No / This paper presents new chronological data applied to the problem of providing a date for the construction of a prehistoric building, with a case study from the Old Scatness Broch, Shetland. The innovative methodology employed utilises the combination of radiocarbon and optically stimulated luminescence (OSL) dates with the archaeological information, which includes the stratigraphic relationships of sampled deposits, context information, and evidence relating to the formation of the deposit. This paper discusses the scientific validity of the dates produced, and the advantages that the methodology employed at this site offers for archaeological interpretation. The combined dating evidence suggests that the broch at Old Scatness is earlier than the conventionally accepted dates for broch construction. More broadly it shows the value of integration of the specialists at the planning stages of the excavation. The application of a Bayesian statistical model to the sequences of dates allowed investigation of the robustness of the dates within the stratigraphic sequences, as well as increasing the resolution of the resulting chronology. In addition, the value of utilising multiple dating techniques on the same deposit was demonstrated, as this allowed different dated events to be directly compared as well as issues relating to the formation of the sampled deposit. This in turn impacted on the chronological significance of the resulting dating evidence, and therefore the confidence that could be placed in the results.

No

Yes / Precise chronologies underpin all aspects of archaeological interpretation and, in addition to improvements in scientific dating methods themselves, one of the most exciting recent developments has been the use of Bayesian statistical analysis to reinterpret existing information. Such approaches allow the integration of scientific dates, stratigraphy and typological data to provide chronologies with improved precision. Settlement period sites in Iceland offer excellent opportunities to explore this approach, as many benefit from dated tephra layers and AMS radiocarbon dates. Whilst tephrochronology is widely used and can provide excellent chronological control, this method has limitations; the time span between tephra layers can be large and they are not always present. In order to investigate the improved precision available by integrating the scientific dates with the associated archaeological stratigraphy within a Bayesian framework, this research reanalyses the dating evidence from three recent large scale excavations of key Viking Age and medieval sites in Iceland; Aðalstræti, Hofstaðir and Sveigakot. The approach provides improved chronological precision for the dating of significant events within these sites, allowing a more nuanced understanding of occupation and abandonment. It also demonstrates the potential of incorporating dated typologies into chronological models and the use of models to propose sequences of activities where stratigraphic relationships are missing. Such outcomes have considerable potential in interpreting the archaeology of Iceland and can be applied more widely to sites with similar chronological constraints. / British Academy (MD120020) awarded to C. Batt. Rannís PhD funding for M.Schmid. / The full text was made available at the end of the publisher's embargo.

Traditional methods of analyzing functional Magnetic Resonance Images use a linear combination of just a few static regressors. This work demonstrates an alternative approach using a physiologically inspired nonlinear model. By using a particle filter to optimize the model parameters, the computation time is kept below a minute per voxel without requiring a linearization of the noise in the state variables. The activation results show regions similar to those found in Statistical Parametric Mapping; however, there are some notable regions not detected by that technique. Though the parameters selected by the particle filter based approach are more than sufficient to predict the Blood-Oxygen-Level-Dependent signal response, more model constraints are needed to uniquely identify a single set of parameters. This illposed nature explains the large discrepancies found in other research that attempted to characterize the model parameters. For this reason the final distribution of parameters is more medically relevant than a single estimate. Because the output of the particle filter is a full posterior probability, the reliance on the mean to estimate parameters is unnecessary. This work presents not just a viable alternative to the traditional method of detecting activation, but an extensible technique of estimating the joint probability distribution function of the Blood-Oxygen-Level-Dependent Signal parameters. / Master of Science

A recent application of point processes has emerged from the electronic trading of financial assets. Many securities are now traded on purely electronic exchanges where demand and supply are aggregated in limit order books. Buy and sell trades in the asset as well as quote additions and cancellations can then be interpreted as events that not only determine the shape of the order book, but also define point processes that exhibit a rich internal structure. A large class of such point processes are those driven by a diffusive intensity process. A flexible choice with favourable analytic properties is a Cox-Ingersoll-Ross (CIR) diffusion. We adopt a Bayesian perspective on the statistical inference for these doubly stochastic processes, and focus on filtering the latent intensity process. We derive analytic results for the moment generating function of its posterior distribution. This is achieved by solving a partial differential equation for a linearised version of the filtering equation. We also establish an efficient and simple numerical evaluation of the posterior mean and variance of the intensity process. This relies on extending an equivalence result between a point process with CIR-intensity and a partially observed population process. We apply these results to empirical datasets from foreign exchange trading. One objective is to assess whether a CIR-driven point process is a satisfactory model for the variations in trading activity. This is answered in the negative, as sudden bursts of activity impair the fit of any diffusive intensity model. Controlling for such spikes, we conclude with a discussion of the stochastic control of a market making strategy when the only information available are the times of buy and sell trades.

