improvements of WALS-RBPD against WALS-BPD, where maximum improvements are observed in glacial (humid) regions with skill scores of 29.89% (28.69%) in MAE, 27.25% (23.89%) in ubRMSE, and 24.37% (28.95%) in MB. On the other hand, the highest improvements are observed against DBMA-BPD with average improvements across glacial (humid) regions of 39.74% (36.93%), 38.27% (33.06%), and 39.16% (30.47%) in MB, MAE, and ubRMSE, respectively. It is recommended that the development of RBPDs can be a potential alternative for data-scarce regions and areas with complex topography.

scholarly journals Calibrating Multimodel Forecast Ensembles with Exchangeable and Missing Members Using Bayesian Model Averaging

2010 ◽  
Vol 138 (1) ◽  
pp. 190-202 ◽  
Author(s):  
Chris Fraley ◽  
Adrian E. Raftery ◽  
Tilmann Gneiting
Keyword(s):  
Kalman Filter ◽  
Pacific Northwest ◽  
Ensemble Kalman Filter ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Multimodel Ensembles ◽  
The Individual ◽  
Ensemble Systems

Abstract Bayesian model averaging (BMA) is a statistical postprocessing technique that generates calibrated and sharp predictive probability density functions (PDFs) from forecast ensembles. It represents the predictive PDF as a weighted average of PDFs centered on the bias-corrected ensemble members, where the weights reflect the relative skill of the individual members over a training period. This work adapts the BMA approach to situations that arise frequently in practice; namely, when one or more of the member forecasts are exchangeable, and when there are missing ensemble members. Exchangeable members differ in random perturbations only, such as the members of bred ensembles, singular vector ensembles, or ensemble Kalman filter systems. Accounting for exchangeability simplifies the BMA approach, in that the BMA weights and the parameters of the component PDFs can be assumed to be equal within each exchangeable group. With these adaptations, BMA can be applied to postprocess multimodel ensembles of any composition. In experiments with surface temperature and quantitative precipitation forecasts from the University of Washington mesoscale ensemble and ensemble Kalman filter systems over the Pacific Northwest, the proposed extensions yield good results. The BMA method is robust to exchangeability assumptions, and the BMA postprocessed combined ensemble shows better verification results than any of the individual, raw, or BMA postprocessed ensemble systems. These results suggest that statistically postprocessed multimodel ensembles can outperform individual ensemble systems, even in cases in which one of the constituent systems is superior to the others.

scholarly journals Improving Predictions using Ensemble Bayesian Model Averaging

2012 ◽  
Vol 20 (3) ◽  
pp. 271-291 ◽  
Author(s):  
Jacob M. Montgomery ◽  
Florian M. Hollenbach ◽  
Michael D. Ward
Keyword(s):  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
The Pacific ◽  
The Social ◽  
Out Of Sample ◽  
Forecast Models ◽  
Future Events ◽  
Component Models

We present ensemble Bayesian model averaging (EBMA) and illustrate its ability to aid scholars in the social sciences to make more accurate forecasts of future events. In essence, EBMA improves prediction by pooling information from multiple forecast models to generate ensemble predictions similar to a weighted average of component forecasts. The weight assigned to each forecast is calibrated via its performance in some validation period. The aim is not to choose some “best” model, but rather to incorporate the insights and knowledge implicit in various forecasting efforts via statistical postprocessing. After presenting the method, we show that EBMA increases the accuracy of out-of-sample forecasts relative to component models in three applied examples: predicting the occurrence of insurgencies around the Pacific Rim, forecasting vote shares in U.S. presidential elections, and predicting the votes of U.S. Supreme Court Justices.

scholarly journals Probabilistic Quantitative Precipitation Forecasting Using Bayesian Model Averaging

2007 ◽  
Vol 135 (9) ◽  
pp. 3209-3220 ◽  
Author(s):  
J. Mc Lean Sloughter ◽  
Adrian E. Raftery ◽  
Tilmann Gneiting ◽  
Chris Fraley
Keyword(s):  
Pacific Northwest ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Ensemble Member ◽  
Original Form ◽  
Cube Root ◽  
Precipitation Forecasting ◽  
The North

Abstract Bayesian model averaging (BMA) is a statistical way of postprocessing forecast ensembles to create predictive probability density functions (PDFs) for weather quantities. It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are posterior probabilities of the models generating the forecasts and reflect the forecasts’ relative contributions to predictive skill over a training period. It was developed initially for quantities whose PDFs can be approximated by normal distributions, such as temperature and sea level pressure. BMA does not apply in its original form to precipitation, because the predictive PDF of precipitation is nonnormal in two major ways: it has a positive probability of being equal to zero, and it is skewed. In this study BMA is extended to probabilistic quantitative precipitation forecasting. The predictive PDF corresponding to one ensemble member is a mixture of a discrete component at zero and a gamma distribution. Unlike methods that predict the probability of exceeding a threshold, BMA gives a full probability distribution for future precipitation. The method was applied to daily 48-h forecasts of 24-h accumulated precipitation in the North American Pacific Northwest in 2003–04 using the University of Washington mesoscale ensemble. It yielded predictive distributions that were calibrated and sharp. It also gave probability of precipitation forecasts that were much better calibrated than those based on consensus voting of the ensemble members. It gave better estimates of the probability of high-precipitation events than logistic regression on the cube root of the ensemble mean.

