The Annals of Applied Statistics

Profiling time course expression of virus genes—an illustration of Bayesian inference under shape restrictions

Li-Chu Chien, I-Shou Chang, Shih Sheng Jiang, Pramod K. Gupta, Chi-Chung Wen, Yuh-Jenn Wu, and Chao A. Hsiung

Full-text: Open access


There have been several studies of the genome-wide temporal transcriptional program of viruses, based on microarray experiments, which are generally useful in the construction of gene regulation network. It seems that biological interpretations in these studies are directly based on the normalized data and some crude statistics, which provide rough estimates of limited features of the profile and may incur biases. This paper introduces a hierarchical Bayesian shape restricted regression method for making inference on the time course expression of virus genes. Estimates of many salient features of the expression profile like onset time, inflection point, maximum value, time to maximum value, area under curve, etc. can be obtained immediately by this method. Applying this method to a baculovirus microarray time course expression data set, we indicate that many biological questions can be formulated quantitatively and we are able to offer insights into the baculovirus biology.

Article information

Ann. Appl. Stat., Volume 3, Number 4 (2009), 1542-1565.

First available in Project Euclid: 1 March 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Baculovirus Bernstein polynomials genome-wide expression profile Markov chain Monte Carlo microarray experiments shape restricted regression


Chien, Li-Chu; Chang, I-Shou; Jiang, Shih Sheng; Gupta, Pramod K.; Wen, Chi-Chung; Wu, Yuh-Jenn; Hsiung, Chao A. Profiling time course expression of virus genes—an illustration of Bayesian inference under shape restrictions. Ann. Appl. Stat. 3 (2009), no. 4, 1542--1565. doi:10.1214/09-AOAS258.

