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In the electronic measurement of the Boltzmann constant based on Johnson noise thermometry, the ratio of the power spectral densities of thermal noise across a resistor at the triple point of water, and pseudo-random noise synthetically generated by a quantum-accurate voltage-noise source is constant to within 1 part in a billion for frequencies up to 1 GHz. Given this ratio, and the values of other known or measured parameters, one can determine the Boltzmann constant. Due, in part, to mismatch between transmission lines, the experimental ratio spectrum varies with frequency. We model this spectrum as an even polynomial function of frequency where the constant term in the polynomial determines the Boltzmann constant. When determining this constant (offset) from experimental data, the assumed complexity of the ratio spectrum model and the maximum frequency analyzed (fitting bandwidth) dramatically affects results. We select the complexity of the model by cross-validation. For each of many fitting bandwidths, we determine the component of uncertainty of the offset term that accounts for random and systematic effects associated with imperfect knowledge of model complexity. We select the fitting bandwidth that minimizes this uncertainty. In the most recent measurement of the Boltzmann constant, results were determined, in part, by application of an earlier version of the method described here. Here, we extend the earlier analysis by considering a broader range of fitting bandwidths and quantify an additional component of uncertainty that accounts for imperfect performance of our fitting bandwidth selection method. For idealized simulated data our method correctly selects the true complexity of the ratio spectrum model for all cases considered. A new analysis of data from the recent experiment yields evidence for a temporal trend in the offset parameters., Comment: 25 pages, 8 figures. New version has a modified abstract, added text in Introduction, new entries in Table 5, additional references, and a new title. The main technical results are unchanged

In a neutron lifetime experiment conducted at the National Institute of Standards and Technology, protons produced by neutron decay events are confined in a Penning trap. In each run of the experiment, there is a trapping stage of duration $\tau$. After the trapping stage, protons are purged from the trap. A proton detector provides incomplete information because it goes dead after detecting the first of any purged protons. Further, there is a dead time $\delta$ between the end of the trapping stage in one run and the beginning of the next trapping stage in the next run. Based on the fraction of runs where a proton is detected, I estimate the trapping rate $\lambda$ by the method of maximum likelihood. I show that the expected value of the maximum likelihood estimate is infinite. To obtain a maximum likelihood estimate with a finite expected value and a well-defined and finite variance, I restrict attention to a subsample of all realizations of the data. This subsample excludes an exceedingly rare realization that yields an infinite-valued estimate of $\lambda$. I present asymptotically valid formulas for the bias, root-mean-square prediction error, and standard deviation of the maximum likelihood estimate of $\lambda$ for this subsample. Based on nominal values of $\lambda$ and the dead time $\delta$, I determine the optimal duration of the trapping stage $\tau$ by minimizing the root-mean-square prediction error of the estimate., Comment: 21 pages, 4 figures This is a revised version of "Optimal Proton Trapping". Based on a review, some aspects of the techical argument were refined

In CLEAN (Cryogenic Low Energy Astrophysics with Noble gases), a proposed neutrino and dark matter detector, background discrimination is possible if one can determine the location of an ionizing radiation event with high accuracy. We simulate ionizing radiation events that produce multiple scintillation photons within a spherical detection volume filled with liquid neon. We estimate the radial location of a particular ionizing radiation event based on the observed count data corresponding to that event. The count data are collected by detectors mounted at the spherical boundary of the detection volume. We neglect absorption, but account for Rayleigh scattering. To account for wavelength-shifting of the scintillation light, we assume that photons are absorbed and re-emitted at the detectors. Here, we develop spatial Maximum Likelihood methods for event reconstruction, and study their performance in computer simulation experiments. We also study a method based on the centroid of the observed count data. We calibrate our estimates based on training data.