### Core Ph.D Courses

**STAT G6101x. Statistical Modeling and Data Analysis I. 4 pts.**

The first semester of a 2 semesters sequence in applied statistics for first year doctoral students in Statistics. Statistical methods including linear and generalized regression; random-effects models; methods for categorical data; survival analysis; and nonparametric methods. The use of statistical packages. Modeling. Exploratory data analysis; modern nonparametric regression. Restricted to students in the doctoral program in Statistics.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Autumn 2014 :: STAT G6101 | |||||

STAT 6101 |
17836 001 |
MW 10:10a – 11:25a TBA |
D. Rabinowitz | 18 / 25 |

**STAT G6102y. Statistical Modelling and Data Analysis II. 4 pts.** *Prerequisites:*STAT W6101

Continuation of G6101.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G6102 | |||||

STAT 6102 |
29140 001 |
MW 10:10a – 11:25a 903 SCHOOL OF SOCIAL WORK |
T. Zheng | 14 / 25 |

**STAT G6103y. Statistical Modeling and Data Analysis III. 3 pts.** *Prerequisites:* Intended primarily for doctoral students in Statistics.

Spatial statistical, HMMs, dynamic programming convex optimaztion, numerical linear algebra for statistical applications, grid computing, SDEs.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Autumn 2014 :: STAT G6103 | |||||

STAT 6103 |
72355 001 |
TuTh 1:10p – 2:25p TBA |
A. Gelman | 46 / 75 |

**STAT G6105x. Probability Theory I. 4 pts.** *Prerequisites:* A thorough knowledge of elementary real analysis and some previous knowledge of probability.

Overview of measure and integration theory. Probability spaces and measures, random variables and distribution functions. Independence, Borel-Cantelli lemma, zero-one laws. Expectation, uniform integrability, sums of independent random variables, stopping times, Wald’s equations, elementary renewal theorems. Laws of large numbers. Characteristic functions. Central limit problem; Lindeberg-Feller theorem, infinitely divisible and stable distributions. Cramer’s theorem, introduction to large deviations. Law of the iterated logarithm, Brownian motion, heat equation. For students in the doctoral program in Statistics only. Students in a masters program must seek permission from the Director of the MA program in Statistics; students in an undergraduate program must seek permission from the Director of Undergraduate Studies in Statistics.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Autumn 2014 :: STAT G6105 | |||||

STAT 6105 |
15775 001 |
MW 2:40p – 3:55p TBA |
P. Protter | 19 / 75 |

**STAT G6106y. Probability Theory II. 4 pts.** *Prerequisites:* Statistics G6105.

Conditional distributions and expectations. Martingales; inequalities, convergence and closure properties, optimal stopping theorems, Burkholder-Gundy inequalities, Doob-Meyer decomposition, stochastic integration, Ito’s rule. Brownian motion: construction, invariance principles and random walks, study of sample paths, martingale representation results Girsanov Theorem. The heat equation, Feynman-Kac formula. Dirichlet problem, connections with potential theory. Introduction to Markov processes: semigroups and infinitesimal generators, diffusions, stochastic differential equations. For students in the doctoral program in Statistics only. Students in a masters program must seek permission from the Director of the MA program in Statistics; students in an undergraduate program must seek permission from the Director of Undergraduate Studies in Statistics.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G6106 | |||||

STAT 6106 |
26536 001 |
MW 1:10p – 2:25p 520 MATHEMATICS BUILDING |
V. de la Pena | 15 / 75 |

**STAT G6107x. Theory of Statistical Inference I. 4 pts.**

A general introduction to mathematical statistics and statistical decision theory. Elementary decision theory, Bayes inference, Neyman-Pearson theory, hypothesis testing, most powerful unbiased tests, confidence sets. Estimation: methods, theory, and asymptotic properties. Likelihood ratio tests, multivariate distribution. Elements of general linear hypothesis, invariance, nonparametric methods, sequential analysis. For students in the doctoral program in Statistics only. Students in a masters program must seek permission from the Director of the MA program in Statistics; students in an undergraduate program must seek permission from the Director of Undergraduate Studies in Statistics.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Autumn 2014 :: STAT G6107 | |||||

STAT 6107 |
61521 001 |
TuTh 1:10p – 2:25p TBA |
A. Maleki | 16 / 25 |

**STAT G6108y. Theory of Statistical Inference II. 4 pts.** *Prerequisites:*STAT G6107

Continuation of STAT G6107. For students in the doctoral program in Statistics only. Students in a masters program must seek permission from the Director of the MA program in Statistics; students in an undergraduate program must seek permission from the Director of Undergraduate Studies in Statistics.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G6108 | |||||

STAT 6108 |
14250 001 |
TuTh 1:10p – 2:25p 903 SCHOOL OF SOCIAL WORK |
A. Maleki | 14 / 25 |

**STAT G6110x. Probability Theory III. 3 pts.** *Prerequisites:* Stat G6105 and G6106

This course is intended to follow two semesters of graduate measure theoretic probability theory. The topics to be covered will include the following, but may be slightly changed from year to year depending on the preferences of the professor and also of the students: Advanced stochastic Integration for Semimartingales; Stochastic Differential Equations and Markov Processes; Connections to Partial Differential Equations. An introduction to the General Theory of Mathematical Finance. The Modern Theory of the Discretization of Processes and Statistical Methods for Volatility Estimation within an Ito Process Context.

