320 likes | 333 Vues
Task 6 Statistical Approaches Scope of Work. Bob Youngs NGA Workshop #5 March 25, 2003. Working Group 6. Norm Abrahamson David Brillinger Brian Chiou Bob Youngs. Primary Objectives.
E N D
Task 6Statistical ApproachesScope of Work Bob Youngs NGA Workshop #5 March 25, 2003
Working Group 6 • Norm Abrahamson • David Brillinger • Brian Chiou • Bob Youngs
Primary Objectives • Identify regression techniques that address uncertain/missing predictor variables, multiple levels of overlapping correlation in the residuals, and censoring/truncation of response • Assess the significance of these issues in developing ground motion models • Provide statistical tools to the NGA developers to assist them in addressing these issues
Progress to Date • Treatment of Data Censoring/Truncation • Have identified an approach and begun implementation • Treatment of correlations due to cross-classification of data (earthquake terms and site terms) • Have identified one method for analysis, but may not be an important issue in NGA
Progress to Date (cont’d) • Treatment of other correlations (spatial within a given earthquake, and between frequencies) • Have not determined extent of need for treatment in NGA • Treatment of missing/uncertain predictor variables • Identifying potential approaches to be explored
Censored Data • Known number of recordings where value of yi < Zcensor and value of xiis known (McLaughlin, 1991)
Truncated Data • Unknown number of recordings where value of yi < Ztrunc , value of xiis unknown (Toro, 1981)
Example Large Synthetic Data Set (1000)ln(y)=1 + 2ln(r + 3) + 4r
Example Small Synthetic Data Set (20)ln(y)=1 + 2ln(r + 3) + 4r
Minimum PGA versusNumber of Records/Earthquake in NGA Data Set
Addition Work to be Done • Incorporate into random effects model • Investigate stability of estimation algorithms – maximum likelihood appears to be primary approach • Evaluate sensitivity to selection of truncation level – treat as uncertain?
Source and Site Data Correlations • Earthquake effect – correlation in peak motions from the ith earthquake • presently incorporated by random effects and two-stage regression approaches • Site effect – correlations in peak motions recorded at the jth site. • This effect is cross-classified with the earthquake effect – eliminates block-diagonal variance matrix, requiring “tricks”
Potential Data Correlations from Earthquake and Site Classifications
Tentative Conclusions • Earthquake effect already addressed by developers • Cross-classification by site effect term not a significant issue because of limited number of sites with many recordings • Need to do some testing with simulated data sets to confirm this conclusion
Additional Correlations • Spatial Correlation of adjacent sites • Readily handled as nested classifications provided one has the correlation model • Need to investigate the potential extent in NGA data • Correlation between adjacent spectral frequencies in a “global” regression • Is this of interest to then developers?
Missing Predictor Variables • Site classification variables • VS30, NEHRP Categories, Other Site Categories, • Depth to VS of 1.0 and 2.5 km/sec • Rupture geometry variables • Directivity variables • Hanging wall/footwall determinations • Confined to smaller events/distant recordings where effect is believed to be minimal?
Possible Approaches • Estimation of variable by an external model • Example: correlation of VS30 with surficial geology • Correlations with other variables in the NGA data set • Technique used in multivariate normal models
Treatment of Uncertainty in Predictor Variables • Magnitude uncertainty • partition of earthquake random effect into an magnitude error term and an event term (Rhodes, 1997) • Propagation of variable uncertainty into resulting model parameter uncertainty • Formal errors in variable methods • Simulation methods