A comparison of different Bayesian design criteria to compute efficient conjoint choice experiments.

Bayesian design theory applied to nonlinear models is a promising route to cope with the problem of design dependence on the unknown parameters. The traditional Bayesian design criterion which is often used in the literature is derived from the second derivatives of the loglikelihood function. However, other design criteria are possible. Examples are design criteria based on the second derivative of the log posterior density, the expected posterior covariance matrix, or on the amount of information provided by the experiment. Not much is known in general about how well these criteria perform in constructing efficient designs and which criterion yields robust designs that are efficient for various parameter values. In this study, we apply these Bayesian design criteria to conjoint choice experimental designs and investigate how robust the resulting Bayesian optimal designs are with respect to other design criteria for which they were not optimized. We also examine the sensitivity of each design criterion to the prior distribution. Finally, we try to find out which design criterion is most appealing in a non-Bayesian framework where it is accepted that prior information must be used for design but should not be used in the analysis, and which one is most appealing in a Bayesian framework when the prior distribution is taken into account both for design and for analysis.Bayesian design criterion; Posterior density; Expected posterior covariance matrix; Conjoint choice design; Laplace approximation; Fisher information;

Bayesian Design of Tandem Networks for Distributed Detection With Multi-bit Sensor Decisions

We consider the problem of decentralized hypothesis testing under communication constraints in a topology where several peripheral nodes are arranged in tandem. Each node receives an observation and transmits a message to its successor, and the last node then decides which hypothesis is true. We assume that the observations at different nodes are, conditioned on the true hypothesis, independent and the channel between any two successive nodes is considered error-free but rate-constrained. We propose a cyclic numerical design algorithm for the design of nodes using a person-by-person methodology with the minimum expected error probability as a design criterion, where the number of communicated messages is not necessarily equal to the number of hypotheses. The number of peripheral nodes in the proposed method is in principle arbitrary and the information rate constraints are satisfied by quantizing the input of each node. The performance of the proposed method for different information rate constraints, in a binary hypothesis test, is compared to the optimum rate-one solution due to Swaszek and a method proposed by Cover, and it is shown numerically that increasing the channel rate can significantly enhance the performance of the tandem network. Simulation results for $M$-ary hypothesis tests also show that by increasing the channel rates the performance of the tandem network significantly improves

Bayesian Design in Clinical Trials

In the last decade, the number of clinical trials using Bayesian methods has grown dramatically. Nowadays, regulatory authorities appear to be more receptive to Bayesian methods than ever. The Bayesian methodology is well suited to address the issues arising in the planning, analysis, and conduct of clinical trials. Due to their flexibility, Bayesian design methods based on the accrued data of ongoing trials have been recommended by both the US Food and Drug Administration and the European Medicines Agency for dose-response trials in early clinical development. A distinctive feature of the Bayesian approach is its ability to deal with external information, such as historical data, findings from previous studies and expert opinions, through prior elicitation. In fact, it provides a framework for embedding and handling the variability of auxiliary information within the planning and analysis of the study. A growing body of literature examines the use of historical data to augment newly collected data, especially in clinical trials where patients are difficult to recruit, which is the case for rare diseases, for example. Many works explore how this can be done properly, since using historical data has been recognized as less controversial than eliciting prior information from experts’ opinions. In this book, applications of Bayesian design in the planning and analysis of clinical trials are introduced, along with methodological contributions to specific topics of Bayesian statistics. Finally, two reviews regarding the state-of-the-art of the Bayesian approach in clinical field trials are presented

An algorithm for generating all possible 2(p-q) fractional factorial designs and its use in scientific experimentation

An algorithm and computer program are presented for generating all the distinct 2(p-q) fractional factorial designs. Some applications of this algorithm to the construction of tables of designs and of designs for nonstandard situations and its use in Bayesian design are discussed. An appendix includes a discussion of an actual experiment whose design was facilitated by the algorithm

Partial stochastic dominance for the multivariate Gaussian distribution

Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the partial stochastic dominance result that the cumulative distribution function of the maximum of a multivariate normal random vector, with positive intraclass correlation coefficient, intersects the cumulative distribution function of a standard normal random variable at most once. This result can be applied to the Bayesian design of a clinical trial in which several experimental treatments are compared to a single control.Comment: 7 page