Statistical unfolding of elementary particle spectra: Empirical Bayes estimation and bias-corrected uncertainty quantification

We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising in data analysis at the Large Hadron Collider at CERN consists in estimating the intensity function of an indirectly observed Poisson point process. Unfolding typically proceeds in two steps: one first produces a regularized point estimate of the unknown intensity and then uses the variability of this estimator to form frequentist confidence intervals that quantify the uncertainty of the solution. In this paper, we propose forming the point estimate using empirical Bayes estimation which enables a data-driven choice of the regularization strength through marginal maximum likelihood estimation. Observing that neither Bayesian credible intervals nor standard bootstrap confidence intervals succeed in achieving good frequentist coverage in this problem due to the inherent bias of the regularized point estimate, we introduce an iteratively bias-corrected bootstrap technique for constructing improved confidence intervals. We show using simulations that this enables us to achieve nearly nominal frequentist coverage with only a modest increase in interval length. The proposed methodology is applied to unfolding the $Z$ boson invariant mass spectrum as measured in the CMS experiment at the Large Hadron Collider.Comment: Published at http://dx.doi.org/10.1214/15-AOAS857 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: substantial text overlap with arXiv:1401.827

Effect of selenite and selenised yeast supplementation on selenium concentration of Finnish organic milk – a farm study.

Experiment was conducted at 15 certified organic dairy farms in Eastern Finland during spring 2008. Farms were allocated to three balanced groups according annual milk yield, herd size and housing system. Three types of selenium (Se) supplementations: selenium yeast (SY), sodium selenite (SS) or their (50:50) combination (SYS) was used. Daily Se doses were adjusted according to milk yield basis (average 3 mg/d). Experimental model was 3 X 3 Latin square, consisting from 3 experiment periods. The length of each period was 28 days. RehuRaisio provided experimental feeds. In the end of each period bulk-tank milk samples were collected and analysed for Se at MTT Agrifood Research Finland. The Se supplementation form was crucial for milk Se concentration (P<0.001), when Se concentration of basic fodder was extreme low (<0.01 mg/kg DM). SS (n=15) resulted to milk Se concentration of 0.012 mg/kg, but SYS (n=15) resulted to 1.9-fold and SY (n=14) to 2.3-fold higher milk Se concentrations

Selenium concentration of Finnish organic milk - a farm survey

Bulk-tank milk samples were collected in January (2008) from 45 organic farms in Eastern Finland to examine their milk quality. Beside diets, current Se supplementation practices were also documented

Shock waves in the dissipative Toda lattice

We consider the propagation of a shock wave (SW) in the damped Toda lattice. The SW is a moving boundary between two semi-infinite lattice domains with different densities. A steadily moving SW may exist if the damping in the lattice is represented by an ``inner'' friction, which is a discrete analog of the second viscosity in hydrodynamics. The problem can be considered analytically in the continuum approximation, and the analysis produces an explicit relation between the SW's velocity and the densities of the two phases. Numerical simulations of the lattice equations of motion demonstrate that a stable SW establishes if the initial velocity is directed towards the less dense phase; in the opposite case, the wave gradually spreads out. The numerically found equilibrium velocity of the SW turns out to be in a very good agreement with the analytical formula even in a strongly discrete case. If the initial velocity is essentially different from the one determined by the densities (but has the correct sign), the velocity does not significantly alter, but instead the SW adjusts itself to the given velocity by sending another SW in the opposite direction.Comment: 10 pages in LaTeX, 5 figures available upon regues

Collective Effects in Settling of Spheroids under Steady-State Sedimentation

We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.Peer reviewe

Sedimentation dynamics of spherical particles in confined geometries

We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing Lx. By systematically varying Lx we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of Lx. We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to Lx. We also find that the behavior of the corresponding diffusion coefficients as a function of Lx is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.Peer reviewe

Streptococcus pneumoniae antimicrobial resistance decreased in the Helsinki Metropolitan Area after routine 10-valent pneumococcal conjugate vaccination of infants in Finland

Since the introduction of 10-valent pneumococcal conjugate vaccine (PCV10) into the Finnish national vaccination program in September 2010, the incidence of invasive pneumococcal disease in children has decreased steeply in Finland. We studied the antimicrobial susceptibility of invasive and non-invasive Streptococcus pneumoniae (pneumococcus) isolated in the Helsinki Metropolitan Area during 2009-2014. We divided the data into two age groups: isolates from patients <5 years old and ae5 years old. We also studied the serotype distribution of invasive isolates and of a subset of non-invasive multidrug-resistant isolates. The invasive isolate numbers recovered from patients aged <5 years old declined from 33/228 (15%) in 2009 to 8/208 (4%) in 2014 (p <0.001) and non-invasive isolate numbers declined during the same time period from 221/595 (37%) to 119/432 (28%) (p <0.001). At the same time, the proportion of penicillin non-susceptible non-invasive isolates in this age group decreased from 25% (56/220) to 13% (15/119) (p = 0.001) and multidrug-resistant isolates from 22% (49/220) to 6% (7/119) (p <0.001), respectively. The number of PCV10 serotype isolates also decreased among the serotyped multidrug-resistant non-invasive isolates. Among patients aged ae5 years old, the isolate numbers did not show a similar decreasing trend compared to the younger group and, further, the number of non-PCV10 serotype isolates increased in invasive cases. To conclude, the antimicrobial non-susceptibility of pneumococcus has decreased markedly, especially among young patients (<5 years old), following PCV10 implementation in Finland.Peer reviewe

Regeneration of Stochastic Processes: An Inverse Method

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.Comment: 5 pages, two columns, 7 figs. to appear, The European Physical Journal B (2006