Faming Liang

Professor,  Department of Statistics,  Purdue University, West Lafayette, IN 47907.

Office: Math Building 520;    Phone: (765) 494-4452;    Email: fmliang@purdue.edu

Courses taught:

  •       Computing for Statistics

  •       Computer Intensive Statistical Methods

  •       Linear Model

  •       Regression Analysis

  •       Probability

  •       Mathematical Statistics

  •       Introduction to Linear Models

  •       Probability (graduate course)

  •       Statistical Inference (graduate course)

  •       Computing for Bioinformatics (graduate course)

  •       Monte Carlo Methods (graduate course

Job Openings:

A two-year postdoctoral position to work on Machine Learning, Big Data, and/or Bioinformatics. Interested candidates with a strong background in statistical computing and theory should forward their CV, selected reprints, a research statement (2-3 pages) and the contact information (phone and email) for three references to Professor Faming Liang at fmliang@purdue.edu.

Lecturing Assignment for Spring Semester of 2018:

STAT598 Special Topic: Monte Carlo Methods for Complex Data



Research Interests: 

  • Markov Chain Monte Carlo

  • Big Data
  • Bioinformatics

  • Spatial Statistics
  • Machine Learning

  • Statistical Genetics
  • Stochastic Optimization

Research Group 

Recent Talks

Editorial Service

  •  Associate Editor, Journal of Computational and Graphical Statistics, 2006-Present.

  •  Associate Editor, Journal of American Statistical Association, 2010-Present

  •  Associate Editor, Bayesian Analysis, 2010-2016

  •  Associate Editor, Technometrics, 2013-2017
  •   Associate editor, Biometrics, 2006-2008


  •   IMS fellow, 2013.

  •   ASA fellow, 2011.

  •   Elected member, International Statistical Institute (ISI), 2005.

  •   Dean's Citation Award 2016.

  •   Youden Prize 2017

Selected Publications:

  • Books

  1.  Kendall, W.S., Liang, F., and Wang, J.S. (2005) (Editors) Markov Chain Monte Carlo: Innovations and Applications. World Scientific: Singapore.  ISBN 981-256-427-6.

      2.   Liang, F., Liu, C. and Carroll, R.J. Advanced Markov chain Monte Carlo: Learning from Past Samples.  Wiley.  ISBN: 978-0-470-74826-8.


  •      R Packages 

  1.       Liang, F., Wu, M., and Tian, Y. (2008)  Bayesian LatentChIP.

  2.       Wu, M. and Liang, F. (2009)  Testing multiple hypotheses using population information of samples. CodeSupplementary Material.

  3.     Cheng, Y. and Liang, F. (2016)  RSAgeo: Resampling-Based Analysis of Geostatistical Data, available at https://cran.r-project.org/web/packages/RSAgeo/.

  4.    Jia, B., Liang, F., Shi, R., and Xu, S. (2017) equSA: Estimate Directed and Undirected Graphical Models and Construct Networks, available at https://cran.r-project.org/web/packages/equSA/.
  5.    Jia, B. and Liang, F. (2017)  ICmiss Package and Manual.

  6.  Jia. B and Liang, F. (2017) Bayesian neural networks: package and manual


  •        Articles

  1. Wong, W.H. and Liang, F. (1997) Dynamic weighting in Monte Carlo and optimization, Proc. Natl. Acad. Sci. USA, 94, 14220-14224.

  2. Liang, F. and Wong, W.H. (1999) Dynamic weighting in simulations of spin systems, Phys. Lett. A, 252, 257-262.

  3. Cong, J., Kong, T., Xu, D., Liang, F., Liu, J.S., and Wong, W.H. (1999) Relaxed simulated tempering for VLSI floorplan designs, Proc. Asia and South Pacific Design Automation Conf., Hong Kong, pp13-16.

  4. Cong, J., Kong, T., Xu, D., Liang, F., Liu, J.S., and Wong, W.H. (2000) Dynamic weighting Monte Carlo for constrained floorplan design in mixed signal application,Proc. Asia and South Pacific Design Automation Conf., Japan.

  5. Sanderson P, Taylor D., Ali M., Liew S.C., Couturier S., Lee G., Truong Y., Liang F., Gin K. and Holden H. (1999) Development of a methodology for monitoring variations in turbid waters draining modified wetlands in southeast Sumatra, Indonesia: preliminary results for suspended sediments, Eighth International Symposium on the Interactions Between Sediments and Water}, Beijing, pp. 13-17.

