Multivariate functional additive mixed models

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by, for example, repeated measurements or crossed study designs. Modelling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modelling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.

A functional proportional hazard cure rate model for interval-censored data

Existing survival models involving functional covariates typically rely on the Cox proportional hazards structure and the assumption of right censorship. Motivated by the aim of predicting the time of conversion to Alzheimer’s disease from sparse biomarker trajectories in patients with mild cognitive impairment, we propose a functional mixture cure rate model with both functional and scalar covariates for interval censoring and sparsely sampled functional data. To estimate the nonparametric coefficient function that depicts the effect of the shape of the trajectories on the survival outcome and cure probability, we utilize the functional principal component analysis to extract the functional features from the sparsely and irregularly sampled trajectories. To obtain parameter estimates from the mixture cure rate model with interval censoring, we apply the expectation-maximization algorithm based on Poisson data augmentation. The estimation accuracy of our method is assessed via a simulation study and we apply our model on Alzheimer’s disease Neuroimaging Initiative data set.

How Artificial Intelligence can Guide Marcellus Development

The application of Artificial Intelligence for planning has received increased attention in the energy industry in the past few years, particularly for the increased production efficiency requirements and environmental standards. The objective of this paper is to show the successful integration of production, completion, subsurface and spatial data using machine-learning algorithms to predict production performance for future development wells. The internal Marcellus Business Unit (MBU) well database, populated with data of 500+ historical wells, has been used in this study. Production data, treated as timeseries, has been processed using functional Principal Component Analysis (PCA) to allow removal of outliers and mode detection. Utilizing this data, a suite of machine-learning algorithms has been applied to reconstruct gas production from available and target well data. Uncertainty quantification has been provided for production curves to identify the quality of prediction. During the study, the sensitivity analysis on input variables has been performed iteratively to screen and rank the most important variables for prediction. The workflow, Unconventional Reservoir Assistant (URA), has been implemented in a proprietary cloud-based platform providing the necessary means for data upload, integration, pre-processing, and finally model training and deployment. This allows the user to focus on the evaluation of model output quality, data filter and workspace generation for continuous model testing and improvement. The full well dataset, split into trained and tested data, has been used for prediction as a preliminary guide to where the most prolific areas of development are located. Results were ranked based on production expected by pad and based on normalized performance. The information was then used to compare with type curves and original development order. In parallel, economic evaluation of break-even was performed to rank all future pads. Consequently, integration of the model prediction and breakeven ranking were used to generate the final development order for the MBU. The URA tool has shown preliminary success in predicting production performance for the pilot development area. Multiple case studies have been run achieving blind test results with high accuracy for historical prediction. Results show some dependency of predictor variable ranking on the field development area, providing insight on how subsurface may affect well dynamic behavior. This paper describes how the integration of URA can complement the development workflow for unconventional reservoirs and be used to predict performance based on complex data integration. The methodology used is superior to standard machine learning models providing only production indicators, as it gives the user the possibility to evaluate economics and completion design sensitivity for future well activities. The methodology can be further extended as a proxy model for well schedule optimization in planning or for better insight into well refrac selection.

Estimating Growth in Height from Limited Longitudinal Growth Data Using Full-Curves Training Dataset: A Comparison of Two Procedures of Curve Optimization—Functional Principal Component Analysis and SITAR

A variety of models are available for the estimation of parameters of the human growth curve. Several have been widely and successfully used with longitudinal data that are reasonably complete. On the other hand, the modeling of data for a limited number of observation points is problematic and requires the interpolation of the interval between points and often an extrapolation of the growth trajectory beyond the range of empirical limits (prediction). This study tested a new approach for fitting a relatively limited number of longitudinal data using the normal variation of human empirical growth curves. First, functional principal components analysis was done for curve phase and amplitude using complete and dense data sets for a reference sample (Brno Growth Study). Subsequently, artificial curves were generated with a combination of 12 of the principal components and applied for fitting to the newly analyzed data with the Levenberg–Marquardt optimization algorithm. The approach was tested on seven 5-points/year longitudinal data samples of adolescents extracted from the reference sample. The samples differed in their distance from the mean age at peak velocity for the sample and were tested by a permutation leave-one-out approach. The results indicated the potential of this method for growth modeling as a user-friendly application for practical applications in pediatrics, auxology and youth sport.