Optimal,nearly optimal and robust procedures for the exponential distribution with relative linear exponential loss

In this paper, the problem of sequentially estimating the mean of the exponential distribution with relative linear exponential loss and fixed cost for each observation is considered within the Bayesian framework. An optimal procedure with a deterministic stopping rule is derived. Since the corresponding value of the optimal deterministic stopping rule cannot be obtained directly, an approximate optimal deterministic stopping rule and an asymptotically pointwise optimal rule are proposed. In addition, we propose a robust procedure with a deterministic stopping rule, which does not depend on the parameters of the prior distribution. All of the proposed procedures are shown to be asymptotically optimal. Some numerical studies are conducted to investigate the performances of the proposed procedures. A real data set is provided to illustrate the use of the proposed procedures.     

Trade-off sensitive experimental design: a multicriterion,decision theoretic,Bayes linear approach

We show how mutually utility independent hierarchies, which weigh the various costs of an experiment against benefits expressed through a mixed Bayes linear utility representing the potential gains in knowledge from the experiment, provide a flexible and intuitive methodology for experimental design which remains tractable even for complex multivariate problems. A key feature of the approach is that we allow imprecision in the trade-offs between the various costs and benefits. We identify the Pareto optimal designs under the imprecise specification and suggest a criterion for selecting between such designs. The approach is illustrated with respect to an experiment related to the oral glucose tolerance test.     

On the detection of changes in autoregressive time series,II. Resampling procedures

We study an autoregressive time series model with a possible change in the regression parameters. Approximations to the critical values for change-point tests are obtained through various bootstrapping methods. Theoretical results show that the bootstrapping procedures have the same limiting behavior as their asymptotic counterparts discussed in Hušková et al. [2007. On the detection of changes in autoregressive time series, I. Asymptotics. J. Statist. Plann. Inference 137, 1243–1259]. In fact, a small simulation study illustrates that the bootstrap tests behave better than the original asymptotic tests if performance is measured by the α$\alpha$- and β$\beta$-errors, respectively.     

Divergence versus decision P-values: A distinction worth making in theory and keeping in practice: Or,how divergence P-values measure evidence even when decision P-values do not

There are two distinct definitions of “P-value” for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was expected under the model, such as a sum of squares or a deviance statistic. A P-value is then the ordinal location of the measure in a reference distribution computed from the model and the data, and is treated as a unit-scaled index of compatibility between the data and the model. In the other definition, a P-value is a random variable on the unit interval whose realizations can be compared to a cutoff α to generate a decision rule with known error rates under the model and specific alternatives. It is commonly assumed that realizations of such decision P-values always correspond to divergence P-values. But this need not be so: Decision P-values can violate intuitive single-sample coherence criteria where divergence P-values do not. It is thus argued that divergence and decision P-values should be carefully distinguished in teaching, and that divergence P-values are the relevant choice when the analysis goal is to summarize evidence rather than implement a decision rule.     

Independence in multi-way contingency tables: S.N. Roy's breakthroughs and later developments

In the mid-1950s S.N. Roy and his students contributed two landmark articles to the contingency table literature [Roy, S.N., Kastenbaum, M.A., 1956. On the hypothesis of no “interaction” in a multiway contingency table. Ann. Math. Statist. 27, 749–757; Roy, S.N., Mitra, S.K., 1956. An introduction to some nonparametric generalizations of analysis of variance and multivariate analysis. Biometrika 43, 361–376]. The first article generalized concepts of interaction from 2×2×2$2\times 2\times 2$ contingency tables to three-way tables of arbitrary size and to larger tables. In the second article, which is the source of our primary focus, various notions of independence were clarified for three-way contingency tables, Roy's union–intersection test was applied to construct chi-squared tests of hypotheses about the structure of such tables, and the chi-squared statistics were shown not to depend on the distinction between response and explanatory variables. This work pre-dates by many years later developments that expressed such results in the context of loglinear models. It pre-dates by a quarter century the development of graphical models. We summarize the main results in these key articles and discuss the connection between them and the later developments of loglinear modeling and of graphical modeling. We also mention ways in which these later developments have themselves been further generalized.     

Optimal SIR algorithm vs. fully adapted auxiliary particle filter: a non asymptotic analysis

Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques. In this paper we comparatively analyse, from a non asymptotic point of view, the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID) and the fully adapted APF (FA). We compute the (finite samples) conditional second order moments of Monte Carlo (MC) estimators of a moment of interest of the filtering pdf, and analyse under which circumstances the FA-based estimator outperforms (or not) the optimal Sequential Importance Sampling (SIS)-based one. Our analysis is local, in the sense that we compare the estimators produced by one time step of the different SMC algorithms, starting from a common set of weighted points. This analysis enables us to propose a hybrid SIS/FA algorithm which automatically switches at each time step from one loop to the other. We finally validate our results via computer simulations.     

Acquired immune deficiency syndrome predictions for England and Wales (1992-97): sensitivity analysis,information, decision

Some implications of the use of the back-calculation method for estimating future trends in HIV infections and AIDS incidence in England and Wales are explored. "This paper explores in...detail some aspects of the latest projections which have only been hinted at in the report published by the Public Health Laboratory Service in 1993. The value of additional information on the HIV epidemic in discriminating between different, otherwise equally plausible, scenarios is demonstrated. The role of the backcalculation approach in determining whether, and how, the incubation distribution has been affected by increased uptake of pre-AIDS prophylaxis and treatment is discussed."