Lefschetz Center for Dynamical Systems Seminar
Biostatistics Seminar/Lectureship Series
Abstract: The effects of a job training program, Job Corps, on both employment and wages are evaluated using data from a randomized study. Principal stratification is used to address, simultaneously, the complications of noncompliance, wages that are only partially defined because of nonemployment, and unintended missing outcomes. The first two complications are of substantive interest, whereas the third is a nuisance. The objective is to find a parsimonious model that can be used to inform public policy. We conduct a likelihood-based analysis using finite mixture models estimated by the expectation-maximization (EM) algorithm. We maintain an exclusion restriction assumption for the effect of assignment on employment and wages for noncompliers, but not on missingness. We provide estimates under the “missing at random” assumption, and assess the robustness of our results to deviations from it. The plausibility of meaningful restrictions is investigated by means of scaled log-likelihood ratio statistics. Substantive conclusions include the following. For compliers, the effect on employment is negative in the short term; it becomes positive in the long term, but these effects are small at best. For always employed compliers, that is, compliers who are employed whether trained or not trained, positive effects on wages are found at all time periods. Our analysis reveals that background characteristics of individuals differ markedly across the principal strata. We found evidence that the program should have been better targeted, in the sense of being designed differently for different groups of people, and specific suggestions are offered. Previous analyses of this dataset, which did not address all complications in a principled manner, led to less nuanced conclusions about Job Corps.
Abstract: We introduce a stochastic version of the classical Perron's method to construct viscosity solutions to linear parabolic equations associated to stochastic differential equations. Using this method, we construct easily two viscosity (sub and super) solutions that squeeze in between the expected payoff. If a comparison result holds true, then there exists a unique viscosity solution which is a martingale along the solutions of the stochastic differential equation. The unique viscosity solution is actually equal to the expected payoff. This amounts to a verification result (Ito's Lemma) for non-smooth viscosity solutions of the linear parabolic equation. We show how the method can be extended to non-linear problems, like free boundary problems associated to optimal stopping or Dynkin games and Hamilton-Jacobi-Bellman equations in stochastic control. The presentation is based on joint work with Erhan Bayraktar.
Center for Fluid Mechanics Seminar
Large collections of swimming microorganisms are able to produce
collective motions on a scale much larger than the scale of a single
organism. In particular, the collective behavior leads to velocities larger
than that of an isolated organism, fluid structures larger than the size of an
organism, enhanced transport in the fluid, and enhanced stress fluctuations
which produce altered rheological properties. Many models attempt to treat
this onset of collective behavior as a “phase transition.” However, it is
unlike normal phase transitions because the system is far from equilibrium.
The active motion of each swimming organism pushes the system away
from equilibrium. I will discuss our efforts to understand these systems
with both theory and computer simulations. In particular, I will discuss the
importance of periodic versus confining geometries, features that are not
captured in mean-field theories, and the influence of the suspending fluid.
Host: Petia Vlahovska Petia_Vlahovska@brown.edu
Many important algorithms involve transporting measures forward and it is an empirical fact that methods that approximate the measure by an empirical measure work effectively.
In this talk we explain why Monte Carlo works badly in high dimensions (like 2 or 3) and
explain other algorithms that outperform it.
This is a joint work with Wonjung Lee.
Abstract: We are concerned with nonlinear additive eigenvalue problems for viscous Hamilton-Jacobi equations which appear in stochastic ergodic control. Certain qualitative properties of principal eigenvalues and associated eigenfunctions are studied. Such analysis plays a key role in studying the recurrence and transience of feedback diffusions for the corresponding stochastic control problems. Our results can be regarded as a nonlinear extension of the criticality theory for Schrödinger operators with decaying potentials.
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