CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Near-infrared Instrumentation For Rapid-response Astronomy

Ɣ-ray bursts (GRBs) are the Universe's most luminous transient events. Since the discovery of GRBs was announced in 1973, efforts have been ongoing to obtain data over a broader range of the electromagnetic spectrum at the earliest possible times following the initial detection. The discovery of the theorized ``afterglow'' emission in radio through X-ray bands in the late 1990s confirmed the cosmological nature of these events. At present, GRB afterglows are among the best probes of the early Universe (z ≳ 9). In addition to informing theories about GRBs themselves, observations of afterglows probe the circum-burst medium (CBM), properties of the host galaxies and the progress of cosmic reionization. To explore the early-time variability of afterglows, I have developed a generalized analysis framework which models near-infrared (NIR), optical, ultra-violet (UV) and X-ray light curves without assuming an underlying model. These fits are then used to construct the spectral energy distribution (SED) of afterglows at arbitrary times within the observed window. Physical models are then used to explore the evolution of the SED parameter space with time. I demonstrate that this framework produces evidence of the photodestruction of dust in the CBM of GRB 120119A, similar to the findings from a previous study of this afterglow. The framework is additionally applied to the afterglows of GRB 140419A and GRB 080607. In these cases the evolution of the SEDs appears consistent with the standard fireball model. Having introduced the scientific motivations for early-time observations, I introduce the Rapid Infrared Imager-Spectrometer (RIMAS). Once commissioned on the 4.3 meter Discovery Channel Telescope (DCT), RIMAS will be used to study the afterglows of GRBs through photometric and spectroscopic observations beginning within minutes of the initial burst. The instrument will operate in the NIR, from 0.97 μm to 2.37 μm, permitting the detection of very high redshift (z ≳ 7) afterglows which are attenuated at shorter wavelengths by Lyman-ɑ absorption in the intergalactic medium (IGM). A majority of my graduate work has been spent designing and aligning RIMAS's cryogenic (~80 K) optical systems. Design efforts have included an original camera used to image the field surrounding spectroscopic slits, tolerancing and optimizing all of the instrument's optics, thermal modeling of optomechanical systems, and modeling the diffraction efficiencies for some of the dispersive elements. To align the cryogenic optics, I developed a procedure that was successfully used for a majority of the instrument's sub-assemblies. My work on this cryogenic instrument has necessitated experimental and computational projects to design and validate designs of several subsystems. Two of these projects describe simple and effective measurements of optomechanical components in vacuum and at cryogenic temperatures using an 8-bit CCD camera. Models of heat transfer via electrical harnesses used to provide current to motors located within the cryostat are also presented.