Description

Simple random sampling. Sampling for proportions. Estimation of sample size. Sampling with varying probabilities. Sampling: stratified, systematic, cluster, double, sequential, incomplete. Also listed as SURV 440.

Prerequisites

STAT 401 or STAT 420

Topics

Basic concepts

Populations, samples, sampling frames.
Sampling design, statistics, bias.
Sampling and nonsampling errors.
(0.5 week)

Simple Random Sampling

Estimates of population mean, total, proportion and variance and their sampling properties.
Confidence limits, use of normal approximation.
Auxiliary information, ratio and regression estimators.
(4.5 weeks)

Stratified Samples

Definitions, weighting and estimators.
Optimal allocation, poststratification.
(2 weeks)

Unbiased Estimation for Cluster and Two-Stage Sampling

Single-stage, two-stage, and multi-stage cluster sampling.
Fixed and random clusters.
With-replacement and without-replacement sampling of PSU's.
Approximate variance estimators.
(4 weeks)

Advanced Topics

Variance estimation, categorical data analysis, regression in complex surveys.

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017

  • Liquid drops on Rough surfaces

    Speaker: Inwon Kim (UCLA) -

    When: Thu, September 14, 2017 - 3:30pm
    Where: Kirwan Hall 3206
  • Data-based stochastic model reduction for chaotic systems

    Speaker: Fei Lu (John Hopkins University) - http://www.math.jhu.edu/~feilu/

    When: Thu, October 12, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: The need to develop reduced nonlinear statistical-dynamical models from time series of partial observations of complex systems arises in many applications such as geophysics, biology and engineering. The challenges come mainly from memory effects due to the nonlinear interactions between resolved and unresolved scales, and from the difficulty in inference from discrete data.

    We address these challenges by introducing a discrete-time stochastic parametrization framework, in which we infer nonlinear autoregression moving average (NARMA) type models to take the memory effects into account. We show by examples that the NARMA type stochastic reduced models that can capture the key statistical and dynamical properties, and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the Kuramoto-Sivashinsky equation of spatiotemporally chaotic dynamics.

  • A free boundary problem with facets

    Speaker: Will Feldman (University of Chicago) -

    When: Thu, October 19, 2017 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: I will discuss a variational problem on the lattice analogous to the Alt-Caffarelli problem. The scaling limit is a free boundary problem for the Laplacian with a discontinuous constraint on the normal derivative at the boundary. The discontinuities cause the formation of facets in the free boundary. The problem is related to models for contact angle hysteresis of liquid drops studied by Caffarelli-Lee and Caffarelli-Mellet.