Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Testing Gait with Ankle-Foot Orthoses in Children with Cerebral Palsy by Using Functional Mixed-Effects Analysis of Variance

Dr Morrissey is part funded by the NIHR/HEE Senior Clinical Lecturer scheme. Tis report presents independent research part-funded by the National Institute for Health Research (NIHR) CAT SCL-2013-04-00

Bartlett's Test Applied to Variance Component Models

Exact methods for testing equality between variance components obtained from several cases of the same type of balanced orthogonal design are discussed. In particular, methods for successively testing equality of a number of components using Bartlett's tests are outlined for univariate and multivariate responses. Two clinical trial examples of repeated-measures data are presented. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..

Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer-adaptive practice

We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person-by-item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer-adaptive practice mathematical environment