Importance sampling as a variational approximation

There is a well-recognized need to develop Bayesian computational methodologies that scale well to large data sets. Recent attempts to develop such methodology have often focused on two approaches—variational approximation and advanced importance sampling methods. This note shows how importance sampling can be viewed as a variational approximation, achieving a pleasing conceptual unification of the two points of view. We consider a particle representation of a distribution as defining a certain parametric model and show how the optimal approximation (in the sense of minimization of a Kullback-Leibler divergence) leads to importance sampling type rules. This new way of looking at importance sampling has the potential to generate new algorithms by the consideration of deterministic choices of particles in particle representations of distributions.     

Precision studies in supramolecular chemistry: a 1H NMR study of hydroxymethoxyacetophenone/β-cyclodextrin complexes

The association constants for the interactions of 2-hydroxy-4-methoxyacetophenone, 2-hydroxy-5-methoxyacetophenone, 2-hydroxy-6-methoxyacetophenone, 3-hydroxy-4-methoxyacetophenone and 4-hydroxy-3-methoxyacetophenone with β-cyclodextrin in water were measured by (1)H NMR and by isothermal titration calorimetry. Very good agreement was obtained between the different methods. The errors associated with the NMR method for measuring mM binding affinities were estimated to be 10-30%, and by isothermal titration calorimetry, 10-20%. Rotating frame nuclear Overhauser effect spectroscopy studies show that the solution phase host-guest complexes formed by β-cyclodextrin with these hydroxymethoxyacetophenone derivatives are not structurally well defined but that the hydroxymethoxyacetophenone derivatives are mostly associated with the narrow primary hydroxyl rim.