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.     

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...     

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.     

Covalent crosslinking of 1-D photonic crystals of microporous Si by hydrosilylation and ring-opening metathesis polymerization

Free-standing porous Si multilayer dielectric mirrors, prepared by electrochemical etching of crystalline Si, are treated with a ruthenium ring-opening metathesis polymerization (ROMP) catalyst followed by norbornene to produce flexible, stable composite materials in which poly(norbornene) is covalently attached to the porous Si matrix.     

Synthese von 1, 3, 4-Oxadiazolen und 4, 5-Dihydro-1, 2, 4-triazinen aus 3-Dimethylamino-2, 2-dimethyl-2 H-azirin und Carbohydraziden

Synthesis of 1,3,4-Oxadiazoles and 4,5-Dihydro-l,2,4-triazines from 3-Dimethylamino-2,2-dimethyl-2 Hazirine and Carbohydrazides 3-Dimethylamino-2, 2-dimethyl-2 H-azirine ( 1 ) reacts with aromatic carbohydrazides to give 2-(1-amino-1-methylethyl)-5-aryl-1, 3, 4-oxadiazoles ( 7 , 10 , 11 ). With ethyl carbazate the azirine 1 forms the aminoester 15 , which is easily cyclized to the 4, 5-dihydro-1, 2, 4-triazin-3 (2H)-one 16 . From the reaction of 1 with oxamohydrazide ( 17 ) and oxalodihydrazide 19 the 4, 5-dihydro-1, 2, 4-triazin-3-carboxamide 18 and the symmetric compound 20 , respectively, have been isolated. Reactions supporting the structures of the new compounds are described.