Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Lawyer rankings either do not matter for litigation outcomes or are redundant

I investigate the success of litigants in tax cases in England and Wales between 1996 and 2010. I explore the effect upon success of having better-ranked legal representation, according to rankings of barristers published by Chambers. I find that, for a variety of model specifications, there is no significant positive effect of having better-ranked legal representation. After conducting a sensitivity analysis, I conclude that better-ranked legal representation might have a positive effect on litigation outcomes, but only if better-ranked lawyers receive cases that are substantially more difficult to win. However, if better-ranked lawyers receive substantially more difficult cases, this suggests consumers of legal representation are sophisticated enough to dispense with legal rankings

The comparative responsiveness of Hospital Universitario Princesa Index and other composite indices for assessing rheumatoid arthritis activity

Objective To evaluate the responsiveness in terms of correlation of the Hospital Universitario La Princesa Index (HUPI) comparatively to the traditional composite indices used to assess disease activity in rheumatoid arthritis (RA), and to compare the performance of HUPI-based response criteria with that of the EULAR response criteria. Methods Secondary data analysis from the following studies: ACT-RAY (clinical trial), PROAR (early RA cohort) and EMECAR (pre-biologic era long term RA cohort). Responsiveness was evaluated by: 1) comparing change from baseline (Delta) of HUPI with Delta in other scores by calculating correlation coefficients; 2) calculating standardised effect sizes. The accuracy of response by HUPI and by EULAR criteria was analyzed using linear regressions in which the dependent variable was change in global assessment by physician (Delta GDA-Phy). Results Delta HUPI correlation with change in all other indices ranged from 0.387 to 0.791); HUPI's standardized effect size was larger than those from the other indices in each database used. In ACT-RAY, depending on visit, between 65 and 80% of patients were equally classified by HUPI and EULAR response criteria. However, HUPI criteria were slightly more stringent, with higher percentage of patients classified as non-responder, especially at early visits. HUPI response criteria showed a slightly higher accuracy than EULAR response criteria when using Delta GDA-Phy as gold standard. Conclusion HUPI shows good responsiveness in terms of correlation in each studied scenario (clinical trial, early RA cohort, and established RA cohort). Response criteria by HUPI seem more stringent than EULAR''s