Statistics
http://hdl.handle.net/2262/76
Statistics2017-02-27T14:03:07ZVariational Bayes approximation for inverse regression problems
http://hdl.handle.net/2262/79383
Variational Bayes approximation for inverse regression problems
Vatsa, Richa
Inverse regression is a tool to predict an unknown explanatory variable for given observations of a response variable in a regression problem. The prediction problem is usually carried out in two stages: firstly, to fit the model relationship between the variables, and secondly, to predict the unknown explanatory variable. Both the problems, model fitting and prediction involve considerable computational burden. Previous work on the Bayesian approach to the problem have used MCMC, INLA and other numerical methods. This thesis aims to present an alternative fast variational Bayes (VB) approximation to Bayesian inference for inverse regression problems which claims to avoid the limitations of previous work. The VB method assumes independence between the parameters in the posterior distribution, thus provides fast approximations to Bayesian estimation problems. In contrast to INLA, it can be applied to models with many unknown parameters. In the thesis, the VB method is applied to a wider class of inverse regression problems classified into two classes: inverse latent regression and inverse non-latent regression which present challenges for the methodâ€™s accuracy and tractability. The VB method itself is not without limitations. Quick VB solutions are obtained at the cost of some loss of accuracy. Also, tractable application of the method is limited to conjugate- exponential (CE) models. It is attempted to increase the accuracy and tractability of the method outside CE models with the use of further approximations, such as a Gaussian approximation.
2011-01-01T00:00:00ZStatistical models for food authenticity
http://hdl.handle.net/2262/79374
Statistical models for food authenticity
Toher, Deirdre Ann
The authentication of food samples pose a particular problem for regulators. The routine testing of premium food products, most likely to be subject to manipulation for commercial gain, is only feasible if the testing method does not damage the product. Near Infrared (NIR) spectroscopy is one such method that is both fast and non-invasive. However, unlike other spectroscopic methods, peaks in the resulting NIR curves are at imprecise locations, requiring further statistical analysis if it is to be used for the classification of samples.
Three NIR datasets are examined in this thesis - two are related to the identification of adulterated samples, the third is a study on the identification of types of meats. Other commonly available, non-NIR, datasets are used for illustrative purposes.
2009-01-01T00:00:00ZAdvances in Bayesian model development and inversion in multivariate inverse inference problems : with application to palaeoclimate reconstruction
http://hdl.handle.net/2262/79366
Advances in Bayesian model development and inversion in multivariate inverse inference problems : with application to palaeoclimate reconstruction
Sweeney, James
An extremely challenging example of a multivariate inverse inference problem is the statistical reconstruction of palaeoclimate from fossil pollen data, which represents the motivating research problem considered in this thesis. The model training dataset, consisting of highly multivariate, zero-inflated compositional counts for vegetation, as well as measurements on several climate covariates, presents numerous challenges of model choice and inference. The addressing of these challenges provides the focus for the research contributions presented herein.
2012-01-01T00:00:00ZFast approximate inverse Bayesian inference in non-parametric multivariate regression with application to palaeoclimate reconstruction
http://hdl.handle.net/2262/78617
Fast approximate inverse Bayesian inference in non-parametric multivariate regression with application to palaeoclimate reconstruction
Salter-Townshend, Michael
Bayesian statistical methods often inyolye computationally intensive inference procedures. Sampling algorithms represent the current standard for fitting and testing models. Such methods, while flexible, are computationally intensive and suffer from long run times and high potential sampling error. New methods for fitting non-parametric approximations offer a fast and accurate alternative. Essentially, a multivariate Gaussian distribution is used to approximate the posterior of the model parameters.
2009-01-01T00:00:00Z