Likelihood diagnostics and Bayesian analysis of a micro-economic disequilibrium model for retail services

In this paper we apply Maximum Likelihood and Bayesian methods to explain differences in floorspace productivity among retail establishments in the grocery trade. The model we develop is a switching model where sales are either supply-determined or demand-determined. Under excess supply the model allows for so-called ‘trading-down’, i.e., an increase in the share of selling area, and, thereby, a decrease in service level. To estimate our model we employ a cross-section of observations on individual shops. We present maximum likelihood results, and also study the shape of the likelihood surface by means of Monte Carlo numerical integration methods. With a uniform prior we obtain marginal posterior density functions both of the parameters of interest and of the average probability of the excess supply regime in the sample. The average probability of excess supply is 0.23, with a standard deviation of 0.06. This shows that, according to our estimates, excess demand is the rule and excess supply the exception in the sample that we analyse

One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form

In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form, F(f(x)), and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for certain values of the parameter the height of the localization probability can be higher in the smaller wellComment: 16 pages, 6 figures, published versio

A discrete history of the Lorentzian path integral

In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach solves the problems of (i) having a well-defined Wick rotation, (ii) possessing a coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over geometries. Although little is known as yet about the existence and nature of an underlying continuum theory of quantum gravity in four dimensions, there are already a number of beautiful results in d=2 and d=3 where continuum limits have been found. They include an explicit example of the inequivalence of the Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the cancellation of the conformal factor, and the discovery that causality can act as an effective regulator of quantum geometry.Comment: 38 pages, 16 figures, typos corrected, some comments and references adde