Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution

Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC methodology, in many applications the computational cost of ABC necessitates the choice of summary statistics and tolerances that can potentially severely bias the estimate of the posterior. We propose a new “piecewise” ABC approach suitable for discretely observed Markov models that involves writing the posterior density of the parameters as a product of factors, each a function of only a subset of the data, and then using ABC within each factor. The approach has the advantage of side-stepping the need to choose a summary statistic and it enables a stringent tolerance to be set, making the posterior “less approximate”. We investigate two methods for estimating the posterior density based on ABC samples for each of the factors: the first is to use a Gaussian approximation for each factor, and the second is to use a kernel density estimate. Both methods have their merits. The Gaussian approximation is simple, fast, and probably adequate for many applications. On the other hand, using instead a kernel density estimate has the benefit of consistently estimating the true piecewise ABC posterior as the number of ABC samples tends to infinity. We illustrate the piecewise ABC approach with four examples; in each case, the approach offers fast and accurate inference

A Search for Selectrons and Squarks at HERA

Data from electron-proton collisions at a center-of-mass energy of 300 GeV are used for a search for selectrons and squarks within the framework of the minimal supersymmetric model. The decays of selectrons and squarks into the lightest supersymmetric particle lead to final states with an electron and hadrons accompanied by large missing energy and transverse momentum. No signal is found and new bounds on the existence of these particles are derived. At 95% confidence level the excluded region extends to 65 GeV for selectron and squark masses, and to 40 GeV for the mass of the lightest supersymmetric particle.Comment: 13 pages, latex, 6 Figure

Search for W' bosons decaying to an electron and a neutrino with the D0 detector

This Letter describes the search for a new heavy charged gauge boson W' decaying into an electron and a neutrino. The data were collected with the D0 detector at the Fermilab Tevatron proton-antiproton Collider at a center-of-mass energy of 1.96 TeV, and correspond to an integrated luminosity of about 1 inverse femtobarn. Lacking any significant excess in the data in comparison with known processes, an upper limit is set on the production cross section times branching fraction, and a W' boson with mass below 1.00 TeV can be excluded at the 95% C.L., assuming standard-model-like couplings to fermions. This result significantly improves upon previous limits, and is the most stringent to date.Comment: submitted to Phys. Rev. Let

Measurement of the ratios of the Z/G* + >= n jet production cross sections to the total inclusive Z/G* cross section in ppbar collisions at sqrt(s) = 1.96 TeV

We present a study of events with Z bosons and jets produced at the Fermilab Tevatron Collider in ppbar collisions at a center of mass energy of 1.96 TeV. The data sample consists of nearly 14,000 Z/G* -> e+e- candidates corresponding to the integrated luminosity of 0.4 fb-1 collected using the D0 detector. Ratios of the Z/G* + >= n jet cross sections to the total inclusive Z/G* cross section have been measured for n = 1 to 4 jet events. Our measurements are found to be in good agreement with a next-to-leading order QCD calculation and with a tree-level QCD prediction with parton shower simulation and hadronization.Comment: 7 pages, 2 figures, slightly modified, submitted to Phys. Lett.

Measurement of the Isolated Photon Cross Section in p-pbar Collisions at sqrt{s}=1.96 TeV

The cross section for the inclusive production of isolated photons has been measured in p anti-p collisions at sqrt{s}=1.96 TeV with the D0 detector at the Fermilab Tevatron Collider. The photons span transverse momenta 23 to 300 GeV and have pseudorapidity |eta|<0.9. The cross section is compared with the results from two next-to-leading order perturbative QCD calculations. The theoretical predictions agree with the measurement within uncertainties.Comment: 7 pages, 5 figures, submitted to Phys.Lett.

Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt{s} = 1.96 TeV using Kinematic Characteristics of Lepton + Jets Events

We present a measurement of the top quark pair ttbar production cross section in ppbar collisions at a center-of-mass energy of 1.96 TeV using 230 pb**{-1} of data collected by the DO detector at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), large missing transverse energy, and at least four jets, and extract the ttbar content of the sample based on the kinematic characteristics of the events. For a top quark mass of 175 GeV, we measure sigma(ttbar) = 6.7 {+1.4-1.3} (stat) {+1.6- 1.1} (syst) +/-0.4 (lumi) pb, in good agreement with the standard model prediction.Comment: submitted to Phys.Rev.Let

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s)=1.96 TeV using Lepton + Jets Events with Lifetime b-tagging

We present a measurement of the top quark pair ($t\bar{t}$) production cross section ($\sigma_{t\bar{t}}$) in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using 230 pb$^{-1}$ of data collected by the D0 experiment at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), missing transverse energy, and jets in the final state. We employ lifetime-based b-jet identification techniques to further enhance the $t\bar{t}$ purity of the selected sample. For a top quark mass of 175 GeV, we measure $\sigma_{t\bar{t}}=8.6^{+1.6}_{-1.5}(stat.+syst.)\pm 0.6(lumi.)$ pb, in agreement with the standard model expectation.Comment: 7 pages, 2 figures, 3 tables Submitted to Phys.Rev.Let

Search for a scalar or vector particle decaying into Zgamma in ppbar collisions at sqrt(s) = 1.96 TeV

We present a search for a narrow scalar or vector resonance decaying into Zgamma with a subsequent Z decay into a pair of electrons or muons. The data for this search were collected with the D0 detector at the Fermilab Tevatron ppbar collider at a center of mass energy sqrt(s) = 1.96 TeV. Using 1.1 (1.0) fb-1 of data, we observe 49 (50) candidate events in the electron (muon) channel, in good agreement with the standard model prediction. From the combination of both channels, we derive 95% C.L. upper limits on the cross section times branching fraction (sigma x B) into Zgamma. These limits range from 0.19 (0.20) pb for a scalar (vector) resonance mass of 600 GeV/c^2 to 2.5 (3.1) pb for a mass of 140 GeV/c^2.Comment: Published by Phys. Lett.