  6. Liu, J.S., Liang, F., and Wong. W.H. (2000) The use of multiple-try method and local optimization in Metropolis sampling, J. Amer. Statist. Assoc.,95, 121-134.

  7. Liang, F. and Wong. W.H. (2000) Evolutionary Monte Carlo sampling: applications to $C_p$ model sampling and change-point problem. Statistica Sinica,10, 317-342.

  8. Truong, Y. K., Liang, F., Sanderson, P. G., Taylor, D. and Liew, S. C. (2000) M onitoring variations in turbid waters draining modified wetlands in southeast Su matra, Indonesia: A functional data analytic approach. In Nonparametric approach to Knowledge Discovery, Nara, Japan, December 14-17, 2000. Proceedings.

  9. Liu, J.S., Liang, F., and Wong. W.H. (2001) A theory for dynamic weighting in Monte Carlo, J. Amer. Statist. Assoc., 96, 561-573.

  10. Liang, F. and Wong. W.H. (2001) Real-parameter evolutionary sampling with applications in Bayesian Mixture Models, J. Amer. Statist. Assoc., 96, 653-666. 

  11. Liang, F., Truong, Y.K. and Wong, W.H. (2001) Automatic Bayesian model averaging for linear regression and applications in Bayesian curve fitting. Statistica Sinica , 11, 1005-1029. 

  12. Liang, F. and Wong, W.H. (2001) Evolutionary Monte Carlo for Protein Folding simulations, Journal of Chemical Physics , 115, 3374-3380.

  13. Liang, F. (2002) Some connections between Bayesian and non-Bayesian methods for regression model selection.   Statistics & Probability Letters , 57, 53-63.

  14. Liang, F. (2002) Dynamically Weighted Importance Sampling in Monte Carlo Computation, J. Amer. Statist. Assoc. , 97, 807-821.

  15. Liang, F. (2003) An Effective Bayesian Neural Network Classifier with a Comparison Study to Support Vector Machine,  Neural Computation, 15, 1959-1989.

  16.  Liang, F. (2003) Use of sequential structure in simulation from high dimensional systems, Physical Review E,  67, 56101-56107.

  17. Zhang, J., Liang, F., Dassen, W. and de Gunst, M. (2003)  Search for Haplotype-Interactions that are susceptible to type I diabetes using unphased genotype dataAmerican J. Human Genetics, 73,   1385-1401.

  18. Liang, F. (2004). Generalized 1/k-Ensemble Algorithm, Physical Review E, 69, 66701-66707.

  19.  Liang, F. (2004) Annealing Contour Monte Carlo for Structure Optimization in an Off-lattice Protein ModelJournal of Chemical Physics, 120, 6756-6763. (This paper is selected  by editors expert for re-publication in the April 1, 2004 issue of  Virtual Journal of Biological Physcis Research.)

  20.  Liang, F. (2004) Annealing contour Monte Carlo for neural network training. Proceedings on Cybernetics and Informatics Technologies, Systems and Applications, Volume III, pp.130-135.

  21. Liang, F. and Kuk, Y.C.A. (2004)  A finite population estimation study with Bayesian neural networksSurvey Methodology30, 219-234.

  22. Liang, F. (2005) Bayesian neural networks for non-linear time series forecastingStatistics and Computing, 15, 13-29.

  23.  Liang, F. and Liu, C. (2005)  Efficient MCMC estimation of discrete distributionsComputational Statistics and Data Analysis49, 1039-1052.

  24. Liang, F. (2005) Evidence Evaluation for Bayesian Neural Networks. Neural Computation17, 1385-1410.

  25. Liang, F. (2005) Generalized Wang-Landau algorithm for Monte Carlo Computation. J. Amer. Statist. Assoc., 100, 1311-1327.

  26. Liang, F. (2005) Determination of normalizing constants for simulated tempering. Physica A, 356, 468-480.

  27. Liang, F. (2005). Annotated bibliography: Advanced Markov chain Monte Carlo methods.  ISBA Bulletin12(4),  2-5.

  28. Liang, F. and Huang, J. (2006) Book  Review: Statistical and Computational Inverse Problems.  Technometrics, 48, 146.

