In which we consider evolutionary trends in body size, aided by regression modeling and the bootstrap. Assignment Advanced Data Analysis from an Elementary Point of View

Quantifying uncertainty by looking at sampling distributions. The bootstrap principle: sampling distributions under a good estimate of the truth are close to the true sampling distributions. Parametric bootstrapping. Non-parametric bootstrapping. Many examples. When does the bootstrap fail? Reading: Notes, chapter 5 (R for figures and examples; pareto.R; wealth.dat)R for in-class examples Advanced Data Analysis from an Elementary Point of View

Fortunately, however, the methods of those who can handle big data are neither grotesque nor incomprehensible, and we will hear about them on Monday. Alekh Agarwal, "Computation Meets Statistics: Trade-offs and Fundamental Limits for Large Data Sets" Abstract: The past decade has seen the emergence of datasets of unprecedented scale, with both large sample sizes and dimensionality. Massive data sets arise in various domains, among them computer vision, natural language processing,...

Attention conservation notice: Only of interest if you (1) care about combinatorial stochastic processes and their statistical applications, and (2) will be in Pittsburgh on Wednesday afternoon. It is only in very special weeks, when we have been very good, that we get two seminars. Harry Crane, "The Cut-and-Paste Process" Abstract: In this talk, we present the cut-and-paste process, a novel infinitely exchangeable process on the state space of partitions of the natural numbers whose samples...

Attention conservation notice: Associate editor at a non-profit scientific journal endorses a call for boycotting a for-profit scientific journal publisher. I have for years been refusing to publish in or referee for journals publisher by Elsevier; pretty much all of the commercial journal publishers are bad deals1, but they are outrageously worse than most. Since learning that Elsevier had a business line in putting out publications designed to look like peer-reviewed journals, and calling...

Attention conservation notice: Only of interest if you (1) care about covariance matrices and (2) will be in Pittsburgh on Monday. Since so much of multivariate statistics depends on patterns of correlation among variables, it is a bit awkward to have to admit that in lots of practical contexts, correlations matrices are just not very stable, and can change quite drastically. (Some people pay a lot to rediscover this.) It turns out that there are more constructive responses to this situation...

The constructive alternative to complaining about linear regression is non-parametric regression. There are many ways to do this, but we will focus on the conceptually simplest one, which is smoothing; especially kernel smoothing. All smoothers involve local averaging of the training data. The bias-variance trade-off tells us that there is an optimal amount of smoothing, which depends both on how rough the true regression curve is, and on how much data we have; we should smooth less as we...

In which we try to discern whether poor countries grow faster. Assignment, R, penn-select.csv data set Advanced Data Analysis from an Elementary Point of View

Goals of statistical analysis: summaries, prediction, scientific inference. Evaluating predictions: in-sample error, generalization error; over-fitting. Cross-validation for estimating generalization error and for model selection. Justifying model-based inferences; Luther and Süleyman. Reading: Notes, chapter 3 (R for examples and figures). Advanced Data Analysis from an Elementary Point of View

Multiple linear regression: general formula for the optimal linear predictor. Using Taylor's theorem to justify linear regression locally. Collinearity. Consistency of ordinary least squares estimates under weak conditions. Linear regression coefficients will change with the distribution of the input variables: examples. Why R2 is usually a distraction. Linear regression coefficients will change with the distribution of unobserved variables (omitted variable problems). Errors in...