Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Online information seeking by patients with bipolar disorder:results from an international multisite survey

Background: Information seeking is an important coping mechanism for dealing with chronic illness. Despite a growing number of mental health websites, there is little understanding of how patients with bipolar disorder use the Internet to seek information. Methods: A 39 question, paper-based, anonymous survey, translated into 12 languages, was completed by 1222 patients in 17 countries as a convenience sample between March 2014 and January 2016. All patients had a diagnosis of bipolar disorder from a psychiatrist. Data were analyzed using descriptive statistics and generalized estimating equations to account for correlated data. Results: 976 (81 % of 1212 valid responses) of the patients used the Internet, and of these 750 (77 %) looked for information on bipolar disorder. When looking online for information, 89 % used a computer rather than a smartphone, and 79 % started with a general search engine. The primary reasons for searching were drug side effects (51 %), to learn anonymously (43 %), and for help coping (39 %). About 1/3 rated their search skills as expert, and 2/3 as basic or intermediate. 59 % preferred a website on mental illness and 33 % preferred Wikipedia. Only 20 % read or participated in online support groups. Most patients (62 %) searched a couple times a year. Online information seeking helped about 2/3 to cope (41 % of the entire sample). About 2/3 did not discuss Internet findings with their doctor. Conclusion: Online information seeking helps many patients to cope although alternative information sources remain important. Most patients do not discuss Internet findings with their doctor, and concern remains about the quality of online information especially related to prescription drugs. Patients may not rate search skills accurately, and may not understand limitations of online privacy. More patient education about online information searching is needed and physicians should recommend a few high quality websites.