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.

  • Unsteady flow barriers at scales from geophysics to microfluidics: identification, control, and optimizing transport


    Speaker: Sanjeeva Balasuriya (University of Adelaide) -

    When: Thu, February 25, 2016 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: Unsteady flows typically possess blobs of particles moving coherently, in addition to regions in which extensive mixing occurs. The boundaries of each of these structures might be considered to be "unsteady flow barriers." Exactly defining what these are is, however, problematic. Such flow barriers may be thought to demarcate geophysical features such as the Antarctic Circumpolar Vortex (ozone hole), or the interface between two fluids that one desires to mix together for DNA synthesis in a microfluidic device. This talk will examine some recent results on the control of unsteady flow barriers, and how one might attempt to optimize mixing across an unsteady flow barrier. Additionally, some ongoing work on how these ideas can be used to correct errors in oceanic velocity data obtained from satellite observations will be briefly discussed.
  • The flow near the ground state for semilinear evolution equations


    Speaker: P. Raphael (University of Nice) -

    When: Tue, February 16, 2016 - 11:00am
    Where: Math 3206

    View Abstract

    Abstract: I will consider the question of the study of the flow near the ground state solitary wave for semilinear heat or Schrodinger type equations. I will illustrate on some recent examples both the problem of construction of non trivial dynamics, in particular singularity formation, and the one of the complete classification of the flow. The approach will allow us to distinguish the construction problem, and in particular the one of minimal elements (with one or possibly more blow up bubbles), and the more involved stability problem. Applications will be given in particular in the mass and energy critical settings.


  • Why gradient flows of some energies good for defect equilibria are not good for dynamics, and an improvement


    Speaker: Prof. Amit Acharya, Joint CSCAMM/Applied Math Seminar (Civil and Environmental Engineering, Carnegie Mellon University) -

    When: Thu, February 11, 2016 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: Line defects appear in the microscopic structure of crystalline materials (e.g. metals) as well as liquid crystals, the latter an intermediate phase of matter between liquids and solids. Mathematically, their study is challenging since they correspond to topological singularities that result in blow-up of total energies of finite bodies when utilizing most commonly used classical models of energy density; as a consequence, formulating nonlinear dynamical models (especially pde) for the representation and motion of such defects is a challenge as well. I will discuss the development and implications of a single pde model intended to describe equilibrium states and dynamics of these defects. The model alleviates the nasty singularities mentioned above and it will also be shown that incorporating a conservation law for the topological charge of line defects allows for the correct prediction of some important features of defect dynamics that would not be possible just with the knowledge of an energy function.
  • The Optimal Transportation Problem: applications and numerical methods


    Speaker: Prof. Adam Oberman (McGill University (joint Numerical Analysis/PDE seminar)) - http://www.adamoberman.net/

    When: Thu, February 4, 2016 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: The Optimal Transportation problem has been the subject of a great deal of attention by theoreticians in last couple of decades. The Wasserstein (or Earth Mover) distance allows for the metrization of the space of probability measures. However computation of these distances (and the associated maps) has been intractable, except for very small problems.

    Current applications of Optimal Transportation include: Freeform Illumination Optics for shaping light or laser beams, Shape Interpolation (in computer graphics), Machine learning (comparing histograms), discretization of nonlinear PDEs (using the gradient flow in the Wasserstein metric), parameter estimation in geophysics, matching problems in mathematical economics, and Density Functional Theory in physical chemistry.

    Recent advances have allowed for more efficient computation of solutions of the Monge-Kantorovich problem of optimal transportation. In the special, but important case of quadratic costs, the map can be obtained from the solution of the elliptic Monge-Ampere partial differential equation with nonstandard boundary conditions. For more general costs, the Kantorovich plan can be approximated by a finite dimensional linear program. In this talk we will compare the cost and quality of the solutions obtained by two different methods.

    I will also discuss some nonlinear PDE problems (curvature flows, 2-Hessian equation) which can be solved using similar techniques to those applied to the Monge-Ampere PDE.
  • Anomalous diffusion for some kinetic equations


    Speaker: Marjolaine Puel (University of Nice Sophia-Antipolis) -

    When: Thu, November 19, 2015 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: Kinetic equations involve a large number of variables, time, space and velocity and one important part of the study of those equation consists in giving an approximation of their solution for large time and large observation length. For example, when we model collisions via the linear Boltzmann equation, it is well known that when the equilibria are given by Gaussian distributions, we can approximate the solution by the product of an equilibrium that gives the dependence with respect to velocity multiplied by a density depending on time and position that satisfies a diffusion equation. But different models like inelastic collisions lead to heavy tails equilibria for which depending on the power of the tail, we get different situations. When the diffusion coefficient is no more defined, in the case of linear Boltzmann, the density satisfies a fractional diffusion equation. The same kind of problem arises when the interaction between particles are modeled via the Fokker Planck operator with an additional difficulty. I will present a probabilistic method to study the critical case where we obtain still a diffusion but with an anomalous scaling and present the problems arising for the subcritical exponents.

  • Energy scaling laws for compressed thin elastic sheets


    Speaker: Ian Tobasco (Courant Institute) -

    When: Thu, November 5, 2015 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: A long-standing open problem in elasticity is to identify the minimum energy scaling law of a crumpled sheet of paper as thickness tends to zero. Though much is known about scaling laws for thin sheets in tensile settings, the compressive regime is mostly unexplored. I will discuss the analysis of two examples: an axially compressed thin elastic cylinder, and an indented cone. My focus in this talk will be the dependence of the minimum energy on the thickness and loading in the Foppl-von Karman model. I will prove upper and lower bounds for these scalings. The material for this talk is drawn from two papers in preparation; the work on indented cones is in collaboration with H. Olbermann and S. Conti.
  • Spectral representation of generalized Laguerre semigroups and hypocoercitivity


    Speaker: Pierre Patie (Cornell University) -

    When: Thu, October 1, 2015 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: The first aim of this to talk is to present an original methodology for developing the spectral representation of a class of non-self-adjoint (NSA) invariant semigroups. This class is defined in terms of self-similar semigroups on the positive real line and we name it the class of generalized Laguerre semigroups. Our approach is based on an in-depth analysis of an intertwinning relationship that we establish between this class and the classical Laguerre semigroup which is self-adjoint. We proceed by discussing substantial difficulties that one may face when studying the spectral representation of NSA operators.
    Finally, we also show that our approach enables us to get precise information regarding the speed of convergence towards stationarity. In particular, we observe in some cases the hypocoercivity phenomena which, in our context, can be interpreted in terms of the spectral norms.

  • Transonic problems on multidimensional conservation laws


    Speaker: Eun Heui Kim (California State University Long Beach) -

    When: Thu, September 24, 2015 - 3:30pm
    Where: Math 3206
  • Fractional thin film equations and hydraulic fractures


    Speaker: Antoine Mellet (UMD) -

    When: Thu, September 17, 2015 - 3:30pm
    Where: Math 3206
  • Nonlinear Schrödinger equations: The interplay of modeling, numerics and physics


    Speaker: Norbert Mauser (Wolfang Pauli Institute and Univ. of Vienna) -

    When: Fri, August 14, 2015 - 11:00am
    Where: Math 1311