Simulation-based Tests that Can Use Any Number of Simulations

Conventional procedures for Monte Carlo and bootstrap tests require that B, the number of simulations, satisfy a specific relationship with the level of the test. Otherwise, a test that would instead be exact will either overreject or underreject for finite B. We present expressions for the rejection frequencies associated with existing procedures and propose a new procedure that yields exact Monte Carlo tests for any positive value of B. This procedure, which can also be used for bootstrap tests, is likely to be most useful when simulation is expensive.resampling, Monte Carlo test, bootstrap test, percentiles, simulation

Inference via kernel smoothing of bootstrap P values

Resampling methods such as the bootstrap are routinely used to estimate the finite-sample null distributions of a range of test statistics. We present a simple and tractable way to perform classical hypothesis tests based upon a kernel estimate of the CDF of the bootstrap statistics. This approach has a number of appealing features: i) it can perform well when the number of bootstraps is extremely small, ii) it is approximately exact, and iii) it can yield substantial power gains relative to the conventional approach. The proposed approach is likely to be useful when the statistic being bootstrapped is computationally expensive.resampling, Monte Carlo test, bootstrap test, percentiles, kernel, smoothing

Nonparametric Estimation of Conditional Distributions in the Presence of Continuous and Categorical Data

A method is proposed for the consistent nonparametric estimation of conditional probability and probability density functions along with associated gradients when both the conditioned and conditioning variables are categorical, continuous, or a mixture of both types. The method builds on the work of Aitchison & Aitken (1976) who proposed a novel method for kernel density estimation when using multinomial categorical data types. Simulations show that the proposed method performs quite well for a number of conditional simulated processes that mix both categorical and continuous variables. Applications of the proposed method to (i) the widely-cited Iris dataset of Fisher (1936), (ii) the female labor supply dataset from the Panel Study on Income Dynamics examined in Mroz (1987), and (iii) the Swiss labor force data studied by Gerfin (1996) all demonstrate that the proposed method performs better than conventional parametric models for predicting multinomial discrete choice. The method extends the realm of nonparametric modeling through the seamless blending of both categorical and continuous variables, and is capable of detecting structure in the data which frequently remains undetected by conventional parametric approaches.

Design of 280 GHz feedhorn-coupled TES arrays for the balloon-borne polarimeter SPIDER

We describe 280 GHz bolometric detector arrays that instrument the balloon-borne polarimeter SPIDER. A primary science goal of SPIDER is to measure the large-scale B-mode polarization of the cosmic microwave background in search of the cosmic-inflation, gravitational-wave signature. 280 GHz channels aid this science goal by constraining the level of B-mode contamination from galactic dust emission. We present the focal plane unit design, which consists of a 16$\times$16 array of conical, corrugated feedhorns coupled to a monolithic detector array fabricated on a 150 mm diameter silicon wafer. Detector arrays are capable of polarimetric sensing via waveguide probe-coupling to a multiplexed array of transition-edge-sensor (TES) bolometers. The SPIDER receiver has three focal plane units at 280 GHz, which in total contains 765 spatial pixels and 1,530 polarization sensitive bolometers. By fabrication and measurement of single feedhorns, we demonstrate 14.7$^{\circ}$ FHWM Gaussian-shaped beams with $<$1% ellipticity in a 30% fractional bandwidth centered at 280 GHz. We present electromagnetic simulations of the detection circuit, which show 94% band-averaged, single-polarization coupling efficiency, 3% reflection and 3% radiative loss. Lastly, we demonstrate a low thermal conductance bolometer, which is well-described by a simple TES model and exhibits an electrical noise equivalent power (NEP) = 2.6 $\times$ 10$^{-17}$ W/$\sqrt{\mathrm{Hz}}$, consistent with the phonon noise prediction.Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 201

Observing low elevation sky and the CMB Cold Spot with BICEP3 at the South Pole

BICEP3 is a 520 mm aperture on-axis refracting telescope at the South Pole, which observes the polarization of the cosmic microwave background (CMB) at 95 GHz to search for the B-mode signal from inflationary gravitational waves. In addition to this main target, we have developed a low-elevation observation strategy to extend coverage of the Southern sky at the South Pole, where BICEP3 can quickly achieve degree-scale E-mode measurements over a large area. An interesting E-mode measurement is probing a potential polarization anomaly around the CMB Cold Spot. During the austral summer seasons of 2018-19 and 2019-20, BICEP3 observed the sky with a flat mirror to redirect the beams to various low elevation ranges. The preliminary data analysis shows degree-scale E-modes measured with high signal-to-noise ratio

