A Bayesian look at diagnostics in the univariate linear model

This paper develops diagnostics for data thought to be generated in accordance with the general univariate linear model. A first set of diagnostics is developed by considering posterior probabilities of models that dictate which of k observations form a sample of n observations (k < n/2) are spuriously generated, giving rise to the possible outlyingness of the k observations considered. This in turn gives rise to diagnostics to help assess (estimate) the value of k. A second set of diagnostics is found by using the Kullback-Leibler symmetric divergence, which is found to generate measures of outlyingness and influence. Both sets of diagnostics are compared and related to each other and to other diagnostic statistics suggested in the literature. An example to illustrate to the use of these diagnostic procedures is included

Comparing probabilistic methods for outlier detection

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived

A Bayesian look at diagnostics in the univariate linear model.

This paper develops diagnostics for data thought to be generated in accordance with the general univariate linear model. A first set of diagnostics is developed by considering posterior probabilities of models that dictate which of k observations form a sample of n observations (kspurious and outlying observations; posteriors of models; leverage; Kullback-Leibler measures; outlying and influential observations;

Comparing probabilistic methods for outlier detection.

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived.Diagnostic; Posterior and Predictive distributions; Leverage; Linear models;

A bayesian approach for predicting with polynomial regresión of unknown degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data

Hislop v. Canada: A Retroactive Look

Under the traditional “Blackstonian” approach, a section 52(1) declaration of constitutional invalidity is deemed to be fully retroactive based on the the ory that a government does not have authority to enact an unconstitutional law. Without abandoning this traditional approach, the Supreme Court of Canada has held that a fully retroactive declaration is not always a practical solution and for this reason, among others, has strayed from the traditional approach and limited the retroactive nature of declarations of invalidity in many cases. This paper examines the ways in which the Supreme Court has limited the fully retroactive nature of declarations of invalidity, namely (i) temporary suspensions; (ii) prospective overrulings accompanied by transition periods; (iii) the doctrine of qualified immunity; (iv) the general rule limiting individual remedies in combination with a declaration of invalidity; and (v) res judicata and the de facto doctrine. It the n proceeds to analyze the Court’s decision in Hislop v. Canada, in which the Court attempts to reconcile its previous rulings on the retroactive nature of declarations with the traditional the oretical approach. Finally, this paper critically analyzes the new test developed in Hislop to determine whether a section 52 declaration has retroactive effect

Criminal Lawyers’ Assn. v. Ontario: A Limited Right to Government Information under Section 2(b) of the Charter

Before the development of access to information legislation, government information was not generally available to the public. While the emergence of access to information legislation in Canadian jurisdictions reflected important public policy decisions that providing access to information promotes good government, the courts had always recognized that there was no constitutional right to require the government to disclose information in its possession. In Criminal Lawyers’ Assn. v. Ontario (Ministry of Public Safety and Security) the Supreme Court of Canada unanimously reached the novel conclusion that the right to freedom of information protected by section 2(b) of the Charter contained, in limited circumstances, a derivative right to government information. The new right to government information recognized by the Court is an extremely narrow right, limited to situations “where access is necessary to permit meaningful discussion on a matter of public importance, subject to privileges and functional constraints”. This article discusses the content of the new limited right to government information and its implications

A Bayesian Approach for Predicting with Polynomial Regresión of Unknown Degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data.