Export citation


  • Ayres, M. D., Howard, S. C., Kuzio, J., Lopez-Ferber, M. and Possee, R. D. (1994). The complete DNA sequence of Autographa californica nuclear polyhedrosis virus. Virology 202 586–605.
  • Brunk, H. D. (1955). Maximum likelihood estimates of monotone parameters. Ann. Math. Statist. 26 607–616.
  • Chang, I. S., Chien, L. C., Hsiung, C. A., Wen, C. C. and Wu, Y. J. (2007). Shape restricted regression with random Bernstein polynomials. In Complex Datasets and Inverse Problems (R. Liu, W. Strawderman and C. H. Zhang, eds.). IMS Lecture Notes—Monograph Series 54 187–202. Inst. Math. Statist., Beachwood, OH.
  • Chang, I. S., Chien, L. C., Gupta, P. K., Wen, C. C., Wu, Y. J. and Hsiung, C. A. (2008). Supplement to “Profiling time course expression of virus genes—an illustration of Bayesian inference under shape restrictions.”
  • Chang, I. S., Hsiung, C. A., Wu, Y. J. and Yang, C. C. (2005). Bayesian survival analysis using Bernstein polynomials. Scand. J. Statist. 32 447–466.
  • Dette, H., Neumeyer, N. and Pilz, K. F. (2006). A simple nonparametric estimator of a strictly monotone regression function. Bernoulli 12 469–490.
  • Dunson, D. B. (2005). Bayesian semiparametric isotonic regression for count data. J. Amer. Statist. Assoc. 100 618–627.
  • Duplessis, M., Russell, W. M., Romero, D. A. and Moineau, S. (2005). Global gene expression analysis of two Streptococcus thermophilus bacteriophages using DNA microarray. Virology 340 192–208.
  • Friesen, P. D. and Miller, L. K. (2001). Insect viruses. In Fields’ Virology, 4th ed. (D. M. Knipe, P. M. Howley, D. E. Griffin, M. A. Martin, R. A. Lamb, B. Roizman and S. E. Straus, eds.) 608–609. Lippincott Williams & Wilkins, Philadelphia.
  • Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian Data Analysis, 2nd ed. Chapman & Hall/CRC, Boca Raton.
  • Gelman, A. (2003). A Bayesian formulation of exploratory data analysis and goodness-of-fit testing. Int. Statist. Rev. 71 369–382.
  • Gelman, A., Meng, X. L. and Stern, H. S. (1996). Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Statist. Sinica 6 733–807.
  • Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Statist. Sci. 7 457–511.
  • Gijbels, I. (2003). Monotone regression. Discussion Paper 0334, Institute de Statistique, Université Catholique de Louvain. Available at
  • Hall, P. and Heckman, N. E. (2002). Estimating and depicting the structure of a distribution of random funcions. Biometrika 89 145–158.
  • Heckman, N. E. and Zamar, R. H. (2000). Comparing the shapes of regression functions. Biometrika 87 135–144.
  • Hildreth, C. (1954). Point estimate of ordinates of concave functions. J. Amer. Statist. Assoc. 49 598–619.
  • Hill, J. E., Kuzio, J. and Faulkner, P. (1995). Identification and characterization of the v-cath gene of the baculovirus, CfMNPV. Biochimica et Biophysica Acta 1264 275–278.
  • Iwanaga, M., Takaya, K., Katsuma, S., Ote, M., Tanaka, S., Kamita, S. G., Kang, W. K., Shimada, T. and Kobayashi, M. (2004). Expression profiling of baculovirus genes in permissive and nonpermissive cell lines. Biochemical and Biophysical Research Communications 323 599–614.
  • Jiang, S. S., Chang, I. S., Huang, L. W., Chen, P. C., Wen, C. C., Liu, S. C., Chien, L. C., Lin, C. Y., Hsiung, C. A. and Juang, J. L. (2006). Temporal transcription program of recombinant Autographa californica multiple nucleopolyhedrosis virus. Journal of Virology 80 8989–8999.
  • Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773–795.
  • Knebel-Morsdorf, D., Flipsen, J. T., Roncarati, R., Jahnel, F., Kleefsman, A. W. and Vlak, J. M. (1996). Baculovirus infection of Spodoptera exigua larvae: lacZ expression driven by promoters of early genes pe38 and me53 in larval tissue. Journal of General Virology 77 815–824.
  • Lagreid, A., Hvidsten, T. R., Midelfart, H., Komorowski, J. and Sandvik, A. K. (2003). Predicting gene ontology biological process from temporal gene expression patterns. Genome Research 13 965–979.
  • Lavine, M. and Mockus, A. (1995). A nonparametric Bayes method for isotonic regression. J. Statist. Plann. Inference 46 235–248.
  • Lavine, M. and Schervish, M. J. (1999). Bayes factors: What they are and what they are not. Amer. Statist. 53 119–122.
  • Majtan, T., Halgasova, N., Bukovska, G. and Timko, J. (2007). Transcriptional profiling of bacteriophage BFK20: Coexpression interrogated by “guilt-by-association” algorithm. Virology 359 55–65.
  • Milks, M. L., Washburn, J. O., Willis, L. G., Volkman, L. E. and Theilmann, D. A. (2003). Deletion of pe38 attenuates AcMNPV genome replication, budded virus production, and virulence in Heliothis virescens. Virology 310 224–234.
  • Mishra, G., Chadha, P. and Das, R. H. (2008). Serine/threonine kinase (pk-1) is a component of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) very late gene transcription complex and it phosphorylates a 102 kDa polypeptide of the complex. Virus Research 137 147–149.
  • Petrone, S. (1999). Random Bernstein polynomials. Scand. J. Statist. 26 373–393.
  • Reilly, L. M. and Guarino, L. A. (1994). The pk-1 gene of Autographa californica multinucleocapsid nuclear polyhedrosis virus encodes a protein kinase. Journal of General Virology 75 2999–3006.
  • Smith, I. (2007). Misleading messengers? Interpreting baculovirus transcriptional array profiles. Journal of Virology 81 7819–7821.
  • van Munster, M., Willis, L. G., Elias, M., Erlandson, M. A., Brousseau, R., Theilmann, D. A. and Masson, L. (2006). Analysis of the temporal expression of Trichoplusia ni single nucleopolyhedrovirus genes following transfection of BT1-Tn-5B1-4 cells. Virology 354 154–166.
  • Yang, W. C., Devi-Rao, G. V., Ghazal, P., Wagner, E. K. and Triezenberg, S. J. (2002). General and specific alterations in programming of global viral gene expression during infection by VP16 activation-deficient mutants of herpes simplex virus type 1. Journal of Virology 76 12758–12774.

Supplemental materials