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

A room temperature 19-channel magnetic field mapping device for cardiac signals

We present a multichannel cardiac magnetic field imaging system built in Fribourg from optical double-resonance Cs vapor magnetometers. It consists of 25 individual sensors designed to record magnetic field maps of the beating human heart by simultaneous measurements on a grid of 19 points over the chest. The system is operated as an array of second order gradiometers using sophisticated digitally controlled feedback loops.Comment: 3 pages, 3 figures, submitted to Applied Physics Letter

Measuring Sulfur Isotope Ratios from Solid Samples with the Sample Analysis at Mars Instrument and the Effects of Dead Time Corrections

The Sample Analysis at Mars (SAM) instrument suite comprises the largest science payload on the Mars Science Laboratory (MSL) "Curiosity" rover. SAM will perform chemical and isotopic analysis of volatile compounds from atmospheric and solid samples to address questions pertaining to habitability and geochemical processes on Mars. Sulfur is a key element of interest in this regard, as sulfur compounds have been detected on the Martian surface by both in situ and remote sensing techniques. Their chemical and isotopic composition can belp constrain environmental conditions and mechanisms at the time of formation. A previous study examined the capability of the SAM quadrupole mass spectrometer (QMS) to determine sulfur isotope ratios of SO2 gas from a statistical perspective. Here we discuss the development of a method for determining sulfur isotope ratios with the QMS by sampling SO2 generated from heating of solid sulfate samples in SAM's pyrolysis oven. This analysis, which was performed with the SAM breadboard system, also required development of a novel treatment of the QMS dead time to accommodate the characteristics of an aging detector

The influence of oil extraction process of different rapeseed varieties on the ileal digestibility of crude protein and amino acids in broiler chickens

The current study assessed the effect of rapeseed variety and oil extraction process on the apparent and standardised ileal digestibility (AID, SID) of crude protein (CP) and amino acids (AA) in rapeseed co-products in broiler chickens. PR46W21 and DK Cabernet rapeseed varieties were de-oiled by soft and standard hexane extraction, producing soft rapeseed meal (SRSM) and rapeseed meal (RSM), respectively. The soft, non-standard hexane extraction method was designed to reduce heat treatment that occurs prior to hexane extraction in order to maximise potential genetic differences in digestibility values of rapeseed co-products. The test meals were incorporated into semi-synthetic diets at a level of 500 g/kg; diets were fed to 14-day old paired chickens (n = 6 pairs) for ten days, when ileal digesta was collected post-slaughter from Meckel’s diverticulum to the ileal-caecal junction. The AID and SID of CP and AA were determined using titanium dioxide as inert dietary marker. The variety PR46W21 showed a greater AID and SID of CP, arginine, leucine, methionine, cysteine, phenylalanine, valine and lysine in RSM compared to the DK Cabernet RSM (p < 0.05). The soft processing increased AID and SID of CP, histidine and lysine in SRSM of PR46W21 and DK Cabernet compared to their RSM counterparts (p < 0.05). An interaction between variety and processing was only observed for AID and SID of tryptophan (p < 0.001), as only in PR46W21 standard processing reduced the tryptophan SID compared to its soft processed counterpart. The data support the view that the selection of rapeseed variety and modification of thermal treatment during the oil extraction might improve nutritional value of rapeseed meals

Impact of phonons on dephasing of individual excitons in deterministic quantum dot microlenses

Optimized light-matter coupling in semiconductor nanostructures is a key to understand their optical properties and can be enabled by advanced fabrication techniques. Using in-situ electron beam lithography combined with a low-temperature cathodoluminescence imaging, we deterministically fabricate microlenses above selected InAs quantum dots (QDs) achieving their efficient coupling to the external light field. This enables to perform four-wave mixing micro-spectroscopy of single QD excitons, revealing the exciton population and coherence dynamics. We infer the temperature dependence of the dephasing in order to address the impact of phonons on the decoherence of confined excitons. The loss of the coherence over the first picoseconds is associated with the emission of a phonon wave packet, also governing the phonon background in photoluminescence (PL) spectra. Using theory based on the independent boson model, we consistently explain the initial coherence decay, the zero-phonon line fraction, and the lineshape of the phonon-assisted PL using realistic quantum dot geometries

