ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 03 Oct 2023 11:55:49 GMT2023-10-03T11:55:49Z5071- Data-informed influence analysishttps://scholarbank.nus.edu.sg/handle/10635/105079Title: Data-informed influence analysis
Authors: Critchley, F.; Marriott, P.
Abstract: The likelihood-based influence analysis methodology introduced in Cook (1986) uses a parameterised space of local perturbations of a base model. It is frequently the case that such perturbation schemes involve more parameters of interest and perturbation parameters than there are observations, and hence the perturbation space is often explored rather than estimated, where exploration means discovering the effect on inference of putatively choosing values of perturbation parameters. This paper considers the question of what can be learned about the perturbation parameters through the data. It extends Cook's methodology to take account of information available in the data regarding the perturbations, the general philosophy of the approach being that of learn what you can and explore what you cannot learn. Both local and global analyses are possible, as indicated by the data, while the eigenvector sign indeterminacy of local analysis is removed. Numerical examples are given and further developments are briefly indicated. © 2004 Biometrika Trust.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050792004-01-01T00:00:00Z
- On preferred point geometry in statisticshttps://scholarbank.nus.edu.sg/handle/10635/105262Title: On preferred point geometry in statistics
Authors: Critchley, F.; Marriott, P.; Salmon, M.
Abstract: A brief synopsis of progress in differential geometry in statistics is followed by a note of some points of tension in the developing relationship between these disciplines. The preferred point nature of much of statistics is described and suggests the adoption of a corresponding geometry which reduces these tensions. Applications of preferred point geometry in statistics are then reviewed. These include extensions of statistical manifolds, a statistical interpretation of duality in Amari's expected geometry, and removal of the apparent incompatibility between (Kullback-Leibler) divergence and geodesic distance. Equivalences between a number of new expected preferred point geometries are established and a new characterisation of total flatness shown. A preferred point geometry of influence analysis is briefly indicated. Technical details are kept to a minimum throughout to improve accessibility. © 2002 Elsevier Science B.V. All rights reserved.
Mon, 01 Apr 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052622002-04-01T00:00:00Z
- On the global geometry of parametric models and information recoveryhttps://scholarbank.nus.edu.sg/handle/10635/105274Title: On the global geometry of parametric models and information recovery
Authors: Marriott, P.; Vos, P.
Abstract: We examine the question of which statistic or statistics should be used in order to recover information important for inference. We take a global geometric viewpoint, developing the local geometry of Amari. By examining the behaviour of simple geometric models, we show how not only the local curvature properties of parametric families but also the global geometric structure can be of crucial importance in finite-sample analysis. The tool we use to explore this global geometry is the Karhunen-Loève decomposition. Using global geometry, we show that the maximum likelihood estimate is the most important one-dimensional summary of information, but that traditional methods of information recovery beyond the maximum likelihood estimate can perform poorly. We also use the global geometry to construct better information summaries to be used with the maximum likelihood estimate. © 2004 ISI/BS.
Sun, 01 Aug 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052742004-08-01T00:00:00Z
- Lifetime prediction from only present age: Fact or fiction?https://scholarbank.nus.edu.sg/handle/10635/105195Title: Lifetime prediction from only present age: Fact or fiction?
Authors: Ledford, A.; Marriott, P.; Crowder, M.
Abstract: We focus on the widely used method of J.R. Gott III for predicting future lifetime using only present age as confusion still reigns about whether it is justified. We provide a focused and precise examination of the method so that its validity or otherwise may be established unambiguously. © 2001 Elsevier Science B.V.
Mon, 05 Mar 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051952001-03-05T00:00:00Z
- Elemental thin film depth profiles by ion beam analysis using simulated annealing - A new toolhttps://scholarbank.nus.edu.sg/handle/10635/105496Title: Elemental thin film depth profiles by ion beam analysis using simulated annealing - A new tool
Authors: Jeynes, C.; Barradas, N.P.; Marriott, P.K.; Boudreault, G.; Jenkin, M.; Wendler, E.; Webb, R.P.
Abstract: Rutherford backscattering spectrometry (RBS) and related techniques have long been used to determine the elemental depth profiles in films a few nanometres to a few microns thick. However, although obtaining spectra is very easy, solving the inverse problem of extracting the depth profiles from the spectra is not possible analytically except for special cases. It is because these special cases include important classes of samples, and because skilled analysts are adept at extracting useful qualitative information from the data, that ion beam analysis is still an important technique. We have recently solved this inverse problem using the simulated annealing algorithm. We have implemented the solution in the 'IBA DataFurnace' code, which has been developed into a very versatile and general new software tool that analysts can now use to rapidly extract quantitative accurate depth profiles from real samples on an industrial scale. We review the features, applicability and validation of this new code together with other approaches to handling IBA (ion beam analysis) data, with particular attention being given to determining both the absolute accuracy of the depth profiles and statistically accurate error estimates. We include examples of analyses using RBS, non-Rutherford elastic scattering, elastic recoil detection and non-resonant nuclear reactions. High depth resolution and the use of multiple techniques simultaneously are both discussed. There is usually systematic ambiguity in IBA data and Butler's example of ambiguity (1990 Nucl. Instrum. Methods B 45 160-5) is reanalysed. Analyses are shown: of evaporated, sputtered, oxidized, ion implanted, ion beam mixed and annealed materials; of semiconductors, optical and magnetic multilayers, superconductors, tribological films and metals; and of oxides on Si, mixed metal suicides, boron nitride, GaN, SiC, mixed metal oxides, YBCO and polymers.
Mon, 07 Apr 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1054962003-04-07T00:00:00Z
- On the geometry of measurement error modelshttps://scholarbank.nus.edu.sg/handle/10635/105273Title: On the geometry of measurement error models
Authors: Marriott, P.
Abstract: The problem of undertaking inference in the classical linear model when the covariates have been measured with error is investigated from a geometric point of view. Under the assumption that the measurement error is small, relative to the total variation in the data, a new model is proposed which has good inferential properties. An inference technique which exploits the geometric structure is shown to be computationally simple, efficient and robust to measurement error. The method proposed is illustrated by simulation studies.
Mon, 01 Sep 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052732003-09-01T00:00:00Z
- On the local geometry of mixture modelshttps://scholarbank.nus.edu.sg/handle/10635/105277Title: On the local geometry of mixture models
Authors: Marriott, P.
Abstract: Despite the well-known difficulties of undertaking inference with mixture models, they are frequently used for modelling. These inferential problems arise because the underlying geometry of a mixture family is very complicated. This paper shows that by adding a simplifying assumption, which frequently is natural statistically, the geometric structure is reduced to a much more tractable form. This enables standard inferential techniques to be applied successfully. One result of studying the local geometry is that it unifies the convex and differential geometric theories of mixture models. The techniques proposed are applied to prediction, random effects and measurement error models. © 2002 Biometrika Trust.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052772002-01-01T00:00:00Z