Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

A Facile One‐Pot Synthesis of Pyrrolo[1, 2‐a] Indoles by Intramolecular 1,3‐Dipolar Cycloaddition under Neat‐Microwave Irradiation

A straightforward and general approach for the stereoselective synthesis of fused pyrrolo[1,2‐a] indoles frameworks from>intramolecular 1,3‐dipolar cycloaddition using N‐alkylated Baylis–Hillman derivatives is presented. It was found that the cycloaddition proceeded efficiently under microwave irradiation in solvent‐free condition to afford highly stereoselective cycloadducts in good yield.     

Approximation of the Posterior Distribution in a Change-Point Problem

We consider a family of models that arise in connection with sharp change in hazard rate corresponding to high initial hazard rate dropping to a more stable or slowly changing rate at an unknown change-point . Although the Bayes estimates are well behaved and are asymptotically efficient, it is difficult to compute them as the posterior distributions are generally very complicated. We obtain a simple first order asymptotic approximation to the posterior distribution of . The accuracy of the approximation is judged through simulation. The approximation performs quite well. Our method is also applied to analyze a real data set.     

An efficient total synthesis of the anticancer agent (+)-spisulosine (ES-285) from Garner’s aldehyde

An efficient total synthesis of (+)-spisulosine (ES-285) was completed in nine steps from (S)-Garner’s aldehyde. The vicinal amino alcohol moiety with anti-configuration was achieved by a highly diastereoselective addition of vinyl magnesium bromide to Garner’s aldehyde. The long hydrocarbon chain of the antitumor natural product was installed via olefin cross metathesis of the benzyl-protected allylic alcohol with an appropriate olefin counterpart followed by hydrogenation.     

Beyond the standard model: Working group report

This report summarises the activities of the working group on ‘Physics beyond the Standard Model’. The results of investigations in incorporatingR-parity in grand unification, the possibility of a light charged Higgs boson in extension of MSSM and radiative generation of neutral vector boson self-couplings within the MSSM are described. Also given is an account of activities in neutrino physics, namely a proposal for a study of the atmospheric muon anomaly in deep underground mines, a field theoretic study of neutrino oscillations and a mechanism to generate appropriate masses of three active plus one sterile neutrino species.     

Complete Convergence of Martingale Arrays

We study complete convergence of martingale arrays under rather weak conditions. Our results considerably strengthen many of the results available in the literature. As a tool, we establish a martingale analogue of an inequality of Hoffman-Jørgensen which was earlier known only for independent random variables.     

Recent advances in the chemistry of lignans

The recent literature on the chemistry of simple lignans has been comprehensively reviewed.