Treatment of missing values in process data analysis

Canadian Journal of Chemical Engineering

Volumn 86, Issue 5, 2008, Pages 838-858

  Imtiaz, S A ^a   Shah, S L ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Batch process; Compression; Missing data; Multi rate data; PCA

Indexed keywords

AUTOCORRELATION; BATCH DATA PROCESSING; DATA COMPRESSION; DECISION MAKING; MATHEMATICAL MODELS; MULTIVARIANT ANALYSIS; PRINCIPAL COMPONENT ANALYSIS; RANDOM VARIABLES; REGRESSION ANALYSIS; SENSOR NETWORKS; STATISTICAL METHODS;

BATCH PROCESS; COMPRESSION; MISSING DATA; MULTI-RATE DATA; PCA;

DATA HANDLING;

EID: 54949104972     PISSN: 00084034     EISSN: None     Source Type: Journal    
DOI: 10.1002/cjce.20099     Document Type: Article

References (57)

1. Artega, R. and A. Ferrer, "Dealing with Missing Data in MSPCS: Several Methods, Different Interpretations, Some Examples," J. Chemometr. 16, 408-418 (2002).
2. Baum, L. E., T. Petrie, G. Soules and N. Weiss, "A Maximization Technique Occurring in the Statistical Analysis of Probilistic Function of Markov Chains," Ann. Math. Statist. 41, 164-171 (1970).
3. Bjorck, A. and G. Golub, "Numerical Methods for Computing Angles between Linear Subspaces," Math. Comput. 27, 579-594 (1973).
4. Chen, J. and K. C. Liu, "On-Line Batch Process Monitoring Using Dynamic PCA and Dynamic PLS Models," Chem. Eng. Sci. 57, 6375 (2002).
5. Damien, P., "Gibbs Sampling for Bayesian Non-Conjugate and Hierarchical Models by Using Auxiliary Variables," J.R. Statist. Soc. Ser. B(Methodol.) 61, 331-344 (1999).
6. Dempster, A. P., N. M. Laird and D. B. Rubin, "Maximum Likelihood from Incomplete Data via EM Algorithm," J. R. Statist. Soc. Ser. B (Methodol.) 39(1), 1-38 (1977).
7. Edwards, R. G. and A. D. Sokal, "Generalization of Fortuin-Kasteleyn-Swendsen-Wang Representation and Monte Carlo Algorithm," Phys. Rev. Lett. 38, 2009-2012 (1988).
8. Fisher, R. A., "Theory of Statistical Estimation," Proc. Camb. Phil. Soc. 22, 700-725 (1925).
9. Gelman, A., J. B. Carlin, H. S. Stern and D. B. Rubin, "Bayesian Data Analysis," 2nd ed., Chapman and Hall/CRC, Boca Raton, FL (2004).
10. Gollmer, K. and C. Postens, Detection of Distorted Pattern Using Dynamic Time Warping Algorithm and Application for Supervision of Bioprocess. "IFAC Workshop on On-Line Fault Detection and Supervision in Chemical Process Industries," Newcastle (1995).
11. Grung, B. and R. Manne, "Missing Values in Principal Component Analysis," Chemometr. Intell. Lab. Syst. 42, 125-139 (1998).
12. Hartley, H. O., "Maximum Likelihood Estimation from Incomplete Data," Biometrices 14(2), 174-194 (1958).
13. Higdon, D. M., "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications," J. Am. Statist. Assoc. 93, 585-595 (1998).
14. Imtiaz, S. A., M. A. A. S. Choudhury and S. L. Shah, "Building Multivarite Model from Compressed Data," Ind. Eng. Chem. Res. 46, 481-492 (2007).
15. Jennrich, R. I. and P. F. Sampson, "Rotation for Simple Loadings," Psychometrika 31(3), 313-323 (1966).
16. Knyazev, A. W. and M. E. Argentati, "Principal Angles between Subspaces in an a-based Scalar Product: Algorithms and Perturbation Estimates Data," SIAM J. Sci. Compuat. 23(6), 2008-2040 (2002).
17. Kourti, T. P., J. Lee and J. F. MacGregor, "Experience with Industrial Applications of Projection Methods for Multivariate Statistical Process Control," Comput. Chem. Eng. 20, (Suppl. A): S745-S750 (1996).
18. Krzanowski, W. J., "Between-Groups Comparison of Principal Components," J. Am. Statist. Assoc. 74(367), 703-707 (1979).
19. Laird, N. M. and J. H. Ware, "Random-Effects Models for Longitudinal Data," Biometrics 38, 963-974 (1982).
20. Lakshminarayanan, S. R., R. D. Gudi, S. L. Shah and K. Nandakumar, Monitoring Batch Processes Using Multivariate Statistical Tools: Extensions and Practical Issues. "IFAC Triennial World Congress," San Francisco (1996).
21. Li, K. H., "Hypothesis testing in multiple imputation with emphasis on mixed-up frequencies in contingency tables," Unpublished PhD dissertation, University of Chicago, Statistics Department (1985).
22. Little, R. J. A. and D. B. Rubin, "Statistical Analysis with Missing Data," Vol. 2, John Wiley and Sons, Inc., Hoboken, NJ (2002).
23. Liu, C. and D. B. Rubin, "The ECME Algorithm: A Simple Extension of EM and ECM with Faster Monotone Convergence," Biometrika 81(4), 633-648 (1994).
24. Luyben, W. L., "Process Modeling, Simulation and Control for Chemical Engineers," McGraw-Hill, New York (1990).
25. Marjanovic, O., B. Lennox, D. Sandoz, K. Smith and M. Crofts, "Real-Time Monitoring of an Industrial Batch Process," Comput. Chem. Eng. 30, 1476-1481 (2006).
