Bayesian inference with misspecified models

This article reviews Bayesian inference from the perspective that the designated model is misspecified. This misspecification has implications in interpretation of objects, such as the prior distribution, which has been the cause of recent questioning of the appropriateness of Bayesian inference in this scenario. The main focus of this article is to establish the suitability of applying the Bayes update to a misspecified model, and relies on representation theorems for sequences of symmetric distributions; the identification of parameter values of interest; and the construction of sequences of distributions which act as the guesses as to where the next observation is coming from. A conclusion is that a clear identification of the fundamental starting point for the Bayesian is described.     

A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly inflated. In response, we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroscedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by reexamining the results relating to U.S. stock returns data in Campbell and Yogo (2006 Campbell, J. Y. and Yogo, M. (2006), “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 81, 27–60.[Crossref], [Web of Science ®] , [Google Scholar]). Supplementary materials for this article are available online.     

The portfolio choice problem: comparison of certainty equivalence and optimal Bayes portfolios

For the portfolio problem with unknown parameter values, we compare the conventional certainty equivalence portfolio choice with the optimal Bayes portfolio. In the important single risky asset case a diffuse Bayes rule leads to portfolios that differ significantly from those suggested by a certainty equivalence rule which we show are inadmissible relative to a quadratic utility function for the range of parameters we consider. These results are invariant to arbitrary changes in the utility function parameters. We illustrate the results using a simple mutual fund example.     

Interval Estimation for the Difference of Two Independent Variances

Analytical methods for interval estimation of differences between variances have not been described. A simple analytical method is given for interval estimation of the difference between variances of two independent samples. It is shown, using simulations, that confidence intervals generated with this method have close to nominal coverage even when sample sizes are small and unequal and observations are highly skewed and leptokurtic, provided the difference in variances is not very large. The method is also adapted for testing the hypothesis of no difference between variances. The test is robust but slightly less powerful than Bonett's test with small samples.     

Computing Marginal Likelihoods via Posterior Sampling

This article presents a novel and simple approach to the estimation of a marginal likelihood, in a Bayesian context. The estimate is based on a Markov chain output which provides samples from the posterior distribution and an additional latent variable. It is the mean of this latent variable which provides the estimate for the value of the marginal likelihood.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

Statistics for Quality and Productivity: A New Graduate-Level Statistics Course

The growing popular realization that American product quality and productivity are no longer without challenge for world leadership presents an opportunity for the American statistical community to make stronger contributions to sound industrial practice than it has in the past. Management consultants, such as Deming and Juran, are promoting philosophies that contain strong statistical components and are being heard by top U.S. executives. There are thus growing opportunities for industrial statisticians. Upon reviewing the content of typical graduate-level statistical quality control courses and books in the light of the present situation, we find them to be inadequate and in some cases to suffer from inappropriate emphases. In this article we discuss our perceptions of what is needed in the way of a new graduate-level course in statistics for quality and productivity (SQP). We further offer for discussion a syllabus for such a course (which is a modification of one used at Iowa State in the 1983 spring semester), some comments on how specific topics might be approached, and also a partially annotated list of references for material that we believe belongs in a modern SQP course.     

Editor’s Introduction: All About the Mother

ABSTRACT

This short editorial note introduces a panel titled “All About the Mother” that is being presented in its original conference format with papers by Orna Guralnik, Jade McGleughlin, Julie Leavitt, and Stephen Hartman.     

How Can I Become More Secure?: A Grounded Theory of Earning Secure Attachment

The purpose of this study was to develop a grounded theory of earning secure attachment. This study included 15 women and 5 men who met the criteria of having a self-reported history of attachment insecurity and demonstrated evidence of earned security. The grand tour research question, How do adults with a history of insecure attachment earn security?, was explored using constructivist grounded theory and semi-structured interviews emphasizing processes of positive attachment change. The results describe a process model of change hinging on three interrelated categories: meta-conditions of positive attachment change, making intrapsychic changes, and making interpersonal changes. Clinical implications include the importance of clients committing to the process, clients working with a clinician trained in trauma-focused therapy, and clinicians being surrogate attachment figures for clients.     

Learning Under Authoritarianism: Strategic Adaptations Within International Foundations and NGOs in China

VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations - Within the field of international relations, scholarship supports the notion that international non-governmental...