Asymptotically Minimax Regret by Bayes Mixtures

We study the problems of data compression, gambling and prediction of a sequence $x^n=x_1x_2...x_n$ from an alphabet ${\cal X}$, in terms of regret and expected regret (redundancy) with respect to various smooth families of probability distributions. We evaluate the regret of Bayes mixture distributions compared to maximum likelihood, under the condition that the maximum likelihood estimate is in the interior of the parameter space. For general exponential families (including the non-i.i.d.\ case) the asymptotically mimimax value is achieved when variants of the prior of Jeffreys are used. %under the condition that the maximum likelihood estimate is in the interior of the parameter space. Interestingly, we also obtain a modification of Jeffreys prior which has measure outside the given family of densities, to achieve minimax regret with respect to non-exponential type families. This modification enlarges the family using local exponential tilting (a fiber bundle). Our conditions are confirmed for certain non-exponential families, including curved families and mixture families (where either the mixture components or their weights of combination are parameterized) as well as contamination models. Furthermore for mixture families we show how to deal with the full simplex of parameters. These results also provide characterization of Rissanen's stochastic complexity

Isotope production in proton-, deuteron-, and carbon-induced reactions on Nb 93 at 113 MeV/nucleon

Isotope-production cross sections for p-, d-, and C-induced spallation reactions on Nb93 at 113 MeV/nucleon were measured using the inverse-kinematics method employing secondary targets of CH2, CD2, and C. The measured cross sections for Mo90, Nb90, Y86,88 produced by p-induced reactions were found to be consistent with those measured by the conventional activation method. We performed benchmark tests of the reaction models INCL-4.6, JQMD, and JQMD-2.0 implemented in the Particle and Heavy Ion Transport code System (PHITS) and of the nuclear data libraries JENDL-4.0/HE, TENDL-2017, and ENDF/B-VIII.0. The model calculations also showed generally good agreement with the measured isotope-production cross sections for p-, d-, and C-induced reactions. It also turns out that, among the three nuclear data libraries, JENDL-4.0/HE provides the best agreement with the measured data for the p-induced reactions. We compared the present Nb93 data with the Zr93 data, that were measured previously by the same inverse kinematics method (Kawase et al., Prog. Theor. Exp. Phys. 2017, 093D03 (2017)2050-391110.1093/ptep/ptx110), with particular attention to the effect of neutron-shell closure on isotope production in p- and d-induced spallation reactions. The isotopic distributions of the measured production cross sections in the Zr93 data showed noticeable jumps at neutron number N=50 in the isotopic chains of ΔZ=0 and -1, whereas no such jump appeared in isotopic chain of ΔZ=0 in the Nb93 data. From INCL-4.6 + GEM calculations, we found that the jump formed in the evaporation process is smeared out by the intranuclear cascade component in Nb91 produced by the Nb93(p,p2n) and (d,d2n) reactions on Nb93. Moreover, for Nb93, the distribution of the element-production cross sections as a function of the change in proton number ΔZ is shifted to smaller ΔZ than for Zr93, because the excited Nb prefragments generated by the cascade process are more likely to emit protons than the excited Zr prefragments, due to the smaller proton-separation energies of the Nb isotopes

Cross sections for nuclide production in proton- and deuteron-induced reactions on 93

Isotopic production cross sections were measured for proton- and deuteron-induced reactions on 93Nb by means of the inverse kinematics method at RIKEN Radioactive Isotope Beam Factory. The measured production cross sections of residual nuclei in the reaction 93Nb + p at 113 MeV/u were compared with previous data measured by the conventional activation method in the proton energy range between 46 and 249 MeV. The present inverse kinematics data of four reaction products (90Mo, 90Nb, 88Y, and 86Y) were in good agreement with the data of activation measurement. Also, the model calculations with PHITS describing the intra-nuclear cascade and evaporation processes generally well reproduced the measured isotopic production cross sections