# Doctoral Program

The Statistics Department offers a Doctoral Program with two different tracks that students can choose from: a Mathematical Statistics track and a Biostatistics track. Both tracks are designed to provide doctoral candidates with a firm foundation on probability theory, inference, and classical methodology. In addition, the theory and application of statistical computing, and graphical as well as computer based inference are integral parts of the core curricula. The Biostatistics track provides students the opportunity to focus on one important area of statistical research, namely on the methodology and application of statistics in the life sciences. There is no direct link between the Mathematical Statistics and Biostatistics tracks in the MSc and the Doctoral programs, respectively. That is, a student can pursue a MSc in the Mathematical Statistics track, and then a PhD in the Biostatistics track.

The requirements for the two tracks are:

**Mathematical Statistics/Probability**

- STA 701 – Advanced Statistical Inference I
- STA 702 – Advanced Statistical Inference II
- STA 703 – Advanced Probability
- STA 705 – Advanced Computational Inference
- STA 707 – Advanced Data Analysis

**Biostatistics**

- STA 701 - Advanced Statistical Inference I
- STA 703 - Advanced Probability
- STA 705 - Advanced Computational Inference
- STA 707 - Advanced Data Analysis
- STA 709 - Advanced Survival Analysis

All students must take an additional six courses chosen by the student and approved by the DGS. Three of these will complement and supplement the student's specialization area and research interests. STA 715 (Reading courses) may not be used to satisfy this requirement.

The six electives must be chosen from among STA 612, STA 616, STA 621, STA 624, STA 626, STA 630, STA 635, STA 643, STA 644, STA 653*, STA 661, STA 662, STA 665, CPH 631, CPH 636, and CPH 664*. STA 695 will also be considered on a case by case basis. A course that is required for the selected track may not be used as an elective.

* A student who takes both STA 653 and CPH 664, may only receive credit towards the degree for one of these two courses.

In the following, typical course schedules for both tracks are summarized. Several alternative paths are possible. It is clear from the above track requirements that the only difference in required courses is between STA 702 and STA 709. However, in practice, students often choose to take both of those classes, one for the track, and the other as an elective.

**Mathematical Statistics Track: Typical Course Schedule**

Fall, Year One |
STA 602 Introduction to Statistical Methods | STA 605 Computational Inference | STA 623 Theory of Probability |

Spring, Year One |
STA 603 Introduction to Linear Models and Experimental Design | STA 606 Theory of Statistical Inference I | STA 624 Applied Stochastic Processes |

Fall, Year Two |
STA 607 Theory of Statistical Inference II | STA 643 Advanced Experimental Design | MA 471G or Elective |

Spring, Year Two |
STA 632 Longitudinal Data Analysis | STA 700 Foundations of Probability and Inference | Elective |

Fall, Year Three |
STA 701 Advanced Statistical Inference I | STA 703 Advanced Probability | STA 705 Advanced Computational Inference |

Spring, Year Three |
STA 702 Advanced Statistical Inference II | STA 707 Advanced Data Analysis | Elective |

Fall, Year Four |
Elective | Residency | Residency |

Spring, Year Four |
Elective | Residency | Residency |

**Biostatistics Track: Typical Course Schedule**

Fall, Year One |
STA 602 Introduction to Statistical Methods | STA 605 Computational Inference | STA 623 Theory of Probability |

Spring, Year One |
STA 603 Introduction to Linear Models and Experimental Design | STA 606 Theory of Statistical Inference I | STA 653 Clinical Trials |

Fall, Year Two |
STA 607 Theory of Statistical Inference II | STA 635 Survivability and Life Testing | STA 643 Advanced Experimental Design |

Spring, Year Two |
STA 632 Longitudinal Data Analysis | STA 665 Analysis of Categorical Data | STA 700 Foundations of Probability and Inference |

Fall, Year Three |
STA 701 Advanced Statistical Inference I | STA 703 Advanced Probability | STA 705 Advanced Computational Inference |

Spring, Year Three |
STA 707 Advanced Data Analysis | STA 709 Advanced Survival Analysis | Elective |

Fall, Year Four |
Elective | Residency | Residency |

Spring, Year Four |
Elective | Residency | Residency |

The residency policy at the University of Kentucky is described in the Graduate School Bulletin.

Students must pass a uniform written exam over STA 701 and STA 703 plus respective prerequisites. This exam will normally be offered at the end of May in the third year of the program. The uniform exam can be repeated once. A student can choose their advisor at any time. After completion of tract course requirements and successful completion of the written exam, students must also successfully complete an oral qualifying exam which is scheduled in consultation with the student's advisory committee. A significant part of this exam is to be a dissertation proposal. For details, see the Graduate School Bulletin.

**Recent Dissertation Abstracts**

Below is a list of a few recent dissertation abstracts from students earning a PhD in statistics.

- Aggregated Quantitative Multifactor Dimensionality Reduction - Rebecca E. Crouch
- Multi-state Models with Missing Covariates - Wenjie Lou
- Statistical Methods for Handling Intentional Inaccurate Responders - Kristin J. McQuerry
- Development in Normal Mixture and Mixture of Experts Modeling - Meng Qi
- Developing an Alternative Way to Analyze NanoString Data - Shu Shen
- Empirical Likelihood and Differentiable Functionals - Zhiyuan Shen
- Improved Models for Differential Analysis for Genomic Data - Hong Wang
- Statistical Inference on Dynamical Systems - Hongyuan Wang
- Continuous Time Multi-State Models for Interval Censored Data - Lijie Wan
- Topics in Logistic Regression Analysis - Zhiheng Xie
- Statistical Methods for Environmental Exposure Data Subject to Detection Limits - Yuchen Yang
- Statistical Inference on Trimmed Means, Lorenz Curves, and Partial Area Under ROC Curves by Empirical Likelihood Methods - Yumin Zhao
- New Results in ell_1 Penalized Regression - Edward A. Roualdes
- Multi-State Models for Interval Censored Data with Competing Risk - Shaoceng Wei
- Statistics in the Billera-Holmes-Vogtmann Treespace - Grady S. Weyenberg
- Empirical Likelihood Confidence Band - Shihong Zhu
- Normal Mixture and Contaminated Model with Nuisance Parameter and Applications - Qian Fan
- Genetic Association Testing of Copy Number Variation - Yinglei Li
- Contaminated Chi-square Modeling and its Application in Microarray Data Analysis - Feng Zhou
- James-Stein Type Compound Estimation of Multiple Mean Response Functions and Their Derivatives - Limin Feng
- Polytopes Arising from Binary Multi-way Contingency Tables and Characteristic Imsets for Bayesian Networks - Jing Xi
- Analysis of Spatial Data - Xiang Zhang
- Analysis of Binary Data via Spatial-Temporal Autologistic Regression Models - Zilong Wang
- Some Contributions to the Censored Empirical Likelihood with Hazard-Type Constraints - Yanling Hu
- Parametric Estimation in Competing Risks and Multi-state Models - Yushun Lin
- Bayesian Semiparametric Generalizations of Linear Models using Polya Trees - Angela Schoergendorfer
- Stochastic Dynamics of Gene Transcription - Yan Xie