  29. Liang, F. (2006) A theory on flat histogram Monte Carlo algorothms. Journal of Statistical Physics, 122,  511-529.

  30. Zhu, H., Liang, F., Gu, M. and Peterson, B. (2006) Stochastic Approximation algorithms for estimation of spatial mixed models. In  Handbook of Computing and Statistics with Applications, Vol.   (eds. S.Y. Lee), Elsevier. pp.399-421.

  31. Liang, F., Liu, C. and Wang, N. (2007) A sequentail  Bayesian procedure for identification of differentially expressed genes.  Statistica Sinica, 12, 571-597.

  32. Liang, F., Liu, C. and Carroll, R.J. (2007) Stochastic Approximation in Monte Carlo Computation.   J. Amer. Statist. Assoc., 102, 305-320.

  33. Liang, F. and Wang, N. (2007) Dynamic Hierarchical Clustering of Gene Expression Profiles.  Pattern Recognition Letters,  28,  1062-1076.

  34. Liang, F. (2007) Use of SVD-based probit transformation in clustering gene expression profiles.  Computational Statistics and Data Analysis51, 6355-6366.

  35. Liang, F. (2007) Continuous Contour Monte Carlo for Marginal Density Estimation with an Application
    to a Spatial Statistical Model
    , Journal of Computational and Graphical Statistics, 16(3), 608-632.

  36. Liang, F.  (2007)  Annealing Stochastic Approximation Monte Carlo for Neural Network TrainingMachine Learning, 68(3), 201-233.

  37.  Cheon, S. and Liang, F. (2008) Phylogenetic Tree Reconstruction Using Sequential Stochastic Approximation   Monte Carlo.  BioSystems, 91, 94-107.

  38. Liang, F. (2008) Stochastic Approximation Monte Carlo for MLP Learning In Encyclopedia of Artificial Intelligence, (eds. J.R.R. Dopico,  J.D. de la Calle, and A.P. Sierra), pp.1482-1489.

  39. Zhang, J., J Rggieli, M. Schipper, M. Entius, F. Liang, J. Koerselman, H Ruven, Y van der Graaf, D. Grobbee, and P. Doevendans (2008)  Inflammatory gene haplotype-interaction networks involved in coronary collateral formation. Human Heredity, 66, 252-264.

  40. Liang, F. and Zhang, J. (2008) Estimating FDR under general dependence using stochastic approximationBiometrika,  95(4), 961-977.

  41.  Liang, F. (2008) Clustering gene expression profiles using mixture model ensemble averaging approachJP Journal of Biostatistics, 2(1), 57-80.

  42. Zhang, J. and Liang, F. (2008) Convergence of stochastic approximation under irregular conditions. StatisticaNeerlandica, 62, 393-403.

  43. Yuan, R., Ding, Y., and Liang, F. (2008)  Adaptive Evolutionary Monte Carlo for Optimizations with Applications to Sensor Placement ProblemsStatistics and Computing, 18, 375-390.

  44. Liang, F. (2009) Improving SAMC Using Smoothing Methods: Theory and Applications to Bayesian Model Selection Problems. The Annals of Statistics37, 2626-2654.

  45. Liang, F. (2009) On the use of SAMC for Monte Carlo integration. Statistics & Probability Letters, 79, 581-587.

  46.  Liang, F. and Zhang, J. (2009) Learning Bayesian Networks for Discrete Data. Computational Statistics & Data Analysis, 53, 865-876.

  47. Zhang, X.S., Liang, F., Srinivasan, R., and Van Liew, M. (2009) Estimating uncertainty of streamflow simulation using Bayesian neural networksWater Resources Research, 45, W02403.

  48.  Cheon, S. and Liang, F. (2009) Bayesian phylogeny analysis via stochastic approximation Monte CarloMolecular Phylogenetic & Evolution, 53, 394-403.

  49. Wu, M., Liang, F. and Tian, Y. (2009) Bayesian Modeling of ChIP-chip Data Using Latent Variables. BMCBioinformatics, 10: 352.

  50. Xie, Y., Zhang, Y., and Liang, F. (2009) Crash injury severity analysis using Bayesian ordered probit models.  Journal of Transportation Engineering135(1), 18-25.

  51.  Liang, F. (2009) Learning Bayesian Networks for Gene Expression Data. In Bayesian Modeling in Bioinformatics (Eds. D.K. Dey, S. Ghosh  and B.K. Mallick), pp.349-367.

