High Dimensional Statistical Modelling with Limited Information
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8MbAbstractModern scientific experiments often rely on different statistical tools, regularisation being one of them. Regularisation methods are usually used to avoid overfitting but we may also want use regularisation methods for variable selection, especially when the number of modelling parameters are higher than the total number of observations. However, performing variable selection can often be difficult under limited information and we may get a misspecified model. To overcome this issue, we propose a robust variable selection routine using a Bayesian hierarchical model. We adapt the framework of Narisetty and He to propose a novel spike and slab prior specification for the regression coefficients. We take inspiration from the imprecise beta model and use a set of beta distributions to specify the prior expectation of the selection probability. We perform a robust Bayesian analysis over this set of distributions in order to incorporate expert opinion in an efficient manner. We also discuss novel results on likelihood based approaches for variable selection. We exploit the framework of the adaptive LASSO to propose sensitivity analyses of LASSO type problems. The sensitivity analysis also gives us a novel non deterministic classifier for high dimensional problems, which we illustrate using real datasets. Finally, we illustrate our novel robust Bayesian variable selection using synthetic and real world data. We show the importance of prior hermes replica mens h belt
elicitation in variable selection as well as model fitting and compare our method with other Bayesian approaches for variable selection.