**STAT G6210x and y. Statistical Consulting. 2 pts.** *Prerequisites:* instructor’s permission. Repeated enrollment for credit is permitted.

Available to SSP, SMP

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G6210 | |||||

STAT 6210 |
66844 001 |
M 9:00a – 10:50a 222 PUPIN LABORATORIES |
R. Dolgoarshinnykh | 7 / 15 | |

Autumn 2014 :: STAT G6210 | |||||

STAT 6210 |
77397 001 |
MW 8:40a – 9:55a TBA |
R. Dolgoarshinnykh | 6 / 20 |

**STAT G9001x-G9002y. Seminar In Advanced Mathematical Statistics. 3 pts.**

Departmental seminar in Statistics.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G9002 | |||||

STAT 9002 |
27334 001 |
M 12:10p – 1:10p 903 SCHOOL OF SOCIAL WORK |
A. Maleki Y. Feng |
29 / 45 | |

Autumn 2014 :: STAT G9001 | |||||

STAT 9001 |
65201 001 |
M 4:10p – 5:25p 903 SCHOOL OF SOCIAL WORK |
R. Mazumder S. Mukherjee |
8 / 45 |

**STAT G9003x-G9004y. Seminar In Advanced Probability.. 3 pts.**

Departmental seminar in probability theory.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G9004 | |||||

STAT 9004 |
69407 001 |
F 12:00p – 1:00p 903 SCHOOL OF SOCIAL WORK |
J. Dubedat | 6 / 45 | |

Autumn 2014 :: STAT G9003 | |||||

STAT 9003 |
14893 001 |
F 11:45a – 1:15p 520 MATHEMATICS BUILDING |
J. Dubedat | 3 |

### Ph.D Seminar Courses

**STAT G8220y. Topics in Spatial Statistics. 3 pts. Not offered in 2014-2015.**

This course will provide an overview of some statistical methods for spatial data. The focus will be mainly on spatial point processes and Gaussian random fields. We will study descriptive methods for spatial point data, models for spatial point processes and methods for fitting them to data. We will also look at inhomogeneous point processes, and bootstrap methods. For Gaussian random fields, we will discuss properties such as stationarity and isotropy. We will cover variogram estimation and fitting, kriging, fixed-and increasing-domain asymptotics, as well as methods for modeling non-stationary data. Examples will be taken from journal articles and various research projects covering a variety of fileds, such as astronomy, syndromic surveillance, epidemiology and fMRI.

**STAT G8243x and y. Topics In Advanced Probability. 3 pts.** *Prerequisites:* Statistics G6106 and Department’s permission

Available to SSP, SMP Topic to vary each time course is given. May be repeated for credit.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G8243 | |||||

STAT 8243 |
71085 001 |
W 10:00a – 12:00p 1025 SCHOOL OF SOCIAL WORK |
J. Blanchet | 10 / 25 |

**STAT G8263y. Stochastic Differential Equations and Applications. 3 pts. Not offered in 2014-2015.**

Prerequisite: Statistics G6105–G6106 or member of the Department?s permission. Elements of the general theory of stochastic processes; Martingales; Doob-Meyer decomposition; Strochastic integrals; differential equations; existence and uniqueness of strong and weak partial differential equations; comparison and approximation theorems; Stroock-Varadhan theory; applications to stochastic optimization.

**STAT G8273x. Topics in the Mathematics of Finance. 3 pts.** *Prerequisites:* Math G4161/Stat G6105 and Stat G6106 or instructor’s permission.

Notions of arbitrage, completeness, hedging, and equivalent martingale measures for financial markets. Pricing of contingent claims and optimal portfolios, for both complete and incomplete markets. Equilibrium; the Capital Asset Pricing model. Market frictions: portfolio constraints, transaction costs.

**STAT G8285y. Statistical Analysis and Modeling of Neural Spike Train Data. 3 pts.**

We will discuss a variety of statistical methods for analyzing and modeling spike train data from single and multiple neurons. Statistical topics to be covered include: point proceses; generalized linear models; regularization; state space models; Kalman and particle filtering; the Expectation-Maximization algorithm; and optimiztion/convexity techniques. The course will be structured around applications to neural data, including: spike-triggered averaging; estimation of neural encoding models that inlcude spike-history and multineuronal interaction effects; estimating integrate-and-fire models from extracellular and intracellular data; performing optimal smoothing of noisy voltage- and calcium-imaging data; decoding spike trains; and estimating mutual information between stimuli and neutral responses.