  52. Liang, F. and Cheon, S. (2009) Monte Carlo dynamically weighted importance sampling for spatial models with intractable normalizing constants. Journal of Physics: Conference Series, 197, 012004.
  53. Zhang, P., Hill, C., Xia, Y., and Liang, F. (2010)   Modeling the relationship between EDI implementation
    and firm performance improvement with neural networks.  IEEE Transactions on Automation Science and Engineering, 7, 96-110.

  54. Liang, F. (2010) A double Metropolis-Hastings sampler for spatial models with intractable normalizing constants. Journal of Statistical Computing and Simulation, 80, 1007-1022.

  55. Martinez, J.N., Liang, F., Zhou, L., and Carroll, R.J. (2010)   Longitudinal Functional Principal Component Modeling via Stochastic Approximation Monte Carlo. Canadian Journal of Statistics, 38, 256-270.

  56. Mo, Q. and Liang, F. (2010)  Bayesian modeling of ChIP-chip data through a high-order Ising model.  Biometrics, 66, 1284-1294.

  57. Zhang, J. and Liang, F. (2010) Exponential power mixture models for clustering. Biometrics, 66, 1078-1086.

  58. Mo, Q. and Liang, F. (2010) A hidden Ising model for ChIP-chip data analysis. Bioinformatics, 26, 777-783.

  59. Liang, F. (2010) Trajectory averaging for stochastic approximation  MCMC algorithms. Annals of Statistics, 38, 2823-2856.

  60. Wu, M. and Liang, F. (2010) Testing Multuiple Hypotheses  Using Population Information of Samples.  JPJournal of Biostatistics, 4, 181-201.

  61. Liang, F. (2011) Evolutionary Stochastic Approximation Monte Carlo for Global Optimization.  Statistics and Computing, 21, 375-393.

  62. Yin, G., Ma, Y., Liang, F. and Yuan, Y. (2011) Stochastic generalized method of moments. Journal of Computational and Graphical Statistics, 20, 714-727.

  63. Yu, K., Liang, F., Chatterjee, N., and Ciampa, J. (2011)  Efficient p-Value Evaluation for Resampling-based tests. Biostatistics, 12, 582-593.

  64. Zhang, N., Li, X., Tao k., Jiang, L., Ma, T.,  Yan, S., Yuan, C. Moran, M.S., Liang, F., Haffty, B.G. and Yang, Q. (2011) BCL-2 (-938C>A) polymorphism is associated with breast cancer susceptibility.  BMC Medical Genetics, 12:48.

  65.  Cheon, S. and Liang, F. (2011) Folding small proteins via annealing stochastic approximatio Monte Carlo. BioSystems, 105, 243-249.

  66. Zhang, X., Liang, F., Yu, B. and Zong, Z. (2011) Explicitly integrating parameter, input and  structure uncertainties into Bayesian neural networks for probabilistic hydrologic forecasting.  Journal of Hydrology, 409, 696-709.

  67. Park, J. and Liang, F. (2012) Bayesian analysis of geostatistical models with an auxiliary lattice. Journal of computational and Graphical Statistics, 21, 453-475.

  68. Shi, X., Zhu, H., Ibrahim, J.G., Liang, F., Lieberman, J. and Styner, M. (2012)  Intrinsic regression models for medial representation of subcortical structures. J. Amer. Statist. Assoc., 107, 12-23.

  69. Yu, K., Wacholder, S., Wheeler, W., Wang, Z., Caporaso, N., Landi, M.T., Liang, F.  (2012) A flexible Bayesian model for studying gene-environment interaction.  PLoS Genetics,  8(1): e1002482.

  70. Jin, I.K. and Liang, F. (2013) Fitting social network models using varying truncation stochastic approximation MCMC algorithm. Journal of Computational and Graphical Statistics, 22, 927-952.

  71. Jin, I.K. and Liang, F. (2013) Bayesian SAMC for distributions with intractable normalizing constants,  Computational Statistics & Data Analysis, in press.

  72.  Ryu, D., Liang, F. and Mallick, B.K. (2013). Sea Surface Temperature Modeling using Radial Basis Function Networks with a Dynamically Weighted Particle Filter.  J. Amer. Statist. Assoc., 108, 111-123.

  73. Liang, F., Cheng, Y., Song, Q., Park, J., and Yang, P. (2013). A Resampling-based Stochastic Approximation Method for Analysis of Large Geostatistical Data. J. Amer. Statist. Assoc., 108, 325-339.

