Some topics in the analysis of spherical data.

This thesis is concerned with the statistical analysis of directions in 3 dimensions. An important reference is the book by Mardia (1972). At the time of publication of this book, the repertoire of spherical distributions used for modelling purposes was rather limited, and there was clearly a need to investigate other possibilities. In the last few years there has been some interest in the 8 parameter family of distributions mentioned by Mardia (1975), which is known as the Fisher-Bingham family. In Chapter 1 an outline of the thesis is given. The Fisher-Bingham family is discussed in Chapter 2, and an effective method for calculating the normalising constant is presented. Attention is then focussed on an interesting 6 parameter subfamily, and a simple rule is given for classifying the distributions in this subfamily according to type (unimodal, bimodal, ’closed curve'). Estimation and inference are then discussed, and the Chapter is concluded with a numerical example. In Chapter 3, the family of bimodal distributions presented in Wood (1982) is described. Other bimodal models are also mentioned briefly. The problem of simulating Fisher-Bingham distributions is considered in Chapter 4. Some inequalities are derived and then used to construct suitable envelopes so that an acceptance-rejection procedure can be used. In Chapter 5, the robust estimation of concentration for a Fisher distribution is considered, and L-estimators of the type suggested by Fisher (1982) are investigated. It is shown that the best of these estimators have desirable all-round properties. Indications are also given as to how these ideas can be adapted to other contexts. Possibilities for further research are mentioned in Chapter 6

Nonparametric hypothesis testing for equality of means on the simplex

In the context of data that lie on the simplex, we investigate use of empirical and exponential empirical likelihood, and Hotelling and James statistics, to test the null hypothesis of equal population means based on two independent samples. We perform an extensive numerical study using data simulated from various distributions on the simplex. The results, taken together with practical considerations regarding implementation, support the use of bootstrap-calibrated James statistic

Operating at the extreme: Estimating the upper yield boundary of winter wheat production in commercial practice

© 2020 The Authors. Wheat farming provides 28.5% of global cereal production. After steady growth in average crop yield from 1950 to 1990, wheat yields have generally stagnated, which prompts the question of whether further improvements are possible. Statistical studies of agronomic parameters such as crop yield have so far exclusively focused on estimating parameters describing the whole of the data, rather than the highest yields specifically. These indicators include the mean or median yield of a crop, or finding the combinations of agronomic traits that are correlated with increasing average yields. In this paper, we take an alternative approach and consider high yields only. We carry out an extreme value analysis of winter wheat yield data collected in England and Wales between 2006 and 2015. This analysis suggests that, under current climate and growing conditions, there is indeed a finite upper bound for winter wheat yield, whose value we estimate to be 17.60 tonnes per hectare. We then refine the analysis for strata defined by either location or level of use of agricultural inputs. We find that there is no statistical evidence for variation of maximal yield depending on location, and neither is there statistical evidence that maximum yield levels are improved by high levels of crop protection and fertilizer use

Digital Single-Cell Analysis of Plant Organ Development Using 3DCellAtlas

Diverse molecular networks underlying plant growth and development are rapidly being uncovered. Integrating these data into the spatial and temporal context of dynamic organ growth remains a technical challenge. We developed 3DCellAtlas, an integrative computational pipeline that semiautomatically identifies cell types and quantifies both 3D cellular anisotropy and reporter abundance at single-cell resolution across whole plant organs. Cell identification is no less than 97.8% accurate and does not require transgenic lineage markers or reference atlases. Cell positions within organs are defined using an internal indexing system generating cellular level organ atlases where data from multiple samples can be integrated. Using this approach, we quantified the organ-wide cell-type-specific 3D cellular anisotropy driving Arabidopsis thaliana hypocotyl elongation. The impact ethylene has on hypocotyl 3D cell anisotropy identified the preferential growth of endodermis in response to this hormone. The spatiotemporal dynamics of the endogenous DELLA protein RGA, expansin gene EXPA3, and cell expansion was quantified within distinct cell types of Arabidopsis roots. A significant regulatory relationship between RGA, EXPA3, and growth was present in the epidermis and endodermis. The use of single-cell analyses of plant development enables the dynamics of diverse regulatory networks to be integrated with 3D organ growth.</p

