Monotonic regression based on Bayesian P-splines: an application to estimating price response functions from store-level scanner data

Generalized additive models have become a widely used instrument for flexible regression analysis. In many practical situations, however, it is desirable to restrict the flexibility of nonparametric estimation in order to accommodate a presumed monotonic relationship between a covariate and the response variable. For example, consumers usually will buy less of a brand if its price increases, and therefore one expects a brand's unit sales to be a decreasing function in own price. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for a brand of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response function considerably

Redundancy of minimal weight expansions in Pisot bases

Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer $n$ as a sum $n=\sum_k \epsilon_k U_k$, where the digits $\epsilon_k$ are taken from a finite alphabet $\Sigma$ and $(U_k)_k$ is a linear recurrent sequence of Pisot type with $U_0=1$. The most prominent example of a base sequence $(U_k)_k$ is the sequence of Fibonacci numbers. We prove that the representations of minimal weight $\sum_k|\epsilon_k|$ are recognised by a finite automaton and obtain an asymptotic formula for the average number of representations of minimal weight. Furthermore, we relate the maximal order of magnitude of the number of representations of a given integer to the joint spectral radius of a certain set of matrices

Predicting Mercury's Precession using Simple Relativistic Newtonian Dynamics

We present a new simple relativistic model for planetary motion describing accurately the anomalous precession of the perihelion of Mercury and its origin. The model is based on transforming Newton's classical equation for planetary motion from absolute to real spacetime influenced by the gravitational potential and introducing the concept of influenced direction.Comment: 5 page

The effect of magnetic dipolar interactions on the interchain spin wave dispersion in CsNiF_3

Inelastic neutron scattering measurements were performed on the ferromagnetic chain system CsNiF_3 in the collinear antiferromagnetic ordered state below T_N = 2.67K. The measured spin wave dispersion was found to be in good agreement with linear spin wave theory including dipolar interactions. The additional dipole tensor in the Hamiltonian was essential to explain some striking phenomena in the measured spin wave spectrum: a peculiar feature of the dispersion relation is a jump at the zone center, caused by strong dipolar interactions in this system. The interchain exchange coupling constant and the planar anisotropy energy were determined within the present model to be J'/k_B = -0.0247(12)K and A/k_B = 3.3(1)K. This gives a ratio J/J' \approx 500, using the previously determined intrachain coupling constant J/k_B = 11.8$. The small exchange energy J' is of the same order as the dipolar energy, which implies a strong competition between the both interactions.Comment: 18 pages, TeX type, 7 Postscript figures included. To be published in Phys. Rev.

Dynamic scaling and universality in evolution of fluctuating random networks

We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys. Rev. Lett. 83, 5587 (1999)]. The averaged size and connectivity of the network increase as power-laws in early times but later saturate. Saturated values and times of saturation change with paramaters controlling the local evolution of the network topology. Both saturated values and times of saturation obey also power-law dependences on controlling parameters. Scaling exponents are calculated and universal features are discussed.Comment: 7 pages, 6 figures, Europhysics Letters for

Predicting the relativistic periastron advance of a binary without curving spacetime

Relativistic Newtonian Dynamics, the simple model used previously for predicting accurately the anomalous precession of Mercury, is now applied to predict the periastron advance of a binary. The classical treatment of a binary as a two-body problem is modified to account for the influence of the gravitational potential on spacetime. Without curving spacetime, the model predicts the identical equation for the relativistic periastron advance as the post-Newtonian approximation of general relativity formalism thereby providing further substantiation of this model.Comment: 6 pages, 2 figure

Does More Generous Student Aid Increase Enrolment Rates into Higher Education?: Evaluating the German Student Aid Reform of 2001

Students from low-income families are eligible to student aid under the federal students' financial assistance scheme (BAfoeG) in Germany. We evaluate the effectiveness of a recent reform of student aid that substantially increased the amount received by eligible students to raise enrolment rates into tertiary education. We view this reform as a 'natural experiment' and apply the difference-in-difference methodology using a discrete-time hazard rate model to estimate the causal effect on enrolment rates into higher education. We find that the reform had a small positive but statistically insignificant effect on enrolment rates.Educational transitions, educational finance, natural experiment and difference-indifference estimation