Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty estimates. Classical Monte Carlo methods, particularly Markov Chain Monte Carlo, remain the gold standard for approximate Bayesian inference because they have a robust finite-sample theory and reliable convergence diagnostics. However, alternative methods, which are more scalable or apply to problems where Markov Chain Monte Carlo cannot be used, lack the same finite-data approximation theory and tools for evaluating their accuracy. In this work, we develop a flexible new approach to bounding the error of mean and uncertainty estimates of scalable inference algorithms. Our strategy is to control the estimation errors in terms of Wasserstein distance, then bound the Wasserstein distance via a generalized notion of Fisher distance. Unlike computing the Wasserstein distance, which requires access to the normalized posterior distribution, the Fisher distance is tractable to compute because it requires access only to the gradient of the log posterior density. We demonstrate the usefulness of our Fisher distance approach by deriving bounds on the Wasserstein error of the Laplace approximation and Hilbert coresets. We anticipate that our approach will be applicable to many other approximate inference methods such as the integrated Laplace approximation, variational inference, and approximate Bayesian computationComment: 22 pages, 2 figure

Solid deuterium surface degradation at ultracold neutron sources

Solid deuterium (sD_2) is used as an efficient converter to produce ultracold neutrons (UCN). It is known that the sD_2 must be sufficiently cold, of high purity and mostly in its ortho-state in order to guarantee long lifetimes of UCN in the solid from which they are extracted into vacuum. Also the UCN transparency of the bulk sD_2 material must be high because crystal inhomogeneities limit the mean free path for elastic scattering and reduce the extraction efficiency. Observations at the UCN sources at Paul Scherrer Institute and at Los Alamos National Laboratory consistently show a decrease of the UCN yield with time of operation after initial preparation or later treatment (`conditioning') of the sD_2. We show that, in addition to the quality of the bulk sD_2, the quality of its surface is essential. Our observations and simulations support the view that the surface is deteriorating due to a build-up of D_2 frost-layers under pulsed operation which leads to strong albedo reflections of UCN and subsequent loss. We report results of UCN yield measurements, temperature and pressure behavior of deuterium during source operation and conditioning, and UCN transport simulations. This, together with optical observations of sD_2 frost formation on initially transparent sD_2 in offline studies with pulsed heat input at the North Carolina State University UCN source results in a consistent description of the UCN yield decrease.Comment: 15 pages, 22 figures, accepted by EPJ-

Comparison of ultracold neutron sources for fundamental physics measurements

Ultracold neutrons (UCNs) are key for precision studies of fundamental parameters of the neutron and in searches for new CP violating processes or exotic interactions beyond the Standard Model of particle physics. The most prominent example is the search for a permanent electric dipole moment of the neutron (nEDM). We have performed an experimental comparison of the leading UCN sources currently operating. We have used a 'standard' UCN storage bottle with a volume of 32 liters, comparable in size to nEDM experiments, which allows us to compare the UCN density available at a given beam port.Comment: 20 pages, 30 Figure

A highly stable atomic vector magnetometer based on free spin precession

We present a magnetometer based on optically pumped Cs atoms that measures the magnitude and direction of a 1 $\mu$T magnetic field. Multiple circularly polarized laser beams were used to probe the free spin precession of the Cs atoms. The design was optimized for long-time stability and achieves a scalar resolution better than 300 fT for integration times ranging from 80 ms to 1000 s. The best scalar resolution of less than 80 fT was reached with integration times of 1.6 to 6 s. We were able to measure the magnetic field direction with a resolution better than 10 $\mu$rad for integration times from 10 s up to 2000 s

Observation of Scaling Violations in Scaled Momentum Distributions at HERA

Charged particle production has been measured in deep inelastic scattering (DIS) events over a large range of $x$ and $Q^2$ using the ZEUS detector. The evolution of the scaled momentum, $x_p$, with $Q^2,$ in the range 10 to 1280 $GeV^2$, has been investigated in the current fragmentation region of the Breit frame. The results show clear evidence, in a single experiment, for scaling violations in scaled momenta as a function of $Q^2$.Comment: 21 pages including 4 figures, to be published in Physics Letters B. Two references adde