1,721,009 research outputs found
Statistical Inference for Elliptic and Hypo-elliptic Diffusions: Asymptotic Theory and Numerical Methodologies
Full text linkThe thesis aims to contribute to statistical inference for Stochastic Differential Equations (SDEs), a rich
model class of continuous-time nonlinear Markov processes. The scope of this work includes an impor-
tant model class characterised as hypo-elliptic SDEs that contain a degenerate diffusion matrix. The
statistical inference for hypo-elliptic models has been recently highlighted in both theory and practice but
was still not sufficiently understood analytically compared to the standard SDEs with non-degenerate
diffusion matrix, i.e. elliptic SDEs. To close this gap, we establish theoretical and numerical foundations
for parameter estimation of a broad class of SDEs, including the hypo-elliptic ones.
This thesis first introduces model frameworks that cover such a wide class of SDEs. We then pro-
pose time-discretisation schemes carefully designed for those model frameworks to construct tractable
likelihood functions that are key to conducting statistical inference for SDEs. The use of the developed
likelihood is justified via a standard asymptotic analysis in Statistics; precisely, we show that the max-
imum likelihood type estimator based on the likelihood has the desirable asymptotic properties such
as consistency and Central Limit Theorem (CLT) under the high-frequency observations regime, i.e.
the scenario where the step size between consecutive data points is sufficiently small. In particular,
the proposed estimators can achieve the CLT under a less restrictive condition on the data to make
the parameter estimates reliable with larger step sizes. We also propose tractable higher order time
discretisation schemes for SDEs, which can be used in parametric inference under the low-frequency
observations regime, where one needs to carry out Data Augmentation (DA), i.e. by augmenting the
missing data or latent variables between data points with simulation. We present analytical and numer-
ical results showcasing that the use of developed schemes in DA effectively reduces the discretisation
bias compared to the standard time-discretisation
Stochastic schemes motivated by energetics and Riemannian geometry: optimization, Markov chain Monte Carlo, optimal control and data assimilation
Full text linkStatistical algorithms not only involve drawing realizations from a given distribution or estimating the parameters of the related density, but a wider class of problems such as optimal control, data assimilation and non-convex optimization. Unlike a deterministic search algorithm, e.g. one based on quasi-Newton updates, stochastic search schemes can make use of concepts from both deterministic dynamics and stochastic theory of noise to strike a balance between exploitation and exploration in the design space. In the quest for more efficacious schemes, researchers have drawn on ideas from contemporary physics and differential geometry in arriving at suitably constrained dynamical systems that guide the search, and the work in this dissertation is similarly inspired. To start with, a survey of the state-of-the-art is presented in Chapter 1 to motivate and put in perspective the work in the chapters to follow. Chapter 2 dwells on a Riemannian geometric approach to non-convex optimization, wherein the flow that minimizes a given objective function with progressing iterations is constrained to live on a manifold defined using a metric derivable by treating the objective function as energy. Specifically, the underlying dynamical system is designed as a geometrically adapted Langevin stochastic differential equation (SDE). The same adaptation, albeit with a Riemannian metric given by the Fisher information matrix obtainable from the available likelihood, is used in Chapter 3 to arrive at an MCMC method. In Chapter 4, a time-recursive scheme for stochastic optimal control is proposed using SDEs integrated strictly forward in time, thus bypassing the computationally inexpedient forward-backward route to solve the Hamilton-Jacobi-Bellman (HJB) equation. We address the combined state-parameter estimation problem via stochastic filtering in Chapter 5, with a new proposal for the parameter dynamics for higher accuracy and faster convergence. The thesis is concluded in Chapter 6 with a summary and scope for future research
Exact simulation of diffusions and new inference methods for discrete time data : also included, the one-shot CFTP algorithms
No full textEThOS - Electronic Theses Online ServiceGBUnited Kingdo
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
MCMC methods for sampling function space
No full textApplied mathematics is concerned with developing models with predictive capability, and with probing those models to obtain qualitative and quantitative insight into the phenomena being modelled. Statistics is data-driven and is aimed at the development of methodologies to optimize the information derived from data. The increasing complexity of phenomena that scientists and engineers wish to model, together with our increased ability to gather, store and interrogate data, mean that the subjects of applied mathematics and statistics are increasingly required to work in conjunction in order to significantly progress understanding.This article is concerned with a research program at the interface between these two disciplines, aimed at problems in differential equations where profusion of data and the sophisticated model combine to produce the mathematical problem of obtaining information from a probability measure on function space. In this context there is an array of problems with a common mathematical structure, namely that the probability measure in question is a change of measure from a Gaussian. We illustrate the wide-ranging applicability of this structure. For problems whose solution is determined by a probability measure on function space, information about the solution can be obtained by sampling from this probability measure. One way to do this is through the use of Markov chain Monte-Carlo (MCMC) methods. We show how the common mathematical structure of the aforementioned problems can be exploited in the design of effective MCMC methods
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