Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration (RC), arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to RC, and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next we describe the closely related maximum likelihood and multiple imputation approaches, and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of RC and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey

Newtonian Potential in Quantum Regge Gravity

We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the weak field expansion. In the smooth anti-de Sitter-like phase, which is the only phase where a sensible lattice continuum limit can be constructed in this model, we attempt to determine the shape and mass dependence of the attractive potential close to the critical point in $G$. It is found that non-linear graviton interactions give rise to a potential which is Yukawa-like, with a mass parameter that decreases towards the critical point where the average curvature vanishes. In the vicinity of the critical point we give an estimate for the effective Newton constant.Comment: (47 pages), CERN-TH.7314/9

The asymptotics of an amplitude for the 4-simplex

An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic formula has a contribution from each flat Euclidean metric on the 4-simplex which agrees with the given areas. The oscillatory part of each contribution is determined by the Regge calculus Einstein action for that geometry.Comment: 5 pages amstex, typos correcte

Energetics of Shaker K channels block by inactivation peptides

A synthetic peptide of the NH2-terminal inactivation domain of the ShB channel blocks Shaker channels which have an NH2-terminal deletion and mimics many of the characteristics of the intramolecular inactivation reaction. To investigate the role of electrostatic interactions in both peptide block and the inactivation process we measured the kinetics of block of macroscopic currents recorded from the intact ShB channel, and from ShB delta 6-46 channels in the presence of peptides, at different ionic strengths. The rate of inactivation and the association rate constants (k(on)) for the ShB peptides decreased with increasing ionic strength. k(on) for a more positively charged peptide was more steeply dependent on ionic strength consistent with a simple electrostatic mechanism of enhanced diffusion. This suggests that a rate limiting step in the inactivation process is the diffusion of the NH2-terminal domain towards the pore. The dissociation rates (k(off)) were insensitive to ionic strength. The temperature dependence of k(on) for the ShB peptide was very high, (Q10 = 5.0 +/- 0.58), whereas k(off) was relatively temperature insensitive (Q10 approximately 1.1). The results suggest that at higher temperatures the proportion of time either the peptide or channel spends in the correct conformation for binding is increased. There were two components to the time course of recovery from block by the ShB peptide, indicating two distinct blocked states, one of which has similar kinetics and dependence on external K+ concentration as the inactivated state of ShB. The other is voltage-dependent and at -120 mV is very unstable. Increasing the net charge on the peptide did not increase sensitivity to knock-off by external K+. We propose that the free peptide, having fewer constraints than the tethered NH2-terminal domain binds to a similar site on the channel in at least two different conformations

Interactions of amino terminal domains of Shaker K channels with a pore blocking site studied with synthetic peptides

Synthetic peptides of the five alternative NH2-terminal sequences of Shaker when applied to the cytoplasmic side of ShB channels that have an NH2-terminal deletion (ShB delta 6-46) block the channel with potencies correlated with the rate of inactivation in the corresponding variant. These peptides share no sequence similarity and yet three out of the five have apparent dissociation constants between 2 and 15 microM, suggesting that the specificity requirements for binding are low. To identify the primary structural determinants required for effective block of ShB delta 6-46, we examined the effects of substitutions made to the 20 residue ShB peptide on association and dissociation rates. Nonpolar residues within the peptide appear to be important in stabilizing the binding through hydrophobic interactions. Substitutions to leucine-7 showed there was a clear correlation between hydrophobicity and the dissociation rate constant (koff) with little effect on the association rate constant (kon). Substituting charged residues for hydrophobic residues within the region 4-8 disrupted binding. Within the COOH-terminal half of the peptide, substitutions that increased the net positive charge increased kon with relatively small changes in koff, suggesting the involvement of long-range electrostatic interactions in increasing the effective concentration of the peptide. Neutralizing charged residues produced small changes in koff. Charges within the region 12-20 act equivalently; alterations which conserved net charge produced little effect on either kon or koff. The results are consistent with this region of the peptide having an extended conformation and suggest that when bound this region makes few contacts with the channel protein and remains relatively unconstrained. Analogous mutations within the NH2-terminal domain of the intact ShB channel produced qualitatively similar effects on blocking and unblocking rates

Tullio Regge's legacy: Regge calculus and discrete gravity

The review paper "Discrete Structures in Physics", written in 2000, describes how Regge's discretization of Einstein's theory has been applied in classical relativity and quantum gravity. Here, developments since 2000 are reviewed briefly, with particular emphasis on progress in quantum gravity through spin foam models and group field theories.Comment: 15 pages; a contribution to the forthcoming volume "Tullio Regge: an eclectic genius, from quantum gravity to computer play", Eds. L Castellani, A. Ceresole, R. D'Auria and P. Fr\`e (World Scientific); v2: added references to more relevant work, minor changes to the tex

A note on area variables in Regge calculus

We consider the possibility of setting up a new version of Regge calculus in four dimensions with areas of triangles as the basic variables rather than the edge-lengths. The difficulties and restrictions of this approach are discussed.Comment: 4 pages, amstex. Revision has minor changes and more precise conclusion