The vast majority of experiments in particle physics can be described by the Standard Model of particle physics (SM). However, there are indications for physics beyond it. The only experimentally demonstrated problem of the model is the difficulty to describe neutrino masses and leptonic mixing. There is a plethora of models that try to describe these phenomena and this thesis investigates several possibilities for new models, both full theories and effective frameworks.   The values of the parameters in a model are dependent on the energy scale and we say that the parameters run. The exact behavior of the running depends on the model and it provides a signature of the model. For a model defined at high energies it is necessary to run the parameters down to the electroweak scale in order to perform a comparison to the known values of observed quantities. In this thesis, we discuss renormalization group running in the context of extra dimensions and we provide an upper limit on the cutoff scale. We perform renormalization group running in two versions of a non-supersymmetric SO(10) model and we show that the SM parameters can be accommodated in both versions. In addition, we perform the running for the gauge couplings in a large set of radiative neutrino mass models and conclude that unification is possible in some of them.   The Higgs boson provides new possibilities to study physics beyond the SM. Its properties have to be tested with extremely high precision before it could be established whether the particle is truly the SM Higgs boson or not. In this thesis, we perform Bayesian parameter inference and model comparison. For models where the magnitude of the Higgs couplings is varied, we show that the SM is favored in comparison to all other models. Furthermore, we discuss lepton flavor violating processes in the context of the Zee model. We find that these can be sizeable and close to the experimental limits. / <p>QC 20170221</p>

Ce mémoire a pour but de déterminer des nouvelles méthodes de détection de rupture et/ou de tendance. Après une brève introduction théorique sur les splines, plusieurs méthodes de détection de rupture existant déjà dans la littérature seront présentées. Puis, de nouvelles méthodes de détection de rupture qui utilisent les splines et la statistique bayésienne seront présentées. De plus, afin de bien comprendre d’où provient la méthode utilisant la statistique bayésienne, une introduction sur la théorie bayésienne sera présentée. À l’aide de simulations, nous effectuerons une comparaison de la puissance de toutes ces méthodes. Toujours en utilisant des simulations, une analyse plus en profondeur de la nouvelle méthode la plus efficace sera effectuée. Ensuite, celle-ci sera appliquée sur des données réelles. Une brève conclusion fera une récapitulation de ce mémoire. / This thesis aims to identify new change-point detection methods and/or trend in temporal data. After a brief theoretical introduction on splines, several existing change-point detection already in the literature will be presented. Then, new change-point detection methods using splines and Bayesian statistics will be presented. Moreover, in order to understand the method using Bayesian statistics, an introduction to Bayesian theory will be presented. Using simulations, we will make a comparison of the power of all these methods. Still using simulations, an analysis of the new most effective method will be performed. Then, this method will be applied to real data. A brief conclusion will make a summary of this thesis.

We present an innovative Bayesian method for estimation of statistical parameters of time series data. This method works by comparing coefficients of Karhunen-Lo\`{e}ve expansion of observed and synthetic data with known parameters. We show one new method for generating synthetic data with prescribed properties and we demonstrate on a numerical example how this method can be used for estimation of physically interesting features in power spectra calculated from observed light curves of some X-ray sources.

We provide a flexible means of estimating time-varying parameter models in a Bayesian framework. By specifying the state innovations to be characterized trough a threshold process that is driven by the absolute size of parameter changes, our model detects at each point in time whether a given regression coefficient is con stant or time-varying. Moreover, our framework accounts for model uncertainty in a data-based fashion through Bayesian shrinkage priors on the initial values of the states. In a simulation, we show that our model reliably identifies regime shifts in cases where the data generating processes display high, moderate, and low numbers of movements in the regression parameters. Finally, we illustrate the merits of our approach by means of two applications. In the first application we forecast the US equity premium and in the second application we investigate the macroeconomic effects of a US monetary policy shock. / Series: Research Report Series / Department of Statistics and Mathematics

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2017. / With an increase in opportunistically-collected data, statistical methods that can accommodate unstructured designs are increasingly useful. Spatial capturerecapture (SCR) has such potential, but its applicability for species that are strongly gregarious is uncertain. It assumes that average animal locations are spatially random and independent, which is violated for gregarious species. I used a data set for African elephants (Loxodonta africana) and data simulation to assess bias and precision of SCR population density estimates given violations in location independence. I found that estimates were negatively biased and likely too precise if non-independence was ignored. Encounter heterogeneity models produced more realistic precision but density estimates were positively biased. Lowest bias was achieved by estimating density of groups, group size, and then multiplying to estimate overall population density. Such findings have important implications for the reliability of population density estimates where data are collected by unstructured means. / LG2017