EXPLORING MARKET PRICING STRATEGIES VIA DYNAMIC PROGRAMMING

Price determinants as well as strategies can be studies by use of simulation, particularly if cost and price relationships can be related to market activity [1] [9] [11]. But, through the use of dynamic programming, given the market conditions, one can extend the analysis to include an optimal strategy. This paper describes a dynamic programming approach to studying price strategy. A model is developed to show that in a market characterized by cost/volume and price/volume relationships, profitability can be extended beyond that resulting from a dominant market strategy to an optimal maximizing strategy. Extension of the model is suggested for studying (a) sensitivity of a strategy (solution) to price level and cost changes, (b) optimal timing of withdrawal, and (c) present value analysis.     

Dynamic reasoning and time pressure: Transition from analytical operations to experiential responses

Based upon the Decision Field Theory (Busemeyer and Townsend 1993), we tested a model of dynamic reasoning to predict the effect of time pressure on analytical and experiential processing during decision-making. Forty-six participants were required to make investment decisions under four levels of time pressure. In each decision, participants were presented with experiential cues which were either congruent or incongruent with the analytical information. The congruent/incongruent conditions allowed us to examine how many decisions were based upon the experiential versus the analytical information, and to see if this was affected by the varying degrees of time pressure. As expected, the overall accuracy was reduced with greater time pressure and accuracy was higher when the experiential and analytical cues were congruent than when they were incongruent. Of great interest was the data showing that under high time pressure participants used more experiential cues than at other time pressures. We suggest that the dynamic reasoning paradigm has some future potential for predicting the effects of experiential biases in general, and specifically under time pressure.     

How Latinos Are Transforming the United States: Research, Theory, and Policy

The United States is entering a new era, a period marked by some important demographic changes in the composition of the population, most especially significant increases in the Latino and Latino immigrant segments of society. These population shifts require corresponding interpersonal, organizational, and structural changes. The present issue bridges research and theory across disciplines and includes studies incorporating a variety of methodologies to examine these important areas. These articles begin to fill some of the voids where a systematic and robust corpus of knowledge is lacking. The contributions address topics ranging from issues of identity and interpersonal relations to pressing matters of educational significance to general approaches to navigating the cultural transitions that mark fluid transnational adaptations. Finally, each contribution delineates the policy implications resulting from the processes and literatures that are examined.     

A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces

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. This paper integrates the essential ideas of DE and MCMC, resulting in 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 fixed multiple of the differences of two random parameter vectors that are currently in the population. The selection process of DE-MC works via the usual Metropolis ratio which defines the probability with which a proposal is accepted. In tests with known uncertainty distributions, the efficiency of DE-MC with respect to random walk Metropolis with optimal multivariate Normal jumps ranged from 68% for small population sizes to 100% for large population sizes and even to 500% for the 97.5% point of a variable from a 50-dimensional Student distribution. Two Bayesian examples illustrate the potential of DE-MC in practice. DE-MC is shown to facilitate multidimensional updates in a multi-chain “Metropolis-within-Gibbs” sampling approach. The advantage of DE-MC over conventional MCMC are simplicity, speed of calculation and convergence, even for nearly collinear parameters and multimodal densities.     

Statisticians in stained glass houses

Statistics and stained glass may seem an odd combination, but the windows of Gonville & Caius College, Cambridge, say otherwise. Anthony Edwards explains.     

Bayesian palaeoclimate reconstruction

Summary.  We consider the problem of reconstructing prehistoric climates by using fossil data that have been extracted from lake sediment cores. Such reconstructions promise to provide one of the few ways to validate modern models of climate change. A hierarchical Bayesian modelling approach is presented and its use, inversely, is demonstrated in a relatively small but statistically challenging exercise: the reconstruction of prehistoric climate at Glendalough in Ireland from fossil pollen. This computationally intensive method extends current approaches by explicitly modelling uncertainty and reconstructing entire climate histories. The statistical issues that are raised relate to the use of compositional data (pollen) with covariates (climate) which are available at many modern sites but are missing for the fossil data. The compositional data arise as mixtures and the missing covariates have a temporal structure. Novel aspects of the analysis include a spatial process model for compositional data, local modelling of lattice data, the use, as a prior, of a random walk with long-tailed increments, a two-stage implementation of the Markov chain Monte Carlo approach and a fast approximate procedure for cross-validation in inverse problems. We present some details, contrasting its reconstructions with those which have been generated by a method in use in the palaeoclimatology literature. We suggest that the method provides a basis for resolving important challenging issues in palaeoclimate research. We draw attention to several challenging statistical issues that need to be overcome.     

The cluster that never was: germ warfare experiments and health authority reality in Dorset

In 1997 intense media coverage raised public concerns about germ warfare simulation experiments conducted by the Ministry of Defence during the 1960s, which included the release of bacteria over Dorset. Families in East Lulworth, Dorset, have linked this with allegedly high rates of miscarriages, still-births, congenital malformations, learning and other neurodevelopmental disabilities in their village. The response of the Dorset Health Authority (DHA) included the examination of background information from the Ministry of Defence, national data on congenital malformations in Dorset, health information collected by campaigners and a systematic health survey conducted by the DHA among former and current residents of East Lulworth. The investigation did not confirm the presence of a cluster. It is debatable whether the DHA should have proceeded with their survey when none of the other more immediately available results indicated the presence of a cluster.     

SPC as a tool for creating a successful business measurement framework

Many companies are trying to get to the bottom of what their main objectives are and what their business should be doing. The new Six Sigma approach concentrates on clarifying business strategy and making sure that everything relates to company objectives. It is vital to clarify each part of the business in such a way that everyone can understand the causes of variation that can lead to improvements in processes and performance. This paper describes a situation where the full implementation of SPC methodology has made possible a visual and widely appreciated summary of the performance of one important aspect of the business. The major part of the work was identifying the core objectives and deciding how to encapsulate each of them in one or more suitable measurements. The next step was to review the practicalities of obtaining the measurements and their reliability and representativeness. Finally, the measurements were presented in chart form and the more traditional steps of SPC analysis were commenced. Data from fast changing business environments are prone to many different problems, such as the short previous span of typical data, strange distributions and other uncertainties. Issues surrounding these and the eventual extraction of a meaningful set of information will be discussed in the paper. The measurement framework has proved very useful and, from an initial circulation of a handful of people, it now forms an important part of an information process that provides responsible managers with valuable control information. The measurement framework is kept fresh and vital by constant review and modifications. Improved electronic data collection and dissemination of the report has proved very important.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.