Julian Stander

Quantile regression: applications and current research areas

Summary. Quantile regression offers a more complete statistical model than mean regression and now has widespread applications. Consequently, we provide a review of this technique. We begin with an introduction to and motivation for quantile regression. We then discuss some typical application areas. Next we outline various approaches to estimation. We finish by briefly summarizing some recent research areas.

Bayesian nonparametric quantile regression using splines

A new technique based on Bayesian quantile regression that models the dependence of a quantile of one variable on the values of another using a natural cubic spline is presented. Inference is based on the posterior density of the spline and an associated smoothing parameter and is performed by means of a Markov chain Monte Carlo algorithm. Examples of the application of the new technique to two real environmental data sets and to simulated data for which polynomial modelling is inappropriate are given. An aid for making a good choice of proposal density in the Metropolis-Hastings algorithm is discussed. The new nonparametric methodology provides more flexible modelling than the currently used Bayesian parametric quantile regression approach.

Temperature schedules for simulated annealing

It is well known that the behaviour of the simulated annealing approach to optimization is crucially dependent on the choice of temperature schedule. In this paper, a dynamic programming approach is used to find the temperature schedule which is optimal for a simple minimization problem. The optimal schedule is compared with certain standard non-optimal choices. These generally perform well provided the first and last temperatures are suitably selected. Indeed, these temperatures can be chosen in such a way as to make the performance of the logarithmic schedule almost optimal. This optimal performance is fairly robust to the choice of the first temperature.The dynamic programming approach cannot be applied directly to problems of more realistic size, such as those arising in statistical image reconstruction. Nevertheless, some simulation experiments suggest that the general conclusions from the simple minimization problem do carry over to larger problems. Various families of schedules can be made to perform well with suitable choice of the first and last temperatures, and the logarithmic schedule combines good performance with reasonable robustness to the choice of the first temperature.

Quantile self-exciting threshold autoregressive time series models

In this paper we present a Bayesian approach to quantile self-exciting threshold autoregressive time series models. The simulation work shows that the method can deal very well with nonstationary time series with very large, but not necessarily symmetric, variations. The methodology has also been applied to the growth rate of US real GNP data and some interesting results have been obtained. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

The specification of edge penalties for regular and irregular pixel images

It is shown how some geometrical insights can be used to provide penalties for the various edge configurations in a way that is roughly independent of the pixel discretization. The penalties are consistent over pixels of different sizes, shapes, and orientations, event if these occur in the same pattern. The cases of square, rectangular, hexagonal, and irregular pixels are considered. In an experiment, the penalties perform substantially better than those previously proposed. >

Spatial variation of Anopheles-transmitted Wuchereria bancrofti and Plasmodium falciparum infection densities in Papua New Guinea

The spatial variation of Wuchereria bancrofti and Plasmodium falciparum infection densities was measured in a rural area of Papua New Guinea where they share anopheline vectors. The spatial correlation of W. bancrofti was found to reduce by half over an estimated distance of 1.7 km, much smaller than the 50 km grid used by the World Health Organization rapid mapping method. For P. falciparum, negligible spatial correlation was found. After mass treatment with anti-filarial drugs, there was negligible correlation between the changes in the densities of the two parasites.

A new Bayesian approach to quantile autoregressive time series model estimation and forecasting

This paper proposes a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. We establish that the joint posterior distribution of the model parameters and future values is well defined. The associated Markov chain Monte Carlo algorithm for parameter estimation and forecasting converges to the posterior distribution quickly. We also present a combining forecasts technique to produce more accurate out-of-sample forecasts by using a weighted sequence of fitted QAR models. A moving window method to check the quality of the estimated conditional quantiles is developed. We verify our methodology using simulation studies and then apply it to currency exchange rate data. The results obtained show that an unequally weighted combining method performs better than other forecasting methodology.

Spatial and non-spatial model-based protection procedures for the release of business microdata

In this paper we discuss methodology for the safe release of business microdata. In particular we extend the model-based protection procedure of Franconi and Stander (2002, The Statistician 51: 1–11) by allowing the model to take account of the spatial structure underlying the geographical information in the microdata. We discuss the use of the Gibbs sampler for performing the computations required by this spatial approach. We provide an empirical comparison of these non-spatial and spatial disclosure limitation methods based on the Italian sample from the Community Innovation Survey. We quantify the level of protection achieved for the released microdata and the error induced when various inferences are performed. We find that although the spatial method often induces higher inferential errors, it almost always provides more protection. Moreover the aggregated areas from the spatial procedure can be somewhat more spatially smooth, and hence possibly more meaningful, than those from the non-spatial approach. We discuss possible applications of these model-based protection procedures to more spatially extensive data sets.

A Bayesian Hierarchical Model Approach to Risk Estimation in Statistical Disclosure Limitation

When microdata files for research are released, it is possible that external users may attempt to breach confidentiality. For this reason most National Statistical Institutes apply some form of disclosure risk assessment and data protection. Risk assessment first requires a measure of disclosure risk to be defined. In this paper we build on previous work by [BF98] to define a Bayesian hierarchical model for risk estimation. We follow a superpopulation approach similar to [BKP90] and [Rin03]. For each combination of values of the key variables we derive the posterior distribution of the population frequency given the observed sample frequency. Knowledge of this posterior distribution enables us to obtain suitable summaries that can be used to estimate the risk of disclosure. One such summary is the mean of the reciprocal of the population frequency or Benedetti-Franconi risk, but we also investigate others such as the mode. We apply our approach to an artificial sample of the Italian 1991 Census data, drawn by means of a widely used sampling scheme. We report on results of this application and document the computational difficulties that we encountered. The risk estimates that we obtain are sensible, but suggest possible improvements and modifications to our methodology. We discuss these together with potential alternative strategies.

Informative priors for the bayesian classification of satellite images

Abstract In the Bayesian classification of satellite images, a prior distribution is used that aims to model the belief of spatial homogeneity of the underlying region. We extend this prior distribution to model certain topographical features of the area such as the position of the roads, the slopes, and the aspects. We demonstrate the effectiveness of this prior distribution in a reconstruction algorithm by means of a simulation study in which the quality of the result is assessed by a comparison of estimated and known covertypes. We apply the algorithm to real data with success.