Hierarchical second-order analysis of replicated spatial point patterns with non-spatial covariates

In this paper we propose a method for incorporating the effect of non-spatial covariates into the spatial second-order analysis of replicated point patterns. The variance stabilizing transformation of Ripley’s K function is used to summarize the spatial arrangement of points, and the relationship between this summary function and covariates is modelled by hierarchical Gaussian process regression. In particular, we investigate how disease status and some other covariates affect the level and scale of clustering of epidermal nerve fibres. The data are point patterns with replicates extracted from skin blister samples taken from 47 subjects.Peer reviewe

Convergence of Gaussian Process Regression with Estimated Hyper-parameters and Applications in Bayesian Inverse Problems

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process emulator are a-priori unknown, and are learnt from the data, along with the posterior mean and covariance. We work in the framework of empirical Bayes, where a point estimate of the hyper-parameters is computed, using the data, and then used within the standard Gaussian process prior to posterior update. We provide a convergence analysis that (i) holds for any continuous function $f$ to be emulated; and (ii) shows that convergence of Gaussian process regression is unaffected by the additional learning of hyper-parameters from data, and is guaranteed in a wide range of scenarios. As the primary motivation for the work is the use of Gaussian process regression to approximate the data likelihood in Bayesian inverse problems, we provide a bound on the error introduced in the Bayesian posterior distribution in this context

Actigraphic recording of motor activity in depressed inpatients: a novel computational approach to prediction of clinical course and hospital discharge

Depressed patients present with motor activity abnormalities, which can be easily recorded using actigraphy. The extent to which actigraphically recorded motor activity may predict inpatient clinical course and hospital discharge remains unknown. Participants were recruited from the acute psychiatric inpatient ward at Hospital Rey Juan Carlos (Madrid, Spain). They wore miniature wrist wireless inertial sensors (actigraphs) throughout the admission. We modeled activity levels against the normalized length of admission—‘Progress Towards Discharge’ (PTD)—using a Hierarchical Generalized Linear Regression Model. The estimated date of hospital discharge based on early measures of motor activity and the actual hospital discharge date were compared by a Hierarchical Gaussian Process model. Twenty-three depressed patients (14 females, age: 50.17 ± 12.72 years) were recruited. Activity levels increased during the admission (mean slope of the linear function: 0.12 ± 0.13). For n = 18 inpatients (78.26%) hospitalised for at least 7 days, the mean error of Prediction of Hospital Discharge Date at day 7 was 0.231 ± 22.98 days (95% CI 14.222–14.684). These n = 18 patients were predicted to need, on average, 7 more days in hospital (for a total length of stay of 14 days) (PTD = 0.53). Motor activity increased during the admission in this sample of depressed patients and early patterns of actigraphically recorded activity allowed for accurate prediction of hospital discharge date.This work has been partly-funded by the Spanish Ministerio de Ciencia, Innovación y Universidades (TEC2017-92552-EXP, RTI2018-099655-B-I00, FPU18/00516), the Comunidad de Madrid (Y2018/TCS-4705 PRACTICOCM, B2017/BMD-3740 AGES-CM 2CM), ISCIII (PI16/01852), BBVA Foundation (Deep-DARWiN grant) and AFSP (Grant LSRG-1-005-16). JDLM acknowledges funding support from the Universidad Autónoma de Madrid and European Union-European Commission via the Intertalentum Project & Marie Skłodowska-Curie Actions Grant (GA 713366