26. McKendrick, A. G., "Application of Mathematics to Medical Problems," 44, 98-130 (1926).
27. Meng, X. L. and D. B. Rubin, "Maximum Likelihood Estimation via the ECM Algorithm: A General Framework," Biometrika 80, 267-278 (1993).
28. Meng X. L. and D. A. van Dyk, "The EM Algorithm-An Old Folk Song Sung to a Fast New Tune (with Discussion)," J. R. Statist. Soc. B 59, 511-567 (1997).
29. Mira, A. and L. Tierney, "On the Use of Auxiliary Variables in Markov Chain Monte Carlo Sampling," Technical Report 59 (1997).
30. Myers, C., L. R. Rabiner and A. E. Rosenberg, "Performance Tradeoffs in Dynamic Time Warping Algorithms for Isolated Word Recognition," IEEE Trans. Acuost. Speech Signal Process. ASSP-28(6): 623. (1980).
31. Narasimhan, S. and S. L. Shah, "Model Identification and Error Covariance Matrix Estimation from Noisy Data Using PCA," Presentation, ADCHEM, Hong Kong (2004).
32. Neal, R. M., "Markov Chain Monte Carlo Methods Based on 'Slicing' the Density Function," Technical Report No. 9722, Department of Statistics, University of Toronto (1997).
33. Nelson, P. R. C., P. A. Taylor and J. F. MacGregor, "Missing Data Methods in PCA and PLS: Score Calculations with Incomplete Observations," Chemometr. Intell. Lab. Syst. 35, 45-465 (1996).
34. Nielsen, S. F., "Proper and Improper Multiple Imputation," Int. Statist. Rev. 71(3), 593-627 (2003).
35. Nomikos, P. and J. F. MacGregor, "Monitoring Batch Processes Using Multiway Principal Component Analysis," AIChE J. 40(8), 1361-1375 (1994).
36. Nomikos, P. and J. F. MacGregor, "Multi-Way Partial Least Squares in Monitoring Batch Processes," Chemometr. Intell. Lab. Syst. 30, 97-108 (1995).
37. Nounou, M. N., B. R. Bakshi, P. K. Goel and X. Shen, "Bayesian Principal Component Analysis," J. Chemometr. 16, 576-595 (2002).
38. Orchard, T. and M. A. Woodbury, "A Missing Information Principle: Theory and Applications," Proc. 6th Berkeley Symposium on Math Statist. and Prob. 1, 697-715 (1972).
39. O'Shaughnessy, D., "Speaker Recognition," IEEE ASSP Mag. 3, 4-17 (1986).
40. Roberts, G. O. and J. S. Rosenthal, "Convergence of Slice Sampler Markov Chains," Technical Report, Statistical Laboratory, Cambridge University (1997).
41. Rubin, D. B., "Inference and Missing Data," Biometrika 63, 581-592 (1976).
42. Rubin, D. B., "Formalizing Subjective Notions about the Effect of Nonrespondents in Sample Surveys," J. Am. Statist. Assoc. 72, 538-543 (1977).
43. Rubin, D. B., "Bayesian Inference for Causal Effects: The Role of Randomization," Ann. Statist. 7, 34-58 (1978).
44. Rubin, D. B., "Multiple Imputations for Nonresponse in Surveys," John Wiley and Sons Inc., Hoboken, NJ (1987).
45. Rubin, D. B., "Discussion on Multiple Imputation," Int. Statist. Rev. 71 (3), 619-625 (2003).
46. Schafer, J. L. and N. Schenker, "Missing Data: Our View of the State of the Art," Psychol. Methods 7(2), 147-177 (2002).
47. Silverman, H. F. and D. P. Morgan, "The Application of Dynamic Programming to Connected Speech Recognition," IEEE ASSP Mag. 7, 6-25 (1990).
48. Sundberg, R., "An Iterative Method for Solution of the Likelihood Equations for Incomplete Data from Exponential Families," Communs. Statist. Simuln. Computn. 5, 55-64 (1976).
49. Swendsen, R. H. and J. S. Wang, "Nonuniversal Critical Dynamics in Monte Carlo Simulation," Phys. Rev. Lett. 58, 86-88 (1987).
50. Tanner, M. A. and W. H. Wong, "The Calculation of Posterior Distribution by Data Augmentation," J. Am. Statist. Assoc. 82(398), 528-540 (1990).
51. Thornhill, N. F., M. A. A. S. Choudhury and S. L. Shah, "The Impact of Compression on Data-Driven Process Analysis," J. Process Control 14, 389-398 (2004).
52. Troyanskaya, O., M. Cantor, G. Sherlock, P. Brown, T. Hastie, R. Tibshirani, D. Botstein and R. B. Altman, "Missing Value Estimation Methods for DNA Microarrays," Bioinfomatics 17(6), 520-525 (2001).
53. VanDyk, D. A. and X.-L. Meng, "The Art of Data Augmentation," J. Comput. Graph. Statist. 10(1), 1-50 (2001).
54. van Sprang, E. N. M., H. J. Ramaker, J. A. Westerhuis, S. P. Gurden and A. K. Smilde* "Critical Evaluation of Approaches for On-Line Batch Process Monitoring," Chem. Eng. Sci. 57, 3979-3991 (2002).
55. Walczak, B. and D. L. Massart, "Dealing with Missing Data," Chemometr. Intell. Lab. Syst. 58, 15-27 (2001).
56. Westerhuis, J. A., T. Kourti and J. F. MacGregor, "Comparing Alternative Approaches for Multivariate Statistical Analysis of Batch Process Data," J. Chemometr. 13, 397-413 (1999).
57. Zhang, P., "Multiple Imputation: Theory and Method," Int. Statist. Rev. 71(3), 581-592. (2003).