  74. Zhou, C., Yang, P., Dessler, A.E., and Liang, F. (2013). Statistic of horizontally oriented ice cloud  crystals in optically thick clouds. IEEE Geoscience and Remote Sensing Letters, 10, 986-990.

  75. Liang, F., Song, Q., and Yu, K. (2013).  Bayesian Subset Modeling for High Dimensional Generalized Linear Models.  J. Amer. Statist. Assoc., 108, 589-606.

  76.  Liang, F. and Xiong, M. (2013). Bayesian detection of disease-associated rare variants under posterior consistency.  PLoS One, 8(7), e69633.

  77. Pourhabib, A., Liang, F. and Ding, Y. (2013). Bayesian site selection for fast Gaussian process regression. IIE Transactions, in press.
  78. Liang, F. and Jin, I.K. (2013). A Monte Carlo Metropolis-Hastings Algorithm for Sampling from Distributions with Intractable Normalizing Constants. Neural Computation, 25, 2199-2234.

  79. Cheon, S., Liang, F., Chen, Y., and Yu, K. (2014).  Stochastic Approximation Monte Carlo Importance Sampling for Approximating Exact Conditional Probabilities. Statistics and Computing, 24, 505-520.

  80. Pourhabib, A., Liang, F. and Ding, Y. (2014). Bayesian site selection for fast Gaussian process regression. IIE Transactions46, 543-555.

  81.  Zhang, H., Shi, J., Liang, F., Wheeler, W., Stolzenberg-Solomon R., and Yu K. (2014). A fast multilocus test with adaptive SNP selection for large-scale genetic-association studies. European Journal of Human Genetics, 22, 696-702.

  82. Cheng, Y., Gao, X., and Liang, F. (2014). Bayesian Peak Picking for NMR Spectra. Genomics, Proteomics & Bioinformatics, 12, 39-47.

  83. Jin, I.K. and Liang, F. (2014) Bayesian SAMC for distributions with intractable normalizing constants,  Computational Statistics & Data Analysis, 71, 402-416.
  84. Song, Q., Wu, M. and Liang, F. (2014). Weak Convergence Rates of Population versus Single-Chain Stochastic Approximation MCMC Algorithms. Advances in Applied Probability, 46, 1059-1083. (Supplementary Material)

  85. Liang, F., Cheng, Y., and Guang, L. (2014). Simulated Stochastic Approximation Annealing for Global Optimization with a Square-root Cooling Schedule. J. Amer. Statist. Assoc.109, 847-863.

  86. Liang, F. (2014). An Overview of Stochastic Approximation Monte Carlo. WIREs Computational Statistics, 6, 240-254.

  87. Xu, G., Liang, F. and Genton, M. (2015). A Bayesian Spatio-Temporal Geostatistical Model with an Auxiliary Lattice for Large Datasets. Statistica Sinica, 25,61-79.

  88. Cheng, Y. and Liang, F. (2015) Discussion on "Modeling an Augmented Lagrangian for Improved Blackbox Constrained Optimization"  by Gramacy et al. Technometrics, 61, 39.
  89. Song, Q. and Liang, F. (2015). A Split-and-Merge Bayesian Variable Selection Approach for Ultra-high dimensional Regression. J. Royal Statist. Soc. B, 77(5), 947-972.

  90. Song, Q. and Liang, F. (2015). High Dimensional Variable Selection with Reciprocal L1-Regularization. J. Amer. Statist. Assoc., 110, 1607-1620.

  91. Liang, F., Song, Q. and Qiu, P. (2015). An Equivalent Measure of Partial Correlation Coefficients for High Dimensional Gaussian Graphical Models. J. Amer. Statist. Assoc., 110, 1248-1265.
  92. Liang, F., Jin, I.H., Song, Q. and Liu, J.S. (2016). An Adaptive Exchange Algorithm for Sampling from Distribution with Intractable Normalizing Constants. J. Amer. Statist. Assoc., 111, 377-393.

  93. Liang, F., Shi, R. and Mo, Q. (2016). A split-and-merge approach for singular value decomposition of large-scale matrices. Statistics and Its Interface, 9, 453-459.

  94.  Liang, F., Kim, J. and Song, Q. (2016). A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data.  Technometrics, 58, 304-318.