Promotion of testa rupture during garden cress germination involves seed compartment-specific expression and activity of pectin methylesterases

Pectin methylesterase (PME) controls the methylesterification status of pectins and thereby determines the biophysical properties of plant cell walls, which are important for tissue growth and weakening processes. We demonstrate here that tissue-specific and spatiotemporal alterations in cell wall pectin methylesterification occur during the germination of garden cress (Lepidium sativum). These cell wall changes are associated with characteristic expression patterns of PME genes and resultant enzyme activities in the key seed compartments CAP (micropylar endosperm) and RAD (radicle plus lower hypocotyl). Transcriptome and quantitative real-time reverse transcription-polymerase chain reaction analysis as well as PME enzyme activity measurements of separated seed compartments, including CAP and RAD, revealed distinct phases during germination. These were associated with hormonal and compartment-specific regulation of PME group 1, PME group 2, and PME inhibitor transcript expression and total PME activity. The regulatory patterns indicated a role for PME activity in testa rupture (TR). Consistent with a role for cell wall pectin methylesterification in TR, treatment of seeds with PME resulted in enhanced testa permeability and promoted TR. Mathematical modeling of transcript expression changes in germinating garden cress and Arabidopsis (Arabidopsis thaliana) seeds suggested that group 2 PMEs make a major contribution to the overall PME activity rather than acting as PME inhibitors. It is concluded that regulated changes in the degree of pectin methylesterification through CAP- and RAD-specific PME and PME inhibitor expression play a crucial role during Brassicaceae seed germination

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Saddlepoint approximations for the normalizing constant of Fisher–Bingham distributions on products of spheres and Stiefel manifolds

In an earlier paper Kume & Wood (2005) showed how the normalizing constant of the Fisher– Bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation. In this sequel, we extend the approach to a more general setting and derive saddlepoint approximations for the normalizing constants of multicomponent Fisher– Bingham distributions on Cartesian products of spheres, and Fisher–Bingham distributions on Stiefel manifolds. In each case, the approximation for the normalizing constant is essentially a multivariate saddlepoint density approximation for the joint distribution of a set of quadratic forms in normal variables. Both first-order and second-order saddlepoint approximations are considered. Computational algorithms, numerical results and theoretical properties of the approximations are presented. In the challenging high-dimensional settings considered in this paper the saddlepoint approximations perform very well in all examples considered. Some key words: Directional data; Fisher matrix distribution; Kent distribution; Orientation statistics

Saddlepoint approximations for the Bingham and Fisher-Bingham normalising constants

The Fisher-Bingham distribution is obtained when a multivariate normal random vector is conditioned to have unit length. Its normalising constant can be expressed as an elementary function multiplied by the density, evaluated at 1, of a linear combination of independent noncentral chi(1)(2) random variables. Hence we may approximate the normalising constant by applying a saddlepoint approximation to this density. Three such approximations, implementation of each of which is straightforward, are investigated: the first-order saddlepoint density approximation, the second-order saddlepoint density approximation and a variant of the second-order approximation which has proved slightly more accurate than the other two. The numerical and theoretical results we present show that this approach provides highly accurate approximations in a broad spectrum of cases

Empirical Bayes block shrinkage of wavelet coefficients via the noncentral chi^2 distribution

Empirical Bayes approaches to the shrinkage of empirical wavelet coefficients have generated considerable interest in recent years. Much of the work to date has focussed on shrinkage of individual wavelet coefficients in isolation. In this paper we propose an empirical Bayes approach to simultaneous shrinkage of wavelet coefficients in a block, based on the block sum of squares. Our approach exploits a useful identity satisfied by the noncentral 2 density and provides some tractable Bayesian block shrinkage procedures. Our numerical results indicate that the new procedures perform very well