Prerequisites: STAT GR5205
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.
Prerequisites: STAT GR5205
Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Non-parametric regression, smoothing and model selection.
Prerequisites: STAT GR5205.
Multivariate normal distribution, multivariate regression and classification; canonical correlation; graphical models and Bayesian networks; principal components and other models for factor analysis; SVD; discriminant analysis; cluster analysis.
Prerequisites: STAT GR5205
Bayesian vs frequentist, prior and posterior distributions, conjugate priors, informative and non-informative prior subjective and objective bayes, oneand two sample problems, models for normal data, models for binary data, multivariate normal shrinkage, bayesian linear models, bayesian computation (start early), MCMC algorithms, the Gibbs sampler, hierarchical models, empirical bayes, hypothesis testing, bayes factors, model selection, software: R and WinBUGS
Prerequisites: STAT GR5205
Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.
Prerequisites: STAT GR5205
Statistical methods for rates and proportions, ordered and nominal categorical responses, contingency tables, odds-ratios, exact inference, logistic regression, Poisson regression, generalized linear models.
Prerequisites: STAT GR5206 or the equivalent.
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.
Prerequisites: STAT GR5206 or the equivalent.
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.
Prerequisites: STAT GR5206 or the equivalent.
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.
Prerequisites: STAT GR5206 or the equivalent.
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.
Prerequisites: STAT GR5206 or the equivalent.
This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio on GitHub, and deeper understanding of several core statistical/machine-learning algorithms. Bi-weekly project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.
Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended.
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.
Prerequisites: STAT GR5203 or the equivalent.
This course covers theory of stochastic processes applied to finance. It covers concepts of Martingales, Markov chain models, Brownian motion. Stochastic Integration, Ito's formula as a theoretical foundation of processes used in financial modeling. It also introduces basic discrete and continuous time models of asset price evolutions in the context of the following problems in finance: portfolio optimization, option pricing, spot rate interest modeling.
Prerequisites: STAT GR5264
Available to SSP, SMP. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.
Prerequisites: W4315 and either another statistics course numbered above the 4200 or permission of instructor.
Required for the major in statistics. Data analysis using a computer statistical package and selected exploratory data analysis subroutines. Topics include editing of data for errors, exploratory and standard techniques for one-way analysis of variance, linear regression, and two-way analysis of variance. Material is presented in case-study format.
The end of the Second World War also marked the end of European dominion over most of the world and the rise of the US and the USSR as new global powers. In 1955, leaders of the newly independent Afro-Asian states met in Bandung, Indonesia, in a watershed conference that marked the beginning of a new epoch of Afro-Asian solidarity, decolonization and common anti-colonial struggles. Seven Arab states took part in this watershed conference, and Egypt would later play host to the Afro-Asian People’s Solidarity Organization. This course will introduce students to the legacy of this era as seen from the vantage point of the Arab World and West Asia more broadly. It will consider the ways in which this era has influenced first postcolonial and later decolonial scholarship, and engage some of the works to emerge from the Arab anti-colonial era of the 20th century available in English translation. In the first half of the course, students will consider the main distinctions between postcolonial and decolonial theory, decolonization and decoloniality, and engage with different conceptualizations of colonial modernity. Students will also critically evaluate this theory through works that foreground political economy and the intellectual history the Ottoman Empire, the forerunner to European Empire in the region. In the second half of the course, students will consider the Bandung moment and the centrality of Egypt to the Afro-Asian anti-colonial imaginary, and engage some of Arab and Iranian anti-colonial thinkers and themes in relation to the legacies of the decolonization movements and the resultant knowledges and decolonial pedagogies of the formerly colonized world.
Prerequisites: A course in computer programming.
This course covers visual approaches to exploratory data analysis, with a focus on graphical techniques for finding patterns in high dimensional datasets. We consider data from a variety of fields, which may be continuous, categorical, hierarchical, temporal, and/or spatial in nature. We cover visual approaches to selecting, interpreting, and evaluating models/algorithms such as linear regression, time series analysis, clustering, and classification.
Prerequisites:
EEEB G4850
.
Incoming M.A. students aiming for the thesis-based program are guided through the process of defining a research question, finding an advisor, and preparing a research proposal. By the end of the semester the students will have a written research proposal to submit to potential advisors for revision. Subject to a positive review of the research proposal, students are allowed to continue with the thesis-based program and will start working with their advisor. The course will also provide an opportunity to develop basic skills that will facilitate the reminder of the student's stay at E3B and will help in their future careers.
This course gives students the opportunity to design their own curriculum: To attend lectures, conferences and workshops on historical topics related to their individual interests throughout Columbia University. Students may attend events of their choice, and are especially encouraged to attend those sponsored by the History Department. The Center for International History and the Heyman Center for the Humanities have impressive calendars of events and often feature historians. The goal of this mini-course is to encourage students to take advantage of the many intellectual opportunities throughout the University, to gain exposure to a variety of approaches to history, and at the same time assist them in focusing on a particular area for their thesis topic.
This course offers students an opportunity to expand their curriculum beyond the established course offerings. Interested parties must consult with the QMSS Program Director before adding the class. This course may be taken for 2-4 points.
This course consolidates two components of the systematic professional training and pedagogical formation of graduate students in the Department of Music. G6000 is taught by the chair of the Core Curriculum course, Masterpieces of Western Music (Music Humanities). The course streamlines the process by which students in the four different doctoral degree programs (historical musicology, ethnomusicology, theory, and composition) are trained to teach their own sections of Music Humanities. Students also learn about applying for academic positions, preparing curriculum vitae, submitting journal articles, preparing book proposals, and other professional skills.
Research in medical informatics under the direction of a faculty adviser.
Current topics in the Earth sciences.
Prerequisites: (BMEN E4001) and (BMEN E4002) and (APMA E4200) or equivalent.
Advanced computational modeling and quantitative analysis of selected physiological systems from molecules to organs. Selected systems are analyzed in depth with an emphasis on modeling methods and quantitative analysis. Topics may include cell signaling, molecular transport, excitable membranes, respiratory physiology, nerve transmission, circulatory control, auditory signal processing, muscle physiology, data collection and analysis.