Approximate Bayesian computation via the energy statistic

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of summary statistics. Here we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the so-called two-sample energy statistic. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds, and prove that the rejection ABC algorithm, based on the energy statistic, generates pseudo-posterior distributions that achieves convergence to the correct limits, when implemented with rejection thresholds that converge to zero, in the finite sample setting. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate $g$-and-$k$ distribution. We find that our proposed method compares well with alternative discrepancy measures.Comment: 25 pages, 6 figures, 5 table

General Kerr-NUT-AdS Metrics in All Dimensions

The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric components depend on the radial coordinate r and [D/2] latitude variables \mu_i that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate reparameterisation in which the \mu_i variables are replaced by [D/2]-1 unconstrained coordinates y_\alpha, and having the remarkable property that the Kerr-AdS metric becomes diagonal in the coordinate differentials dy_\alpha. The coordinates r and y_\alpha now appear in a very symmetrical way in the metric, leading to an immediate generalisation in which we can introduce [D/2]-1 NUT parameters. We find that (D-5)/2 are non-trivial in odd dimensions, whilst (D-2)/2 are non-trivial in even dimensions. This gives the most general Kerr-NUT-AdS metric in $D$ dimensions. We find that in all dimensions D\ge4 there exist discrete symmetries that involve inverting a rotation parameter through the AdS radius. These symmetries imply that Kerr-NUT-AdS metrics with over-rotating parameters are equivalent to under-rotating metrics. We also consider the BPS limit of the Kerr-NUT-AdS metrics, and thereby obtain, in odd dimensions and after Euclideanisation, new families of Einstein-Sasaki metrics.Comment: Latex, 24 pages, minor typos correcte

Branching ratio and CP asymmetry of Bs→π+π−B_s \to \pi^+ \pi^- decays in the perturbative QCD approach

In this paper, we calculate the decay rate and CP asymmetry of the $B_s \to \pi^+\pi^-$ decay in perturbative QCD approach with Sudakov resummation. Since none of the quarks in final states is the same as those of the initial $B_s$ meson, this decay can occur only via annihilation diagrams in the standard model. Besides the current-current operators, the contributions from the QCD and electroweak penguin operators are also taken into account. We find that (a) the branching ratio is about $4 \times 10^{-7}$; (b) the penguin diagrams dominate the total contribution; and (c) the direct CP asymmetry is small in size: no more than $3$; but the mixing-induced CP asymmetry can be as large as ten percent testable in the near future LHC-b experiments.Comment: 12 pages, 4 figures included, RevTe

Pseudo-Killing Spinors, Pseudo-supersymmetric p-branes, Bubbling and Less-bubbling AdS Spaces

We consider Einstein gravity coupled to an n-form field strength in D dimensions. Such a theory cannot be supersymmetrized in general, we nevertheless propose a pseudo-Killing spinor equation and show that the AdS X Sphere vacua have the maximum number of pseudo-Killing spinors, and hence are fully pseudo-supersymmetric. We show that extremal p-branes and their intersecting configurations preserve fractions of the pseudo-supersymmetry. We study the integrability condition for general (D,n) and obtain the additional constraints that are required so that the existence of the pseudo-Killing spinors implies the Einstein equations of motion. We obtain new pseudo-supersymmetric bubbling AdS_5 X S^5 spaces that are supported by a non-self-dual 5-form. This demonstrates that non-supersymmegtric conformal field theories may also have bubbling states of arbitrary droplets of free fermions in the phase space. We also obtain an example of less-bubbling AdS geometry in D=8, whose bubbling effects are severely restricted by the additional constraint arising from the integrability condition.Comment: typos corrected, extra comments and references added, version appeared in JHE

Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact in dimension D there are [(D-1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension D, and show that in any such metric, the [(D-1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein-Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in D=4 and three charges in D=5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that in all these examples, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.Comment: 32 pages, references added and minor typos fixe

Brane Worlds in Collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed universe is one of a number of colliding D3-branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3-branes the metric remains static during and after the collision. We also obtain a general class of solutions representing $p$-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and negative-tension 3-brane.Comment: RevTex, 4 pages, 1 figure, typos and minor errors correcte

Constraints on masses of charged PGBs in technicolor model from decay B --> γ\gamma

In this paper we calculate the contributions to the branching ratio of B\to X_s \gamma from the charged Pseudo-Goldstone bosons appeared in one generation technicolor model. The current CLEO experimental results can eliminate large part of the parameter space in the m(P^\pm) - m(P_8^\pm) plane, and specifically, one can put a strong lower bound on the masses of color octet charged PGBs P_8^\pm: m(P^{\pm}_8) > 400\;GeV at 95\%C.L for free m(P^{\pm})

Annihilation Type Radiative Decays of BB Meson in Perturbative QCD Approach

With the perturbative QCD approach based on $k_T$ factorization, we study the pure annihilation type radiative decays $B^0 \to \phi\gamma$ and $B^0\to J/\psi \gamma$. We find that the branching ratio of $B^0 \to \phi\gamma$ is $(2.7^{+0.3+1.2}_{-0.6-0.6})\times10^{-11}$, which is too small to be measured in the current $B$ factories of BaBar and Belle. The branching ratio of $B^0\to J/\psi \gamma$ is $({4.5^{+0.6+0.7}_{-0.5-0.6}})\times10^{-7}$, which is just at the corner of being observable in the $B$ factories. A larger branching ratio $BR(B_s^0 \to J/\psi \gamma) \simeq 5 \times 10^{-6}$ is also predicted. These decay modes will help us testing the standard model and searching for new physics signals.Comment: 4 pages, revtex, with 1 eps figur

Lambda and Anti-Lambda Hypernuclei in Relativistic Mean-field Theory

Several aspects about $\Lambda$-hypernuclei in the relativistic mean field theory, including the effective $\Lambda$-nucleon coupling strengths based on the successful effective nucleon-nucleon interaction PK1, hypernuclear magnetic moment and $\bar\Lambda$-hypernuclei, have been presented. The effect of tensor coupling in $\Lambda$-hypernuclei and the impurity effect of $\bar\Lambda$ to nuclear structure have been discussed in detail.Comment: 8 pages, 2 figures, Proceedings of the Sendai International Symposium "Strangeness in Nuclear and Hadronic Systems SENDAI08