# Statistics

## Statistics

**Departmental Contact:**

Prof. Michael E. Sobel

1255 Amsterdam Ave., Room 1005

212-851-2135

mes105@columbia.edu

**STAT S1101D Introduction to Statistics (without calculus). ***3 points*.

Prerequisites: some high school algebra.

Designed for students in fields that emphasize quantitative methods. This course satisfies the statistics requirements of all majors except statistics, economics, and engineering. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, confidence intervals, and hypothesis testing are taught as aids to quantitative reasoning and data analysis. Use of statistical software required. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.

Summer 2019: STAT S1101D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1101 | 001/13662 | |
3 | 0 |

**STAT S1101Q Introduction to Statistics (without calculus). ***3 points*.

Prerequisites: some high school algebra.

Designed for students in fields that emphasize quantitative methods. This course satisfies the statistics requirements of all majors except statistics, economics, and engineering. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, confidence intervals, and hypothesis testing are taught as aids to quantitative reasoning and data analysis. Use of statistical software required. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.

Summer 2019: STAT S1101Q | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1101 | 002/73611 | |
3 | 0 |

**STAT S1201D Introduction to Statistics (with calculus). ***3 points*.

Prerequisites: working knowledge of calculus (differentiation and integration).

Designed for students who desire a strong grounding in statistical concepts with a greater degree of mathematical rigor than in *STAT W1111*. Random variables, probability distributions, pdf, cdf, mean, variance, correlation, conditional distribution, conditional mean and conditional variance, law of iterated expectations, normal, chi-square, F and t distributions, law of large numbers, central limit theorem, parameter estimation, unbiasedness, consistency, efficiency, hypothesis testing, p-value,confidence intervals. maximum likelihood estimation. Satisfies the pre-requisites for *ECON W3412*.

Summer 2019: STAT S1201D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1201 | 001/64699 | |
3 | 0 |

**STAT S1201Q Introduction to Statistics (with calculus). ***3 points*.

Prerequisites: working knowledge of calculus (differentiation and integration).

Designed for students who desire a strong grounding in statistical concepts with a greater degree of mathematical rigor than in *STAT W1111*. Random variables, probability distributions, pdf, cdf, mean, variance, correlation, conditional distribution, conditional mean and conditional variance, law of iterated expectations, normal, chi-square, F and t distributions, law of large numbers, central limit theorem, parameter estimation, unbiasedness, consistency, efficiency, hypothesis testing, p-value,confidence intervals. maximum likelihood estimation. Satisfies the pre-requisites for *ECON W3412*.

Summer 2019: STAT S1201Q | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1201 | 002/21358 | |
3 | 0 |

**STAT S4001D Introduction to Probability and Inference. ***3 points*.

Prerequisites: A good working knowledge of calculus, including derivatives, single and double, limits, sums and series.

Life is a gamble and with some knowledge of probability / statistics is easier evaluate the risks and rewards involved. Probability theory allows us take a known underlying model and estimate how likely will we be able to see future events. Statistical Inference allows us to take data we have seen and estimate the missing parts of an unknown model. The first part of the course focus on the former and the second part the latter.

Summer 2019: STAT S4001D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4001 | 001/12446 | |
3 | 0 |

**STAT S4199D Statistical Computing in SAS. ***3 points*.

Data handling in SAS (including SAS INPUT, reading and writing raw and system files, data set subsetting, concatenating, merging, updating and working with arrays), SAS MACROS, common SAS functions, and graphics in SAS. Review of SAS tools for exploratory data analysis, and common statistical procedures (including, categorical data, dates and longitudinal data, correlation and regression, nonparametric comparisons, ANOVA, multiple regression, multivariate data analysis).

Summer 2019: STAT S4199D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4199 | 001/29053 | |
3 | 0 |

**STAT S4203D Probability. ***3 points*.

Prerequisites: *MATH V1101* Calculus I and *MATH V1102* Calculus II, or the equivalent, and *STAT W1111* or *STAT W1211* (Introduction to Statistics).

Corequisites: *MATH V1201* Calculus III, or the equivalent, or the instructor's permission.

This course can be taken as a single course for students requiring knowledge of probability or as a foundation for more advanced courses. It is open to both undergraduate and master students. This course satisfies the prerequisite for *STAT W3107* and *W4107.* Topics covered include combinatorics, conditional probability, random variables and common distributions, expectation, independence, Bayes' rule, joint distributions, conditional expectations, moment generating functions, central limit theorem, laws of large numbers, characteristic functions.

Summer 2019: STAT S4203D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4203 | 001/72395 | |
3 | 0 |

**STAT S4204Q Statistical Inference. ***3 points*.

Prerequisites: *STAT W3105* Intro. to Probability or *STAT W4105* Probability, or the equivalent.

Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals, maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.

Summer 2019: STAT S4204Q | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4204 | 001/63483 | |
3 | 0 |

**STAT S4206D Statistical Computing and Introduction to Data Science. ***3 points*.

MA students in Statistics should register for STAT S5206

Prerequisites: STAT GU4204 and STAT GU4205

Open to CC, CN, GS, GN, BC, EN, GSAS, GSAS Liberal, and SEAS Graduate Students

Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.

Summer 2019: STAT S4206D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4206 | 001/20142 | |
3 | 0/75 |

**STAT S4221D Time Series Analysis. ***3 points*.

Prerequisites: STAT GU4205 or the equivalent.

Prerequisites: STAT GU4205 or the equivalent. Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.

Summer 2019: STAT S4221D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4221 | 001/71179 | |
3 | 0/25 |

**STAT S4241D Statistical Machine Learning. ***3 points*.

MA students in Statistics should register for STAT S5241

Prerequisites: STAT GU4206

The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.

Summer 2019: STAT S4241D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4241 | 001/62267 | |
3 | 0/75 |

**STAT S4261D Statistical Methods for Finance. ***3 points*.

MA students in Statistics should register for STAT S5261

Prerequisites: STAT GU4204 and STAT GU4205

A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

Summer 2019: STAT S4261D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4261 | 001/10014 | |
3 | 0 |

**STAT S5206D Statistical Computing and Introduction to Data Science. ***3 points*.

Prerequisites: STAT GU5204 and STAT GU5205

Open to MA students in Statistics only

Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.

Summer 2019: STAT S5206D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 5206 | 001/11230 | |
3 | 0 |

**STAT S5221 TIME SERIES ANALYSIS . **

Open to MA students in Statistics only

Prerequisites: STAT GU4205 or the equivalent. Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.

**STAT S5241D Statistical Machine Learning. ***3 points*.

Prerequisites: STAT GR5206 or the equivalent.

Open to MA students in Statistics only

The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.

Summer 2019: STAT S5241D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 5241 | 001/18926 | |
3 | 0 |

**STAT S5261D Statistical Methods for Finance. ***3 points*.

Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended.

Open to MA students in Statistics only

A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

Summer 2019: STAT S5261D | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 5261 | 001/69963 | |
3 | 0 |