where X is the design matrix, ∼ N (0, σI), and β ∼ N (β0, gσ(XTX)−1). The prior on σ is the Jeffreys prior, π(σ) ∝ 1 σ2 , and usually, β0 is taken to be 0 for simplification purposes. The appeal of the method is that there is only one free parameter g for all linear regression. Furthermore, the simplicity of the g-prior model generally leads to easily obtained analytical results. However, we st...

Goodness of fit tests can be categorized under several ways. One categorization may be due to the differences between observed and expected frequencies. The other categorization may be based upon the differences between some values of distribution functions. Still the other one may be based upon the divergence of one distribution from the other. Some widely used and well known divergences like ...

The Student-t regression model suffers from monotone likelihood. This means that the likelihood achieves its maximum value at infinite values of one or more of the parameters, in this case the unknown degrees of freedom. This leads to problems when one uses iterative algorithms to locate the solutions to the non-linear equations generated by the likelihood. Fonseca et al. (2008) deal with this ...

This study aimed to integrate Jeffreys Amazing Statistics Program in teaching and Probability improve the engagement achievement of students. utilized pre-experimental method research design. The respondents were 120 ACTS Computer College Grade 11 Senior High Two instruments used this research: test questionnaires which served as formative summative tests a survey questionnaire form checklist w...

We propose a sampling-based Bayesian t test that allows researchers to quantify the statistical evidence in favor of the null hypothesis. This Savage-Dickey (SD) t test is inspired by the Jeffreys-Zellner-Siow (JZS) t test recently proposed by Rouder, Speckman, Sun, Morey, and Iverson (2009). The SD test retains the key concepts of the JZS test but is applicable to a wider range of statistical ...

This paper is a study of the application of Bayesian Exponentially Tilted Empirical Likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys’ method. For regression quantiles we derive the asymptotic form of the posterior density. We also exami...

In a simple multivariate normal prediction setting, derivation of a predictive distribution can flow from formal Bayes arguments as well as pivoting arguments. We look at two special cases and show that the classical invariant predictive distribution is based on a pivot that does not have a parameter free distribution – that is, is not an ancillary statistic. In contrast, a predictive distribut...

In this paper, we propose one new confidence interval for the binomial proportion; our interval is based on the Edgeworth expansion of a logit transformation of the sample proportion. We provide theoretical justification for the proposed interval and also compare the finite-sample performance of the proposed interval with the three best existing intervals-the Wilson interval, the Agresti-Coull ...