spline fitting
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This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan–Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data’s structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison.

We describe the population-based susceptible-exposed-infected-removed (SEIR) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g. to the daily number of confirmed new cases, as the history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data to produce a robust methodology for calibration of a wide class of models of this type. This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.

Unmanned aerial vehicles (UAV) carrying multispectral cameras are increasingly being used for high-throughput phenotyping (HTP) of above-ground traits of crops to study genetic diversity, resource use efficiency and responses to abiotic or biotic stresses. There is significant unexplored potential for repeated data collection through a field season to reveal information on the rates of growth and provide predictions of the final yield. Generating such information early in the season would create opportunities for more efficient in-depth phenotyping and germplasm selection. This study tested the use of high-resolution time-series imagery (5 or 10 sampling dates) to understand the relationships between growth dynamics, temporal resolution and end-of-season above-ground biomass (AGB) in 869 diverse accessions of highly productive (mean AGB = 23.4 Mg/Ha), photoperiod sensitive sorghum. Canopy surface height (CSM), ground cover (GC), and five common spectral indices were considered as features of the crop phenotype. Spline curve fitting was used to integrate data from single flights into continuous time courses. Random Forest was used to predict end-of-season AGB from aerial imagery, and to identify the most informative variables driving predictions. Improved prediction of end-of-season AGB (RMSE reduction of 0.24 Mg/Ha) was achieved earlier in the growing season (10 to 20 days) by leveraging early- and mid-season measurement of the rate of change of geometric and spectral features. Early in the season, dynamic traits describing the rates of change of CSM and GC predicted end-of-season AGB best. Late in the season, CSM on a given date was the most influential predictor of end-of-season AGB. The power to predict end-of-season AGB was greatest at 50 days after planting, accounting for 63% of variance across this very diverse germplasm collection with modest error (RMSE 1.8 Mg/ha). End-of-season AGB could be predicted equally well when spline fitting was performed on data collected from five flights versus 10 flights over the growing season. This demonstrates a more valuable and efficient approach to using UAVs for HTP, while also proposing strategies to add further value.

A seamless mosaic has been constructed including a 3D terrain model at 50 m grid-spacing and a corresponding terrain-corrected orthoimage at 12.5 m using a novel approach applied to ESA Mars Express High Resolution Stereo Camera orbital (HRSC) images of Mars. This method consists of blending and harmonising 3D models and normalising reflectance to a global albedo map. Eleven HRSC image sets were processed to Digital Terrain Models (DTM) based on an opensource stereo photogrammetric package called CASP-GO and merged with 71 published DTMs from the HRSC team. In order to achieve high quality and complete DTM coverage, a new method was developed to combine data derived from different stereo matching approaches to achieve a uniform outcome. This new approach was developed for high-accuracy data fusion of different DTMs at dissimilar grid-spacing and provenance which employs joint 3D and image co-registration, and B-spline fitting against the global Mars Orbiter Laser Altimeter (MOLA) standard reference. Each HRSC strip is normalised against a global albedo map to ensure that the very different lighting conditions could be corrected and resulting in a tiled set of seamless mosaics. The final 3D terrain model is compared against the MOLA height reference and the results shown of this intercomparison both in altitude and planum. Visualisation and access mechanisms to the final open access products are described.

<p>The Cambrian Explosion is characterised by a large diversification of life. The precise nature of this major evolutionary event is heavily debated, featuring anomalously fast versus more gradual evolutionary scenarios. Our ability to distinguish between such scenarios hinges on the quality of global correlations and corresponding timescales. With Cambrian temporal uncertainties often in the order of millions of years, establishing such correlations and timelines is a challenging task. Here, we present a novel approach to this problem based on a probabilistic Bayesian conceptual framework. Major advantages of the Bayesian approach include the consideration of multiple information sources in a single analysis and explicit uncertainty formulations.</p><p>In the absence of good index fossils, early Cambrian correlations rely heavily on carbon isotope chemostratigraphy and ‘expert-based’ correlations. Inspired by approaches in the radiocarbon community, we have been exploring representations of stable carbon isotope variations using random walk and spline fitting models. Implementation is undertaken using Markov-chain Monte-Carlo (MCMC) approaches. Temporal calibration is mainly dependent on published state-of-the-art U-Pb zircon dating. Our model also allows for the use of different sedimentary facies. Simultaneous analysis of several sections and multiple stratigraphic variables will allow each section to inform the correlation of every other, leading to a single, objectively derived and quantitative reference curve. Ultimately, the aim is to have a coupled Bayesian model setup of both stratigraphy and morphological evolution of the fossil record. These models will better inform us on the origins of diverse animal-dominated ecosystems and their impact on Earth processes.</p>