Evaluating sources of variability in inflorescence number, flower number and the progression of flowering in Sauvignon blanc using a Bayesian modelling framework

The time of flowering is key to understanding the development of grapevines. Flowering coincides with inflorescence initiation and fruit set, important determinants of yield. This research aimed to determine between and within-vine variability in 4-cane-pruned Sauvignon blanc inflorescence number per shoot, number of flowers per inflorescence and flowering progression using an objective method of assessing flowering via image capture and statistical analysis using a Bayesian modelling framework. The inflorescence number and number of flowers per inflorescence were measured by taking images over the flowering period. Flowering progression was assessed by counting open and closed flowers for each image over two seasons. An ordinal multinomial generalised linear mixed-effects model (GLMM) was fitted for inflorescence number, a Poisson GLMM for flower counts and a binomial GLMM for flowering progression. All the models were fitted and interpreted within a Bayesian modelling framework. Shoots arising from cane node one had lower numbers of inflorescences compared to those at nodes 3, 5 and 7, which were similar. The number of flowers per inflorescence was greater for basal inflorescences on a shoot than apical ones. Flowering was earlier, by two weeks, and faster in 2017/18 when compared to 2018/19 reflecting seasonal temperature differences. The time and duration of flowering varied at each inflorescence position along the cane. While basal inflorescences flowered later and apical earlier at lower insertion points on the shoot, the variability in flowering at each position on the vine dominated the date and duration of flowering.This is the first study using a Bayesian modelling framework to assess variability inflorescence presence and flower number, as well as flowering progression via objective quantification of open and closed flower counts rather than the more subjective method of visual estimation in the field or via cuttings. Although flower number differed for apical and basal bunches, little difference in timing and progression of flowering by these categories was observed. The node insertion point along a shoot was more important. Overall, the results indicate individual inflorescence variation and season are the key factors driving flowering variability and are most likely to impact fruit set and yield.

Steinalderkeramikken fra Rogaland – en kronologisk studie

From the 1800’s and onwards, pottery sherds have been found at a number of Neolithic occupation sites in Rogaland County, Southwestern Norway. In this paper, pottery assemblages from nine contexts are analyzed in order to produce an interpretative chronology. Typological analysis is combined with correspondence analysis and Bayesian modelling of radiocarbon dates. The result is a coherent chronological model that accounts for variations in pottery decoration styles between the late Early Neolithic and the Late Neolithic. There is a development in decorative styles from cord and cord-stamp ornamented vessels followed by a period of pots decorated with cord-stamp, small imprints and incisions, and finally a phase with added lines, comb, and cord-stamp. However, the multi-phased nature of the sites suggests that there are still many unanswered questions. New excavations and re-analyses of older sites are necessary for a better understanding of the developments in Neolithic pottery styles.

Conclusions: Towards a Bayesian Modelling Process

In the concluding chapter we summarise the theoretical, methodological and practical outcomes of the model-based process of scientific enquiry presented in the book, against the wider background of recent developments in demography and population studies. We offer a critical self-reflection on further potential and on limitations of Bayesian model-based approaches, alongside the lessons learned from the modelling exercise discussed throughout this book. As concluding thoughts, we suggest potential ways forward for statistically-embedded model-based computational social studies, including an assessment of the future viability of the wider model-based research programme, and its possible contributions to policy and decision making.

Stochastic approximation cut algorithm for inference in modularized Bayesian models

Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model and prevent feedback from suspect modules, using a cut model. After observing data, this leads to the cut distribution which normally does not have a closed form. Previous studies have proposed algorithms to sample from this distribution, but these algorithms have unclear theoretical convergence properties. To address this, we propose a new algorithm called the stochastic approximation cut (SACut) algorithm as an alternative. The algorithm is divided into two parallel chains. The main chain targets an approximation to the cut distribution; the auxiliary chain is used to form an adaptive proposal distribution for the main chain. We prove convergence of the samples drawn by the proposed algorithm and present the exact limit. Although SACut is biased, since the main chain does not target the exact cut distribution, we prove this bias can be reduced geometrically by increasing a user-chosen tuning parameter. In addition, parallel computing can be easily adopted for SACut, which greatly reduces computation time.

