Unbiased Bayes estimates and improper priors

Given two random variables (X, Y) the condition of unbiasedness states that:E(X |Y=y)=y andE(Y |X=x)=x both almost surely (a.s.). If the prior onY is proper and has finite expectation or non-negative support, unbiasedness impliesX=Y a.s. This paper examines the implications of unbiasedness when the prior onY is improper. Since the improper case can be meaningfully analysed in a finitely additive framework, we revisit the whole issue of unbiasedness from this perspective. First we argue that a notion weaker than equality a.s., named coincidence, is more appropriate in a finitely additive setting. Next we discuss the meaning of unbiasedness from a Bayesian and fiducial perspective. We then show that unbiasedness and finite expectation ofY imply coincidence betweenX andY, while a weaker conclusion follows if the improper prior onY is only assumed to have positive support. We illustrate our approach throughout the paper by revisiting some examples discussed in the recent literature.This work was partially supported by C.N.R. grant N.80.02970.10 (G.C.) and by C.N.R. grant altri interventi (P.V.). A preliminary draft was written while the Authors were visiting the Department of Statistics at Carnegie Mellon University.The paper is the result of close cooperation between the two authors. However subsections 3.1 and 3.3 are mainly due to G.C. while subsection 3.2 and section 4 are mainly due to P.V.     

Structures and magnetic properties of tetranuclear nickel(II) complexes with unusual mu3-1,1,3 azido bridges

Pyrazolate-based dinucleating ligands with thioether-containing chelate arms have been used for the synthesis of a family of novel tetranuclear nickel(II) complexes [L2Ni4(N3)3(O2CR)](ClO4)2 that incorporate three azido bridges and one carboxylate (R = Me, Ph). Molecular structures have been elucidated by X-ray crystallography in four cases, revealing Ni4 cores with a unique topology in which two of the azido ligands adopt an unusual mu3-1,1,3 bridging mode. The compounds were further characterized by mass spectrometry, IR spectroscopy, and variable-temperature magnetic susceptibility measurements. Magnetic data analyses indicate a combination of significant intramolecular ferromagnetic and antiferromagnetic exchange interactions that give rise to an overall S(T) = 0 ground state. The sign and the magnitude of the individual couplings have been rationalized in the framework of the common magnetostructural correlations for end-to-end and end-on azido linkages, suggesting that these correlations also remain valid for the respective fragments of multiply bridging mu3-1,1,3 azido ligands.     

Quantitative analysis of 2-furfural and 5-methylfurfural in different Italian vinegars by headspace solid-phase microextraction coupled to gas chromatography-mass spectrometry using isotope dilution

A new method was developed for the determination of 2-furfural (2-F) and 5-methylfurfural (5-MF), two products of Maillard reaction in vinegar, with head-space solid-phase microextraction (HS-SPME) coupled to gas chromatography-mass spectrometry (GC-MS). A divinylbenzene (DVB)/carboxen (CAR)/polydimethylsiloxane (PDMS) fibre was used and SPME conditions were optimised, studying ionic strength effect, temperature effect and adsorption time. Both analytes were determined by calibration established on 2-furfural-d4 (2-F-d4). The method showed good linearity in the range studied (from 16 to 0.12 mg/l), with a regression coefficient r2 of 0.9999. Inter-batch precision and accuracy were found between 14.9 and 6.0% and between -11.7 and 0.2%, respectively. Detection limit was 15 microg/l. The method is simple and accurate and it has been applied to a series of balsamic and non-balsamic vinegars.     

The deprotonation of benzyl alcohol radical cations: a mechanistic dichotomy in the gas phase as in solution

The gas-phase acidity of ionized benzyl alcohol and of some of its derivatives with selected reference bases has been studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry. The aim was to relate the gas-phase reactivity to the behavior in aqueous solution of the radical cations of benzyl alcohols bearing methoxy substituent(s) on the phenyl ring which are known to undergo deprotonation at both the CH2 and OH groups. The dual reactivity behavior is confirmed in the gas phase, in which the prototypical ion, C6H5CH2OH*+, is deprotonated at both the CH2 and OH groups, whereas the ring hydrogens are not involved. An increasing extent of O-deprotonation is shown as the strength of the base increases. Appropriate methyl substitution, as in the radical cations of C6H5C(Me)2OH and C6H5CH2OMe, allows only O- or C-acidity. The two processes are characterized by comparable thermodynamic features with a Gas-phase Basicity (GB) value of 852 kJ mol(-1) for the cumyloxyl radical and 850 kJ mol(-1) for the alpha-methoxybenzyl radical. The possible origin of the observed mechanistic dichotomy is discussed.     

New Approaches to Coupling TLC with TOF-SIMS

JPC – Journal of Planar Chromatography – Modern TLC - A new hyphenated technique that enables coupling of thin-layer chromatography (TLC) with time-of-flight secondary-ion mass...     

Polycondensed nitrogen heterocycles. Part 17. Isoxazolo[4,3-d]pyrazolo[3,4-f][1,2,3]triazepine. A new ring system

The title compounds were prepared by nitration of compounds 2 , reduction of the dinitro derivatives 4 and diazotization of the diamino derivatives 6 followed by an intramolecular coupling reaction. Compound 4a showed good activity against Salmonella cholerasuis and Clostridium perfringens bacteria.     

Structure and dynamics of self-assembled poly(ethylene glycol) based coiled-coil nano-objects.

Herein we describe the structure and dynamics of self-assembled nano-objects generated from poly(ethylene glycol) based (PEG-ylated) coiled-coil hybrid block copolymers. Electron paramagnetic resonance (EPR) experiments on spin-labeled samples provided a strong indication for a parallel alignment of the peptide helices in at least the dimeric coiled-coil nano-object and indicated that the PEG chains are folded rather closely around the peptide core of the nano-objects. The EPR results were supported by AFM studies, which revealed the presence of discrete nanosized objects in thin, spin cast films of the block copolymers on mica substrates. Since their size and structure may be engineered via directed mutations in the amino acid sequence, these nano-objects may be interesting building blocks for the development of supramolecular materials with various potential applications.     

The hydrophobic effect in aqueous solutions of nonelectrolytes. I. Self-interactions of alkylureas

In order to clarify some aspects of the hydrophobic interactions, the enthalpies of dilution of monoethylurea, 1,3-dimethylurea, and 1,3-diethylurea have been determined calorimetrically at 25°C. The calorimetric data, expressed in terms of excess enthalpy, permit the evaluation of the pair and triplet interaction coefficients. The analyses of these and of the analogous coefficientsg _xx andg _xxx, derived from osmotic data, indicate a driving force favorable to the interactions among the hydrated solute molecules. Nevertheless, the positive values of theh _xx andh _xxx coefficients seem to suggest that the source of the effect is a rearrangement of the water molecules rather than a direct association of the solute molecules. There are evidences of a strict correlation between the enthalpic and the entropic effects. Preliminary data were presented at the International Conferences on Chemical Thermodynamics at Baden (1973) and Montpellier (1975). The experimental part was carried out at the Istituto Chimico of the University of Trieste. To whom correspondence should be addressed.