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.


STAT 401 or STAT 420


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.

  • An example of hyperbolic relaxation toward a scalar conservation law with spatial heterogeneity

    Speaker: Magali Tournus (Pennsylvania State University) -

    When: Thu, September 25, 2014 - 3:30pm
    Where: Math 3206
  • Parallelizable Block Iterative Methods for Stochastic Processes

    Speaker: Gil Ariel (Bar Ilan University) -

    When: Thu, October 2, 2014 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: In many applications involving large systems of stochastic differential equations, the states space can be partitioned into groups which are only weakly interacting. For example, molecular dynamics simulations of large molecules undergoing Langevin dynamics may be divided into smaller components, each at equilibrium. If the components are decoupled, then the equilibrium distribution of the entire system is a product of the marginals and can be computed in parallel. However, taking interactions into account, the entire state of the system must be considered as a whole and naïve parallelization is not possible. We propose an iterative method along the lines of the wave-form relaxation approach for calculating all component marginals. The method allows some parallelization between conditionally independent components, depending on the minimal coloring of the graph describing their mutual interactions. Joint work with Ben Leimkuhler and Matthias Sachs (University of Edinburgh).
  • Mixtures In Compressible Navier-Stokes Systems

    Speaker: Didier Bresch (University of Savoie, France) -

    When: Thu, October 30, 2014 - 3:30pm
    Where: Math 3206
  • Analysis of 2+1 Diffusive-Dispersive PDE Arising in River Braiding

    Speaker: Charis Tsikkou (West Virginia University) -

    When: Thu, November 6, 2014 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: In the context of a weakly nonlinear study of bar instabilities in a sediment carrying river, P. Hall introduced an evolution equation for the deposited depth which is dispersive in one spatial direction, while being diffusive in the other. In this talk, we present local existence and uniqueness results using a contraction mapping argument in a Bourgain-type space. We also show that the energy and cumulative dissipation are globally controlled in time. This is joint work with Saleh Tanveer.
  • Kinetics of particles with short-range interactions

    Speaker: Miranda Holmes-Cerfon (Courant Institute) -

    When: Thu, November 20, 2014 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: Particles in soft-matter systems, such as colloids, tend to have very short-range interactions compared to their size. Because of this, traditional theories, that assume the energy landscape is smooth enough, will struggle to capture their dynamics. We propose a new framework to look at such particles, based on taking the limit as the range of the interaction goes to zero. In this limit, the energy landscape is a set of geometrical manifolds plus a single control parameter, while the dynamics on top of the manifolds are given by a hierarchy of Fokker-Planck equations coupled by "sticky" boundary conditions. We show how to compute dynamical quantities such as transition rates between clusters of hard spheres, and then show this agrees quantitatively with experiments on colloids. Finally, we show how dynamical ideas can be used to solve the mathematical problem of enumerating all the nonlinearly rigid packings of hard spheres.