Luminescence age calculation through Bayesian convolution of equivalent dose and dose-rate distributions: the D_e_D_r model

In nature, any mineral grain (quartz or feldspar) receives a dose-rate (Dr) specific to its environment. The dose-rate distributions, therefore, reflect the micro-dosimetric context of grains of similar size. If all the grains have been well bleached at deposition, this distribution corresponds, within uncertainties, to the distribution of equivalent doses (De). Their combination (convolution of the De and Dr distributions in the De_Dr model proposed here) allows the calculation of the true depositional age. If grains whose De values are not representative of this age (hereafter called "outliers") are present in the De distribution, the model allows them to be identified before the age is calculated. As the De_Dr approach relies only on the Dr distribution, the model avoids any assumption representing the De distribution, which is usually difficult to justify. Herein, we outline the mathematical concepts of the De_Dr approach (more details are given in Galharret et al., accepted) and the exploitation of this Bayesian modelling based on an R code available in the R package 'Luminescence'. We also present a series of tests using simulated Dr and De distributions with and without outliers and show that the De_Dr approach can be an alternative to available models for interpreting De distributions.

Mesophotic coral communities escape thermal coral bleaching in French Polynesia

Climate change and consequent coral bleaching are causing the disappearance of reef-building corals worldwide. While bleaching episodes significantly impact shallow waters, little is known about their impact on mesophotic coral communities. We studied the prevalence of coral bleaching two to three months after a heat stress event, along an extreme depth range from 6 to 90 m in French Polynesia. Bayesian modelling showed a decreasing probability of bleaching of all coral genera over depth, with little to no bleaching observed at lower mesophotic depths (greater than or equal to 60 m). We found that depth-generalist corals benefit more from increasing depth than depth-specialists (corals with a narrow depth range). Our data suggest that the reduced prevalence of bleaching with depth, especially from shallow to upper mesophotic depths (40 m), had a stronger relation with the light-irradiance attenuation than temperature. While acknowledging the geographical and temporal variability of the role of mesophotic reefs as spatial refuges during thermal stress, we ought to understand why coral bleaching reduces with depth. Future studies should consider repeated monitoring and detailed ecophysiological and environmental data. Our study demonstrated how increasing depth may offer a level of protection and that lower mesophotic communities could escape the impacts of a thermal bleaching event.

Bayesian tools for uncertainty quantification and propagation in structural dynamics simulations

