Statistical Inference: Model Selection and Nuisance Parameters

Description

This lecture covers statistical inference topics such as model selection using the Kullback-Leibler divergence, the Akaike information criterion, and the network information criterion. It also discusses dealing with nuisance parameters, modified profile likelihoods, and higher-order inference methods.

Official source

https://mediaspace.epfl.ch/media/0_g6esfman

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Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context of learning, this may be the selection of a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection.

The iPad is a brand of iOS and iPadOS-based tablet computers that are developed by Apple Inc, first introduced on January 27, 2010. The iPad range consists of the original iPad lineup and the flagship products iPad Mini, iPad Air, and iPad Pro. The iPhone's iOS operating system (OS) was initially used for the iPad but in September 2019, its OS was switched to a fork of iOS called iPadOS that has better support for the device's hardware and its user interface is customized for the tablets' larger screens.

The iPad Pro is a premium model of Apple's iPad tablet computer. It runs iPadOS, a tablet-optimized version of the iOS operating system. The original iPad Pro was introduced in September 2015, and ran iOS 9. It had an A9X chip, and came in two sizes: 9.7-inch and 12.9 inch. The second-generation iPad Pro, unveiled in June 2017, had an upgraded A10X Fusion chip and swapped the 9.7-inch screen for a larger 10.5-inch display. The third-generation iPad Pro, announced in October 2018, eliminated the home button, and featured Face ID; it came in 11-inch and 12.

The iPad Mini (branded and marketed as iPad mini) is a line of mini tablet computers designed, developed, and marketed by Apple Inc. It is a sub-series of the iPad line of tablets, with screen sizes of 7.9 inches and 8.3 inches. The first-generation iPad Mini was announced on October 23, 2012, and was released on November 2, 2012, in nearly all of Apple's markets. It featured similar internal specifications to the iPad 2, including its display resolution.

The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection. AIC is founded on information theory. When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process.