Outcome of primary percutaneous stent-revascularization in patients with atherosclerotic acute mesenteric ischemia

Background: Patients with acute mesenteric ischemia (AMI) often exhibit severe co-morbidities and significant surgical risks, leading to high perioperative morbidity. Purpose: To investigate the feasibility of primary percutaneous stent-revascularization (PPSR) in atherosclerotic AMI and its impact on patients' outcome. Material and Methods: Retrospective analysis of 19 consecutive patients (7 women, 12 men;median age, 69 years) with AMI caused by atherosclerotic, non-embolic stenoses/occlusions of the splanchnic arteries and PPSR. Alternative minimally invasive techniques were excluded. Clinical characteristics including the Charlson Comorbidity Index adjusted by age (CCIa) and symptom duration, technical and clinical success of PPSR, clinical course, 30-day mortality, and follow-up were evaluated and compared to literature data for surgical approaches. Technical success was defined as residual stenosis of 4 in 17 of 19 patients, 89%). Median symptom duration was 50 h. Technical and clinical success rates of PPSR were 95% (21 of 22 arteries) and 53% (10 of 19 patients). Seven patients underwent subsequent laparotomy with bowel resection in four cases. Thirty-day mortality was 42% (8 of 19 patients). Conclusion: In our study population of patients with atherosclerotic AMI, severe co-morbidities, prolonged acute symptoms, and significant perioperative risks PPSR of splanchnic stenoses were technically feasible and the clinical outcome was acceptable

Laboratory Simulations of the Titan Surface to Elucidate the Huygens Probe GCMS Observations

The Cassini/Huygens mission has vastly increased the information we have available to stndy Satnro's moon Titan. The complete mission has included an array of observational methods including remote sensing techniques, upper atmosphere in-situ saropling, and the descent of the Huygens probe directly through the atmosphere to the surface [1,2]. The instruments on the Huygens probe remain the ouly source of in-situ measurements at the surface of Titan, and work evaluating these measurements to create a pict.rre of the surface environment is ongoing. In particular, the Gas Chromatograph Mass Spectrometer (GCMS) experiment on Huygens found that although there were no heavy hydrocarbons detected in the lower atmosphere, a rich spectrum of mass peaks arose once the probe landed on the surface [3,4], However, to date it has not been possible to extract the identity and abundances of the many minor components of the spectra due to a lack of temperatnre- and instrumentappropriate data for the relevant species. We are performing laboratory stndies designed to elucidate the spectrum collected on Titan's surface, utilizing a cryogenic charober maintained at appropriate temperature and pressure conditions. The experiments will simulate the temperatnre rise experienced by the surface, which led to an enhanced signal of volatiles detected by the Huygens GCMS. The objective of this study is to exaroine the characteristics of various surface analogs as measured by the Huygens GCMS flight spare instrument, which is currently housed in our laboratory at NASA Goddard Space Flight Center (GSFC). This identification cannot be adequately accomplished through theoretical work alone since the thermodynamic properties of many species at these temperatnres (94 K, HASI measurement [5]) are not known

Practical posterior error bounds from variational objectives

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of post-hoc accuracy measures that are both theoretically justified and computationally efficient. In this paper, we provide rigorous bounds on the error of posterior mean and uncertainty estimates that arise from full-distribution approximations, as in variational inference. Our bounds are widely applicable, as they require only that the approximating and exact posteriors have polynomial moments. Our bounds are also computationally efficient for variational inference because they require only standard values from variational objectives, straightforward analytic calculations, and simple Monte Carlo estimates. We show that our analysis naturally leads to a new and improved workflow for validated variational inference. Finally, we demonstrate the utility of our proposed workflow and error bounds on a robust regression problem and on a real-data example with a widely used multilevel hierarchical model.Published versio