Η παρούσα διατριβή επικεντρώνεται στην ανάπτυξη τεχνικών κατά Bayes για την ποσοτικοποίηση και διαχείριση αβεβαιοτήτων (Uncertainty Quantification and Propagation - UQP) σε μηχανικές προσομοιώσεις που βασίζονται σε μοντέλα φυσικής δυναμικών συστημάτων και δεδομένα μετρήσεων που συλλέγονται κατά τη λειτουργία τους. Εισάγει ένα πλαίσιο ιεραρχικής μοντελοποίησης κατά Bayes (Hierarchical Bayesian Modelling - HBM) για να ληφθεί υπόψη η αβεβαιότητα λόγω της μεταβλητότητας που προκύπτει από σφάλματα μοντέλου, πειραματικά δεδομένα, διαδικασία κατασκευής, διαδικασία συναρμολόγησης, καθώς και μη γραμμικότητες που ενεργοποιούνται υπό διαφορετικές συνθήκες φόρτισης. Αρχικά, επεκτείνει το πλαίσιο HBM αναπτύσσοντάς το περαιτέρω για εκτίμηση παραμέτρων φυσικών μοντέλων με βάση τα ιδιομορφικά χαρακτηριστικά. Στη συνέχεια, γενικεύει το πλαίσιο σε μη γραμμικά δυναμικά συστήματα για βαθμονόμηση και ποσοτικοποίηση των αβεβαιοτήτων των παραμέτρων μη γραμμικών μοντέλων. Τέλος, διαμορφώνει το πλαίσιο ώστε να λαμβάνει υπόψη μοντελοποίηση συστημάτων πολλαπλών επιπέδων με βάση τη φυσική, καθώς και μοντέλα αβεβαιοτήτων πολλαπλών επιπέδων χρησιμοποιώντας πειραματικά δεδομένα πολλαπλών επιπέδων. Εισάγονται, αναπτύσσονται και ενσωματώνονται ασυμπτωτικές προσεγγίσεις στο πλαίσιο HBM προκειμένου να αποκτηθούν περισσότερες γνώσεις σχετικά με την ερμηνεία διαφορετικών πηγών αβεβαιότητας. Η εισαγωγή τέτοιων προσεγγίσεων μπορεί να μειώσει σημαντικά τον υπολογιστικό φόρτο του πλαισίου HBM σε σύγκριση με το υψηλό υπολογιστικό φόρτο που απαιτείται σε μια πλήρως δειγματοληπτική μέθοδο. Διεξάγονται προσομοιώσεις και πειραματικές μελέτες για την επαλήθευση της αποτελεσματικότητας των προτεινόμενων μεθοδολογιών. Αποδεικνύεται ότι το προτεινόμενο πλαίσιο HBM παρέχει καλύτερη περιγραφή για τις αβεβαιότητες των παραμέτρων, διακρίνοντας μεταξύ αβεβαιοτήτων πού δεν δύναται να μειωθούν και αβεβαιοτήτων που δύναται να μειωθούν, ενώ το συμβατικό πλαίσιο μοντελοποίησης Bayes (CBM) συχνά υποτιμά τις αβεβαιότητες για τις παραμέτρους και συγκεντρώνει αυτές τις αβεβαιότητες στον όρο του σφάλματος μοντέλου. Επιπλέον, αυτή η διατριβή επανεξετάζει θέματα υποεκτίμησης των αβεβαιοτήτων μέσα στο συμβατικό πλαίσιο μοντελοποίησης, αναπτύσσοντας περαιτέρω μοντέλα που βασίζονται σε χαρακτηριστικά δεδομένων και παρουσιάζοντας νέες διατυπώσεις για τον καθορισμό της συνάρτησης πιθανότητας. Διευκρινίζεται ότι οι προτεινόμενες μέθοδοι προσφέρουν συστηματικές αβεβαιότητες παραμέτρων που είναι ανεξάρτητες από το ρυθμό δειγματοληψίας που χρησιμοποιείται για την ακριβή αναπαράσταση των χρονοιστοριών απόκρισης. Επιπλέον, για τις εφαρμογές στις οποίες είναι διαθέσιμες οι κατανομές πιθανότητας ή τα στατιστικά στοιχεία των μετρήσεων, αυτή η διατριβή παρουσιάζει μια εναλλακτική μεθοδολογία υπό μια σκοπιά ιεραρχικής μοντελοποίησης για τις παραμέτρους του μοντέλου για να ληφθεί υπόψη η αβεβαιότητα λόγω μεταβλητότητας. Αυτή η εναλλακτική προσέγγιση της μεθόδου HBM εφαρμόζεται με επιτυχία σε ένα παράδειγμα ενός δυναμικού συστήματος καθώς και στην ανάλυση καμπύλης κόπωσης S-N για την εκτίμηση παραμέτρων και προβλέψεων μέσω των διαθέσιμων στατιστικών των μετρούμενων ποσοτήτων. Οι προτεινόμενες μεθοδολογίες σε αυτή τη διατριβή παρουσιάζουν μεγάλη ευελιξία και δυνατότητα να εφαρμοστούν και σε άλλους κλάδους της μηχανικής και της επιστήμης.