  95. Lamba, V., Jia, B. and Liang, F. (2016). STAT5A and STAT5B have opposite correlations with drug response gene expression. Biochemical and Biophysical Research Communications, 479(2): 117-124.
  96.  Georgios Karagiannis, Bledar A. Konomi, Guang Lin, and Faming Liang (2017). Parallel and Interactive Stochastic Approximation Annealing Algorithms for Global Optimization. Statistics and Computing, 27(4), 927-945.

  97.  Tianzhou Ma,  Faming Liang, and George C. Tseng (2017). Biomarker detection and categorization in ribonucleic acid sequencing meta-analysis using Bayesian hierarchical models. Applied Statistics, 66(4), 847-867.
  98. Luo, X., Huang, J., Liang, F., Canalesm J.R., Wistuba, I.I., Gazdar, A., Xie, Y., and Xiao, G. (2017). Comprehensive Computational Pathological Image Analyses Predict Lung Cancer Prognosis. Journal of Thoracic Oncology, 12(3), 501-509.

  99.  Lee, S., Liang, F., Cai, L. and Xiao, G. (2017) Integrative analysis of gene networks and their application to lung adenocarinoma studies. Cancer Informatics: 16.

  100. Li, X., Campbell-Thompson, M., Wasserfall, C.H., McGrail, K., Posgai, A., Schultz, A.R., Brusko, T.M., Shuster, J., Liang, F., Muir, A., Schatz, D., Haller, M. and Atkinson, M.A. (2017).  Serum tryosinogen levels in pre-type 1 diabetes--A novel biomarker associating with disease risk.  Diabetes Care,  40(4), 577-582.

  101. Jia, B., Xu, S., Lamba, V.,  Xiao, G., and Liang, F. (2017) Inference of Genetic Network with Next Generation Sequencing Data. Biometrics, 73(4), 1221-1230.

  102. Sundaresan, V., Lin, V.T., Liang, F., Kaye, F.J., and Zhou, L. (2017). Significantly mutated genes and regulatory pathways in SCLC--A Meta Analysis. Cancer Genetics, 216-217, 20-28.
  103. Yu, D., Lim, J., Wang, X., Tang, H., Liang, F. and Xiao, G. (2017) Enhanced construction of gene regulatory networks using hub gene information. BMC Bioinformatics, 18(1):186.

  104. Li, Qi, Yi, F., Wang, T., Xiao, G. and Liang, F. (2017) Lung cancer pathological image analysis using a hidden Potts model. Cancer Informatics, 16, 1-9. Algorithm Implementation

  105. Ma, T., Liang, F., Oesterreich, S., and Tseng, G.C. (2017). A joint Bayesian modeling for integrating microarray and RNA-seq transcriptomic data. Journal of Computational Biology,  24(7), 647-662.

  106. Xue, J. and Liang, F. (2017). A Robust Model-Free Feature Screening Method for Ultrahigh-Dimensional Data. Journal of Computational and Graphical Statistics, 26(4), 803-813.

  107. Lee, S., Liang, F., Cai, L. and Xiao, G. (2018) A two-stage approach of gene network analysis for high-dimensional heterogeneous data.  Biostatistics, 19(2),  216-232 .

  108. Ryu, D., Bilgili, D., Ergonul, O., Liang, F., and Ebrahimi, N. (2018). A Bayesian generalized linear model for Crimean-Congo hemorrhagic fever incidents.  Journal of Agricultural, Biological, and Environmental Statistics, in press.

  109.  Xue, J. and Liang, F. (2018) A double-parallel MCMC algorithm for Bayesian analysis of big data. Statistics and Computing, in press.

  110. Liang, F., Li, Q. and Zhou, L.  (2018) Bayesian Neural Networks for Selection of drug sensitive Genes. J. Amer. Statist. Assoc., in press.

  111. Liang, F., Jia, B., Xue, J., Li, Q. and Luo, Y. (2018) An imputation-regularized optimization algorithm for high-dimensional missing data problems and beyond. J. Royal Statist. Soc. B, in press.  (See arXiv:1802.02251 for an early version of this paper).

  112.  Li, Q., Wang, X., Liang, F., Yi, F., Xie, Y., Gazdar, A., and Xiao, G. (2018).  A Bayesian Hidden Potts Mixture model for Analyzing Lung Cancer Pathological Images. Biostatistics, in press.