Analysis of Temperature-to-Polarization Leakage in BICEP3 and Keck CMB Data from 2016 to 2018

The Bicep/Keck Array experiment is a series of small-aperture refracting telescopes observing degree-scale Cosmic Microwave Background polarization from the South Pole in search of a primordial B-mode signature. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We use high-fidelity, in-situ measurements of the beam response to estimate the temperature-to-polarization (T → P) leakage in our latest data including observations from 2016 through 2018. This includes three years of Bicep3 observing at 95 GHz, and multifrequency data from Keck Array. Here we present band-averaged far-field beam maps, differential beam mismatch, and residual beam power (after filtering out the leading difference modes via deprojection) for these receivers. We show preliminary results of "beam map simulations," which use these beam maps to observe a simulated temperature (no Q/U) sky to estimate T → P leakage in our real data

Analysis of Temperature-to-Polarization Leakage in BICEP3 and Keck CMB Data from 2016 to 2018

The Bicep/Keck Array experiment is a series of small-aperture refracting telescopes observing degree-scale Cosmic Microwave Background polarization from the South Pole in search of a primordial B-mode signature. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We use high-fidelity, in-situ measurements of the beam response to estimate the temperature-to-polarization (T → P) leakage in our latest data including observations from 2016 through 2018. This includes three years of Bicep3 observing at 95 GHz, and multifrequency data from Keck Array. Here we present band-averaged far-field beam maps, differential beam mismatch, and residual beam power (after filtering out the leading difference modes via deprojection) for these receivers. We show preliminary results of "beam map simulations," which use these beam maps to observe a simulated temperature (no Q/U) sky to estimate T → P leakage in our real data

Observing low elevation sky and the CMB Cold Spot with BICEP3 at the South Pole

BICEP3 is a 520 mm aperture on-axis refracting telescope at the South Pole, which observes the polarization of the cosmic microwave background (CMB) at 95 GHz to search for the B-mode signal from inflationary gravitational waves. In addition to this main target, we have developed a low-elevation observation strategy to extend coverage of the Southern sky at the South Pole, where BICEP3 can quickly achieve degree-scale E-mode measurements over a large area. An interesting E-mode measurement is probing a potential polarization anomaly around the CMB Cold Spot. During the austral summer seasons of 2018-19 and 2019-20, BICEP3 observed the sky with a flat mirror to redirect the beams to various low elevation ranges. The preliminary data analysis shows degree-scale E-modes measured with high signal-to-noise ratio

Polarization calibration of the BICEP3 CMB polarimeter at the South Pole

The BICEP3 CMB Polarimeter is a small-aperture refracting telescope located at the South Pole and is specifically designed to search for the possible signature of inflationary gravitational waves in the Cosmic Microwave Background (CMB). The experiment measures polarization on the sky by differencing the signal of co-located, orthogonally polarized antennas coupled to Transition Edge Sensor (TES) detectors. We present precise measurements of the absolute polarization response angles and polarization efficiencies for nearly all of BICEP3's ~800 functioning polarization-sensitive detector pairs from calibration data taken in January 2018. Using a Rotating Polarized Source (RPS), we mapped polarization response for each detector over a full 360 degrees of source rotation and at multiple telescope boresight rotations from which per-pair polarization properties were estimated. In future work, these results will be used to constrain signals predicted by exotic physical models such as Cosmic Birefringence

Microwave multiplexing on the Keck Array

We describe an on-sky demonstration of a microwave-multiplexing readout system in one of the receivers of the Keck Array, a polarimetry experiment observing the cosmic microwave background at the South Pole. During the austral summer of 2018-2019, we replaced the time-division multiplexing readout system with microwave-multiplexing components including superconducting microwave resonators coupled to radio-frequency superconducting quantum interference devices at the sub-Kelvin focal plane, coaxial-cable plumbing and amplification between room temperature and the cold stages, and a SLAC Microresonator Radio Frequency system for the warm electronics. In the range 5-6 GHz, a single coaxial cable reads out 528 channels. The readout system is coupled to transition-edge sensors, which are in turn coupled to 150-GHz slot-dipole phased-array antennas. Observations began in April 2019, and we report here on an initial characterization of the system performance.Comment: 9 pages, 11 figures, Accepted by the Journal of Low Temperature Physics (Proceedings of the 18th International Workshop on Low Temperature Detectors