Faculty of Arts & Sciences

Supervised reading and research in an area of statistics agreed upon by the student and a faculty adviser.

Supervised research for the senior thesis, under the mentorship of a Harvard facultymember.

Similar to Statistics 100, but emphasizes concepts and practice of statistics used in psychology and other social and behavioral sciences. Topics covered: describing center and variability; probability and sampling distributions; estimation and hypothesis testing for comparing means and comparing proportions; contingency tables; correlation and regression; multiple regression; analysis of variance. Emphasis on translation of research questions into statistically testable hypotheses and models, and interpretation of results in context.

A rigorous introduction to statistics for students intending to study economics. Examples drawn from finance, decision analysis and economic decision-making. In addition to descriptive statistics, probability, inference and regression modeling, also covers portfolio optimization, decision analysis, and time series analysis. Students with prior exposure to introductory statistics will find some overlap of material but be exposed to new applications and learn more advanced modeling techniques.

A comprehensive introduction to probability. Basics: sample spaces and events, conditional probability, and Bayes' Theorem. Univariate distributions: density functions, expectation and variance, Normal, t, Binomial, Negative Binomial, Poisson, Beta, and Gamma distributions. Multivariate distributions: joint and conditional distributions, independence, transformations, and Multivariate Normal. Limit laws: law of large numbers, central limit theorem. Markov chains: transition probabilities, stationary distributions, convergence.

The course will cover basic technology platforms, data analysis problems and algorithms in computational biology. Topics include sequence alignment and search, high throughput experiments for gene expression, transcription factor binding and epigenetic profiling, motif finding, RNA/protein structure prediction, proteomics and genome-wide association studies. Computational algorithms covered include hidden Markov model, Gibbs sampler, clustering and classification methods.

Learning from data in order to gain useful predictions and insights. This course introduces methods for five key facets of an investigation: data wrangling, cleaning, and sampling to get a suitable data set; data management to be able to access big data quickly and reliably; exploratory data analysis to generate hypotheses and intuition; prediction based on statistical methods such as regression and classification; and communication of results through visualization, stories, and interpretable summaries. Built around three modules: prediction and elections, recommendation and business analytics, and sampling and social network analysis.

Introduction to time series models and associated methods of data analysis and inference. Auto regressive (AR), moving average (MA), ARMA, and ARIMA processes, stationary and non-stationary processes, seasonal processes, auto-correlation and partial auto-correlation functions, identification of models, estimation of parameters, diagnostic checking of fitted models, forecasting, spectral analysis, and transfer function models.

A serious introduction to statistical inference with linear models and related methods. Topics include t-tools and permutation-based alternatives, multiple-group comparisons, analysis of variance, linear regression, model checking and refinement, and causation versus correlation. Emphasis on thinking statistically, evaluating assumptions, and developing tools for real-life applications.

Sequel to Statistics 139, emphasizing common methods for analyzing continuous non-normal and categorical data. Topics include logistic regression, log-linear models, multinomial logit models, proportional odds models for ordinal data, Gamma and inverse-Gaussian models, over-dispersion, analysis of deviance, model selection and criticism, model diagnostics, and an introduction to non-parametric regression methods.

An introduction to the analysis of capital markets using quantitative methods. Concepts include risk, expected utility, discounting, binomial-tree valuation methods, martingales, continuous time stochastic calculus methods, stochastic discount factors, financial econometric models and Monte Carlo simulations. These concepts are applied to equities, risk management and derivative pricing.

Through a series of forecasting and prediction competitions, each based on a large real-world dataset, students will acquire the tools and experience to explore and model large-scale, real-life data. In addition, the course will cover a series of tools for statistical modeling in real-world environments. Some examples include bagging, boosting, collaborative model development, cross-validation, and model validation and verification.

A graduate introduction to advanced probability. Foundations of probability: exchangeability and de Finetti's type theorem. Martingales: convergence theorems, optional stopping, Polya urn schemes and applications to statistics. Poisson processes: general spaces, marked processes, applications to Bayesian nonparametrics. Gaussian processes: existence theorem, Brownian bridges, meanders and excursions. Empirical processes: inequalities, central limit theorems and the bootstrap. Markov Chains: ergodicity, convergence and MCMC algorithms. Stochastic calculus: Ito's formula.

Meets with Statistics 115, but graduate students are required to do more coding, complete a research project and submit a written report during reading period in addition to completing all work assigned for Statistics 115.

Computational methods commonly used in statistics: random number generation, optimization methods, numerical integration, Monte Carlo methods including Metropolis-Hastings and Gibbs samplers, approximate inference techniques including Expectation-Maximization algorithms, Laplace approximation and variational methods, data augmentation strategies, data augmentation strategies.

Multivariate inference and data analysis. Advanced matrix theory and distributions, including Multivariate Normal, Wishart, and multilevel models. Supervised learning: multivariate regression, classification, and discriminant analysis. Unsupervised learning: dimension reduction, principal components, clustering, and factor analysis.

The modern era of work on missing data problems began in the 1970s and has seen an explosion of developments since then. Seminar will focus on an updated version of a classic text, supplemented with classic articles.

Bootstrap and resampling allow for principled data analysis in diverse areas such as social, biological, or physical sciences. We will implement methods in R, conduct simulation studies, tackle applied projects, and do theoretical work.

Interaction between quantitative methods and law. Teaming with law students: analyze data, prepare expert reports, and give testimony. Learn how to communicate with and present results to untrained but intelligent users, and to defend conclusions.

Exploration of the statistical contributions of Bradley Efron through study of his writings. Both deeply influential and deeply controversial ideas will be discussed; topics include statistical foundations and principles, estimating the number of unseen species, self-consistency, empirical Bayes, large-scale inference, and the bootstrap.

Required of all first-year doctoral students in Statistics.

Focusing on inference problems for stochastic processes and statistical modeling in high dimensions. Contemporary papers from different fields will be discussed and presented by students. Participants will be encouraged to develop their own research problems in this active area.

Conducting causal inference under the Neyman-Rubin model when the number of possible covariates is on the order of the number of observations, or even larger, is non-obvious. Recent developments using a variety of methods and approaches such as (sparse) regularization, nonparametric Bayes, BART, model selection, or dimension reduction, claim to address this problem. We will read and discuss the literature in this emerging area with a critical eye.

Theory of multi-level parametric models, including hidden Markov models, and applications likely to include biostatistics, health services, education, and sports.

Bayesian nonparametric methods including both random discrete measures and random functions. Gaussian processes (e.g., for nonparametric regression), the Chinese Restaurant process (e.g., for clustering), Pitman-Yor processes (e.g., for hierarchical clustering), and Dirichlet processes (e.g., for topic modeling).

Random graph models for biological, social, and information networks, including fixed degree, exponential, power law, small world, and geometric random graphs. Estimation and sampling methods for network data.

Papers in this area will be read with a skeptical but judicious eye. When could these methods offer something tangible, when might they fail, and how can we know in which circumstance we lie?

Hands-on introduction to network statistics, with applications to social, biological and communication networks. Topics in sampling designs and inference. Modeling network evolution. Processes on networks. Critical literature review, in class-presentations, and final projects.

Aimed at helping Statistics PhD students transition through the qualifying exams and into research.