Please refer to the following link:

G8285 – Spring 2009 Syllabus”>http://www.stat.columbia.edu/~liam/teaching/neurostat-spr09/

**STAT G8305x or y. Advanced Topics in Survival Analysis. 3 pts.** *Prerequisites:*STAT G6107–G6108 or instructor’s permission

Counting process representations for the Kaplan-Meier estimator and the maximum Cox partial likelihood estimator; semi-parametric efficiency bounds; censored multivariate outcomes; truncation; stratified analysis; survival analysis in epidemiology.

**STAT G8315y. Analyzing Large Correlated Data with Applications in Genetics and Classifications. 3 pts.** *Prerequisites:* None.

This topics course presents recently developed tools for handling large correlated data sets, focusing on applications in human genetics, microarray analysis, and machine learning.

**STAT G8318x or y. Semiparametric Inference. 3 pts.** *Prerequisites:* Instructor’s permission.

Inference for Euclidean parameters in the presence of infinite dimensional nuisance parameters. Tangent space and asymptotic information bounds, construction of estimates, examples.

**STAT G8320x. Causal Inference. 3 pts.**

Doctoral level introduction to casual inference, counterfactuals, causal estimates, ignorability, identifiability, and practical considerations. Matching, weighting, propensity scores, and sensitivily analyses.

**STAT G8325x and y. Topics In Advanced Statistics. 3 pts.** *Prerequisites:* Statistics G6108 and Department’s permission.

Available to SSP, SMP Topic to vary each time course is given. May be repeated for credit.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G8325 | |||||

STAT 8325 |
14582 001 |
F 4:10p – 6:00p 1025 SCHOOL OF SOCIAL WORK |
R. Mazumder | 13 / 20 | |

STAT 8325 |
10976 002 |
M 10:00a – 12:00p 1025 SCHOOL OF SOCIAL WORK |
S. Lo | 4 / 20 | |

STAT 8325 |
28105 003 |
Tu 10:10a – 12:00p 1025 SCHOOL OF SOCIAL WORK |
Y. Feng | 9 / 20 | |

Autumn 2014 :: STAT G8325 | |||||

STAT 8325 |
28350 001 |
M 10:00a – 12:00p 1025 SCHOOL OF SOCIAL WORK |
M. Puri | 4 / 25 | |

STAT 8325 |
74373 002 |
F 10:10a – 12:40p 903 SCHOOL OF SOCIAL WORK |
H. Xing | 1 / 25 |

**STAT G8327x. Topics in Time Series Analysis. 3 pts. Not offered in 2014-2015.**

Time series models and efficient estimation of their parameters. Probabilistic and statistical aspects of non-linear and continuous-time models for time series data. GARCH, stochastic volatility, and nonlinear and non-Gaussian state-space models, continuous-time ARMA models that are both Brownaina- and Levy-driven, continuous-time GARCH (CO-GARCH), and stochastic volatility models. Recursive on-line identification of linear systems; adaptive filtering and control; Prediction theory and the Kalman filter; seasonal adjustment; frequency domain analysis.

**STAT G8329. Statistical Methods in Genetic Epidemiology. 3 pts. Not offered in 2014-2015.**

*Prerequisites:*Instructor’s permission.

Quick review of basic principles of genetics and genetic epidemiology; classical linkage analysis; genetic association studies; quantitative traits, haplotype relative risk and transmission disequilibrium methods, multipoint methods, methods for multigenic traits; genome-wide scans.

**STAT G8335. Statistical Methods in fMRI Research. 3 pts. Not offered in 2014-2015.**

*Prerequisites:*STAT W4105, W4107, W4315 or the equivalent

Introduction to mathematical and statistical aspects of functional magnetic resonance imaging; Data collection, image reconstruction, experimental design, pre-processing, model fitting, and inference. Extensive reading in classic and current literature.

### Ph.D Working Groups

**STAT G7010x and y. Applied Probability and Risk Seminar.**

A seminar on topics in Applied Probability and Risk.

Course Number |
Call Number/ Section |
Days & Times/ Location |
Instructor | Enrollment | |

Spring 2014 :: STAT G7010 | |||||

STAT 7010 |
69155 001 |
Th 1:10p – 2:25p 652 SCHERMERHORN HALL |
V. de la Pena | 5 / 25 | |

Autumn 2014 :: STAT G7010 | |||||

STAT 7010 |
17379 001 |
Th 1:10p – 2:25p TBA |
V. de la Pena | 0 / 75 |

**STAT G8990x and y. Research in Quantitative Political Science. 3 pts.**

Research in quantitative methods in political science and in social science in general. Application area include American politics, comparative politics, social networks, law and public policy.