A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effects of multiple repairs on Inconel 718 weld mechanical properties

Inconel 718 weldments were repaired 3, 6, 9, and 13 times using the gas tungsten arc welding process. The welded panels were machined into mechanical test specimens, postweld heat treated, and nondestructively tested. Tensile properties and high cycle fatigue life were evaluated and the results compared to unrepaired weld properties. Mechanical property data were analyzed using the statistical methods of difference in means for tensile properties and difference in log means and Weibull analysis for high cycle fatigue properties. Statistical analysis performed on the data did not show a significant decrease in tensile or high cycle fatigue properties due to the repeated repairs. Some degradation was observed in all properties, however, it was minimal

Temperature dependence of the coercive field in single-domain particle systems

The magnetic properties of Cu97Co3 and Cu90Co10 granular alloys were measured over a wide temperature range (2 to 300K). The measurements show an unusual temperature dependence of the coercive field. A generalized model is proposed and explains well the experimental behavior over a wide temperature range. The coexistence of blocked and unblocked particles for a given temperature rises difficulties that are solved here by introducing a temperature dependent blocking temperature. An empirical factor gamma arise from the model and is directly related to the particle interactions. The proposed generalized model describes well the experimental results and can be applied to other single-domain particle system.Comment: 7 pages, 8 figures, revised version, accepted to Physical Review B on 29/04/200

Dynamics of Logamediate Inflation

A computation of the inflationary observables n_{s} and r is made for `logamediate' inflation where the cosmological scale factor expands as $a=\exp (A(\ln t)^{\lambda})$, and is compared to their predicted values in the intermediate inflationary theory, where $a=\exp (Bt^{f})$. Both versions prove to be consistent with observational measurements of the cosmic background radiation. It is shown that the dynamics of a single inflaton field can be mimicked by a system of several fields in an analogous manner to that created by the joint evolution of the fields in assisted power-law inflation.Comment: 7 pages, 5 figures. Extended introductio

On quasi-Jacobi and Jacobi-quasi bialgebroids

We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also that the structures induced on their base manifolds are related via a quasi Poissonization

Combined method to extract spectroscopic information

Spectroscopic factors (SF) play an important role in nuclear physics and astrophysics. The traditional method of extracting SF from direct transfer reactions suffers from serious ambiguities. We discuss a modified method which is based on including the asymptotic normalization coefficient (ANC) of the overlap functions into the transfer analysis. In the modified method the contribution of the external part of the reaction amplitude, typically dominant, is fixed and the SF is determined from fitting the internal part. We illustrate the modified method with $(d,p)$ reactions on ${}^{208}{\rm Pb}, {}^{12}{\rm C}$, and ${}^{84}{\rm Se}$ targets at different energies. The modified method allows one to extract the SF, which do not depend on the shape of the single-particle nucleon-target interaction, and has the potential of improving the reliability and accuracy of the structure information. This is specially important for nuclei on dripline, where not much is known.Comment: accepted in Phys. Rev. C, 4 pages and 2 figure

Reheating induced by competing decay modes

We address the problem of studying the decay of the inflaton field $\phi$ to another scalar field $\chi$ through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the $\chi$ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of non-cuspidal resonance regions associated to higher harmonics and to the emergence of instability `pockets'. We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications.Comment: 14 pages, 4 figures Added references. Corrected typo

Three-body description of direct nuclear reactions: Comparison with the continuum discretized coupled channels method

The continuum discretized coupled channels (CDCC) method is compared to the exact solution of the three-body Faddeev equations in momentum space. We present results for: i) elastic and breakup observables of d-12C at E_d=56 MeV, ii) elastic scattering of d-58Ni at E_d=80 MeV, and iii) elastic, breakup and transfer observables for 11Be+p at E_{11Be}/A=38.4 MeV. Our comparative studies show that, in the first two cases, the CDCC method is a good approximation to the full three-body Faddeev solution, but for the 11Be exotic nucleus, depending on the observable or the kinematic regime, it may miss out some of the dynamic three-body effects that appear through the explicit coupling to the transfer channel.Comment: 12 pages, 10 figures, accepted for publication in Physical Review

DNA-psoralen: single-molecule experiments and first principles calculations

The authors measure the persistence and contour lengths of DNA-psoralen complexes, as a function of psoralen concentration, for intercalated and crosslinked complexes. In both cases, the persistence length monotonically increases until a certain critical concentration is reached, above which it abruptly decreases and remains approximately constant. The contour length of the complexes exhibits no such discontinuous behavior. By fitting the relative increase of the contour length to the neighbor exclusion model, we obtain the exclusion number and the intrinsic intercalating constant of the psoralen-DNA interaction. Ab initio calculations are employed in order to provide an atomistic picture of these experimental findings.Comment: 9 pages, 4 figures in re-print format 3 pages, 4 figures in the published versio