Differential Priors for Elastic Nets

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.

Assessing the impacts of grazing levels on bird density in woodland habitat: a Bayesian approach using expert opinion

Many studies on birds focus on the collection of data through an experimental design, suitable for investigation in a classical analysis of variance (ANOVA) framework. Although many findings are confirmed by one or more experts, expert information is rarely used in conjunction with the survey data to enhance the explanatory and predictive power of the model. We explore this neglected aspect of ecological modelling through a study on Australian woodland birds, focusing on the potential impact of different intensities of commercial cattle grazing on bird density in woodland habitat. We examine a number of Bayesian hierarchical random effects models, which cater for overdispersion and a high frequency of zeros in the data using WinBUGS and explore the variation between and within different grazing regimes and species. The impact and value of expert information is investigated through the inclusion of priors that reflect the experience of 20 experts in the field of bird responses to disturbance. Results indicate that expert information moderates the survey data, especially in situations where there are little or no data. When experts agreed, credible intervals for predictions were tightened considerably. When experts failed to agree, results were similar to those evaluated in the absence of expert information. Overall, we found that without expert opinion our knowledge was quite weak. The fact that the survey data is quite consistent, in general, with expert opinion shows that we do know something about birds and grazing and we could learn a lot faster if we used this approach more in ecology, where data are scarce. Copyright (c) 2005 John Wiley & Sons, Ltd.

Single patient (n-of-1) trials with binary treatment preference

The use of a fully parametric Bayesian method for analysing single patient trials based on the notion of treatment 'preference' is described. This Bayesian hierarchical modelling approach allows for full parameter uncertainty, use of prior information and the modelling of individual and patient sub-group structures. It provides updated probabilistic results for individual patients, and groups of patients with the same medical condition, as they are sequentially enrolled into individualized trials using the same medication alternatives. Two clinically interpretable criteria for determining a patient's response are detailed and illustrated using data from a previously published paper under two different prior information scenarios. Copyright (C) 2005 John Wiley & Sons, Ltd.

The population pharmacokinetics of citalopram after deliberate self-poisoning: A Bayesian approach

Defining the pharmacokinetics of drugs in overdose is complicated. Deliberate self-poisoning is generally impulsive and associated with poor accuracy in dose history. In addition, early blood samples are rarely collected to characterize the whole plasma-concentration time profile and the effect of decontamination on the pharmacokinetics is uncertain. The aim of this study was to explore a fully Bayesian methodology for population pharmacokinetic analysis of data that arose from deliberate self-poisoning with citalopram. Prior information on the pharmacokinetic parameters was elicited from 14 published studies on citalopram when taken in therapeutic doses. The data set included concentration-time data from 53 patients studied after 63 citalopram overdose events (dose range: 20-1700 mg). Activated charcoal was administered between 0.5 and 4 h after 17 overdose events. The clinical investigator graded the veracity of the patients' dosing history on a 5-point ordinal scale. Inclusion of informative priors stabilised the pharmacokinetic model and the population mean values could be estimated well. There were no indications of non-linear clearance after excessive doses. The final model included an estimated uncertainty of the dose amount which in a simulation study was shown to not affect the model's ability to characterise the effects of activated charcoal. The effect of activated charcoal on clearance and bioavailability was pronounced and resulted in a 72% increase and 22% decrease, respectively. These findings suggest charcoal administration is potentially beneficial after citalopram overdose. The methodology explored seems promising for exploring the dose-exposure relationship in the toxicological settings.

How to predict everything: Nostradamus in the role of Copernicus

Statistics is known to be an art as well as a science. The training of mathematical physicists predisposes them towards hypothesising plausible Bayesean priors. Tony Bracken and I were of that mind [1], but in our discussions we also recognised the Bayesean will-o'-the-wisp illustrated below.

Bayesian population pharmacokinetic analysis of sirolimus

Objective: It is usual that data collected from routine clinical care is sparse and unable to support the more complex pharmacokinetic (PK) models that may have been reported in previous rich data studies. Informative priors may be a pre-requisite for model development. The aim of this study was to estimate the population PK parameters of sirolimus using a fully Bayesian approach with informative priors. Methods: Informative priors including prior mean and precision of the prior mean were elicited from previous published studies using a meta-analytic technique. Precision of between-subject variability was determined by simulations from a Wishart distribution using MATLAB (version 6.5). Concentration-time data of sirolimus retrospectively collected from kidney transplant patients were analysed using WinBUGS (version 1.3). The candidate models were either one- or two-compartment with first order absorption and first order elimination. Model discrimination was based on computation of the posterior odds supporting the model. Results: A total of 315 concentration-time points were obtained from 25 patients. Most data were clustered at trough concentrations with range of 1.6 to 77 hours post-dose. Using informative priors, either a one- or two-compartment model could be used to describe the data. When a one-compartment model was applied, information was gained from the data for the value of apparent clearance (CL/F = 18.5 L/h), and apparent volume of distribution (V/F = 1406 L) but no information was gained about the absorption rate constant (ka). When a two-compartment model was fitted to the data, the data were informative about CL/F, apparent inter-compartmental clearance, and apparent volume of distribution of the peripheral compartment (13.2 L/h, 20.8 L/h, and 579 L, respectively). The posterior distribution of the volume distribution of central compartment and ka were the same as priors. The posterior odds for the two-compartment model was 8.1, indicating the data supported the two-compartment model. Conclusion: The use of informative priors supported the choice of a more complex and informative model that would otherwise have not been supported by the sparse data.

Precision-recall operating characteristic (P-ROC) curves in imprecise environments

Traditionally, machine learning algorithms have been evaluated in applications where assumptions can be reliably made about class priors and/or misclassification costs. In this paper, we consider the case of imprecise environments, where little may be known about these factors and they may well vary significantly when the system is applied. Specifically, the use of precision-recall analysis is investigated and compared to the more well known performance measures such as error-rate and the receiver operating characteristic (ROC). We argue that while ROC analysis is invariant to variations in class priors, this invariance in fact hides an important factor of the evaluation in imprecise environments. Therefore, we develop a generalised precision-recall analysis methodology in which variation due to prior class probabilities is incorporated into a multi-way analysis of variance (ANOVA). The increased sensitivity and reliability of this approach is demonstrated in a remote sensing application.