Differential Evolution Markov Chain with snooker updater and fewer chains

Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50–100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5–26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25–50 dimensional Student t 3 distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the mode

Iteratio: Calculating environmental indicator values for species and relevés.

Question: Is it possible to translate vegetation maps into reliable thematic maps of site conditions? Method: This paper presents a new method, called Iteratio, by which a coherent spatial overview of specific environmental conditions can be obtained from a comprehensive vegetation survey of a specific area. Iteratio is a database application which calculates environmental indicator values for vegetation samples (relevés) on the basis of known indicator values of a limited number of plant species. The outcome is then linked to a digitalized vegetation map (map of plant communities) which results in a spatial overview of site conditions. Iteratio requires the indicator values of a minimum of 10–20% of the species occurring. The species are given a relative weight according to their amplitudes: species with a narrow range are weighted stronger, species with a broad range are weighted weaker. Conclusion: The method presented here enables a coherent assessment of site conditions on the basis of a vegetation survey and the indicator values of a limited number of plant species

A new era in retail:Private-label production by national-brand manufacturers and premium-quality private labels

Private labels have witnessed considerable growth in grocery retailing. While existing academic studies have provided valuable insights concerning the evolution of private labels, several issues remain largely unexplored. First, in the face of these large private-label volumes, private-label production opportunities arise. Due to increased private-label competition, national-brand manufacturers increasingly pursue a dual-branding strategy and engage in private-label production next to their national-brand activities. In chapter two of this dissertation, a major motivation for national-brand manufacturers to engage in private-label production, namely whether it creates retailer goodwill, is investigated. It shows that private-label production is indeed rewarded: national-brand manufacturers involved in private-label production for a discounter have a higher likelihood of obtaining national-brand shelf presence at that discounter. The third chapter focuses on one of the main reasons why retailers push private labels, i.e. because they generate high margins, and considers how a retailer’s private-label margins vary within categories. It demonstrates that a retailer’s private-label margins depend on the nature of the private-label supplier-retailer relationship, that they differ across quality tiers and package sizes, and that they are affected by a supplier’s extent of national-brand focus next to its private-label production for the retailer. Finally, this dissertation concentrates on the recent premium private-label trend. Even though premium private labels are seen as “one of the hottest trends in retailing,” retailers are selective in picking their battles with top-quality national brands and do not feel the need to extend their standard private label with a premium private label in every category. The fourth chapter provides insight into why retailers offer premium private labels in some categories, but not in others. The research presented in this dissertation is among the first to empirically investigate the phenomenon of private-label production, and to shed light on the recent trend of premium private labels

Genetic algorithms and Markov Chain Monte Carlo: Differential Evolution Markov Chain makes Bayesian computing easy

Differential Evolution (DE) is a simple genetic algorithm for numerical optimization in real parameter spaces. In a statistical context one would not just want the optimum but also its uncertainty. The uncertainty distribution can be obtained by a Bayesian analysis (after specifying prior and likelihood) using Markov Chain Monte Carlo (MCMC) simulation. In this paper the essential ideas of DE and MCMC are integrated into Differential Evolution Markov Chain (DE-MC). DE-MC is a population MCMC algorithm, in which multiple chains are run in parallel. DE-MC solves an important problem in MCMC, namely that of choosing an appropriate scale and orientation for the jumping distribution. In DE-MC the jumps are simply a multiple of the differences of two random parameter vectors that are currently in the population. Simulations and examples illustrate the potential of DE-MC. The advantage of DE-MC over conventional MCMC are simplicity, speed of calculation and convergence, even for nearly collinear parameters and multimodal densitie

Perturbed KdV equations and their integrability properties

In this thesis we investigate the integrability properties of the regularized long-wave (RLW) equation and modified regularized long-wave (mRLW) equation as perturbations of the integrable Korteweg-de Vries (KdV) equation. We study various properties of numerical mRLW three-soliton scattering and compare these with the corresponding RLW soliton solutions. We find that the numerical mRLW solitons behave much like integrable solitons in the sense that the only result of the three-soliton interaction is the phase shift each soliton experiences, which is approximately equal to the sum of pairwise phase shifts. Furthermore, we investigate the so-called quasi-integrability properties of these RLW and mRLW simulations. Using both analytical and numerical methods, we argue that these models possess an infinite amount of asymptotically conserved charges, i.e., quasi-conserved charges, which are observed in multi-soliton interactions. Finally, we also simulate numerical RLW and mRLW solutions in the presence of additional perturbing terms. This allows us to study soliton-radiation interactions and we find that for certain perturbations, these interactions preserve the quasi-conservation laws to a certain extend

Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering

Let Q be a given n×n square symmetric matrix of nonnegative elements between 0 and 1, similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the n×K fuzzy memberships matrix P is found by least-squares approximation of the off-diagonal elements of Q by inner products of rows of P. By contrast, kernelized fuzzy c-means is not least-squares and requires an additional fuzziness parameter. The aim is to popularize additive fuzzy clustering by interpreting it as a latent class model, whereby the elements of Q are modeled as the probability that two individuals share the same class on the basis of the assignment probability matrix P. Two new algorithms are provided, a brute force genetic algorithm (differential evolution) and an iterative row-wise quadratic programming algorithm of which the latter is the more effective. Simulations showed that (1) the method usually has a unique solution, except in special cases, (2) both algorithms reached this solution from random restarts and (3) the number of clusters can be well estimated by AIC. Additive fuzzy clustering is computationally efficient and combines attractive features of both the vector model and the cluster mode

A new era in retail: Private-label production by national-brand manufacturers and premium-quality private labels.

Private labels have witnessed considerable growth in grocery retailing. While existing academic studies have provided valuable insights concerning the evolution of private labels, several issues remain largely unexplored. First, in the face of these large private-label volumes, private-label production opportunities arise. Due to increased private-label competition, national-brand manufacturers increasingly pursue a dual-branding strategy and engage in private-label production next to their national-brand activities. In chapter two of this dissertation, a major motivation for national-brand manufacturers to engage in private-label production, namely whether it creates retailer goodwill, is investigated. It shows that private-label production is indeed rewarded: national-brand manufacturers involved in private-label production for a discounter have a higher likelihood of obtaining national-brand shelf presence at that discounter. The third chapter focuses on one of the main reasons why retailers push private labels, i.e. because they generate high margins, and considers how a retailer’s private-label margins vary within categories. It demonstrates that a retailer’s private-label margins depend on the nature of the private-label supplier-retailer relationship, that they differ across quality tiers and package sizes, and that they are affected by a supplier’s extent of national-brand focus next to its private-label production for the retailer. Finally, this dissertation concentrates on the recent premium private-label trend. Even though premium private labels are seen as “one of the hottest trends in retailing,” retailers are selective in picking their battles with top-quality national brands and do not feel the need to extend their standard private label with a premium private label in every category. The fourth chapter provides insight into why retailers offer premium private labels in some categories, but not in others. The research presented in this dissertation is among the first to empirically investigate the phenomenon of private-label production, and to shed light on the recent trend of premium private labels.