scholarly journals HỆ THỐNG CHỈ SỐ CẢNH BÁO SỚM KHỦNG HOẢNG TIỀN TỆ VÀ KHỦNG HOẢNG NGÂN HÀNG TẠI VIỆT NAM

2021 ◽  
Vol 36 (06) ◽  
Author(s):  
NGUYỄN THỊ MỸ PHƯỢNG
Keyword(s):  
Least Squares ◽  
Early Warning ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Viet Nam ◽  
Two Stage ◽  
Early Warning Indicators ◽  
Two Stage Least Squares ◽  
Warning Indicators

Dựa trên quan điểm thận trọng, nghiên cứu này tích hợp bốn cách tiếp cận Signal, Logit/Probit, BMA (Bayesian Model Averaging) và 2SLS (Two Stage Least Squares) để phát triển hệ thống các chỉ số cảnh báo sớm (Early Warning Indicators – EWI) về khủng hoảng tiền tệ (KHTT) và khủng hoảng ngân hàng (KHNH)  tại Việt Nam. Kết quả nghiên cứu cho thấy vai trò quan trọng của các chỉ số kinh tế vĩ mô trong cảnh báo sớm KHTT và KHNH tại Việt Nam, đặc biệt là 8 chỉ số, bao gồm chỉ số giá chứng khoán, tỷ giá thực đa phương, xuất khẩu, M2/dự trữ ngoại hối, tiền gửi ngân hàng, dự trữ ngoại hối, số nhân cung tiền M2 và tác động của khủng hoảng tài chính (KHTC) toàn cầu. Thêm vào đó, nghiên cứu cũng tìm thấy bằng chứng về mối quan hệ nhân quả hai chiều giữa KHTT và KHNH tại Việt Nam, đồng thời cung cấp bằng chứng thực nghiệm về tác động của hiện tượng đô la hóa đến khả năng xảy ra KHTT và tác động mạnh mẽ của KHTC toàn cầu đến khả năng xảy ra KHTT và KHNH tại các nền kinh tế mới nổi nhỏ và mở cửa như Việt Nam.

scholarly journals Assessment of Merged Satellite Precipitation Datasets in Monitoring Meteorological Drought over Pakistan

2021 ◽  
Vol 13 (9) ◽  
pp. 1662
Author(s):  
Khalil Ur Rahman ◽  
Songhao Shang ◽  
Muhammad Zohaib
Keyword(s):  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Regional Scale ◽  
Winter Season ◽  
Model Averaging ◽  
Weighted Average ◽  
Meteorological Drought ◽  
Least Square ◽  
Severe Drought ◽  
Satellite Precipitation

The current study evaluates the potential of merged satellite precipitation datasets (MSPDs) against rain gauges (RGs) and satellite precipitation datasets (SPDs) in monitoring meteorological drought over Pakistan during 2000–2015. MSPDs evaluated in the current study include Regional Weighted Average Least Square (RWALS), Weighted Average Least Square (WALS), Dynamic Clustered Bayesian model Averaging (DCBA), and Dynamic Bayesian Model Averaging (DBMA) algorithms, while the set of SPDs is Global Precipitation Measurement (GPM)-based Integrated Multi-Satellite Retrievals for GPM (IMERG-V06), Tropical Rainfall Measurement Mission (TRMM) Multi-Satellite Precipitation Analysis (TMPA 3B42 V7), Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN), and ERA-Interim (re-analyses dataset). Several standardized precipitation indices (SPIs), including SPI-1, SPI-3, and SPI-12, are used to evaluate the performances of RGs, SPDs, and MSPDs across Pakistan as well as on a regional scale. The Mann–Kendall (MK) test is used to assess the trend of meteorological drought across different climate regions of Pakistan using these SPI indices. Results revealed higher performance of MSPDs than SPDs when compared against RGs for SPI estimates. The seasonal evaluation of SPIs from RGs, MSPDs, and SPDs in a representative drought year (2008) revealed mildly to moderate wetness in monsoon season while mild to moderate drought in winter season across Pakistan. However, the drought severity ranges from mild to severe drought in different years across different climate regions. MAPD (mean absolute percentage difference) shows high accuracy (MAPD <10%) for RWALS-MSPD, good accuracy (10% < MAPD <20%) for WALS-MSPD and DCBA-MSPD, while good to reasonable accuracy (20% < MAPD < 50%) for DCBA in different climate regions. Furthermore, MSPDs show a consistent drought trend as compared with RGs, while SPDs show poor performance. Overall, this study demonstrated significantly improved performance of MSPDs in monitoring the meteorological drought.

Bayesian Model Averaging With Exponentiated Least Squares Loss

2018 ◽  
Vol 64 (5) ◽  
pp. 3331-3345
Author(s):  
Dong Dai ◽  
Lei Han ◽  
Ting Yang ◽  
Tong Zhang
Keyword(s):  
Least Squares ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging
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