Bayes Hilbert Spaces

A Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives. The present contribution shows the subspace of square‐log‐integrable densities to be a Hilbert space, which can include probability and infinite measures, measures on the whole real line or discrete measures. It extends the ideas from the Hilbert space of densities on a finite support towards Hilbert spaces on general measure spaces. It is also a generalisation of the Euclidean structure of the simplex, the sample space of random compositions. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. A key tool is the centred‐log‐ratio transformation, a generalization of that used in compositional data analysis, which maps the Hilbert space of measures into a subspace of square‐integrable functions. As a consequence of this structure, distances between densities, orthonormal bases, and Fourier series representing measures become available. As an application, Fourier series of normal distributions and distances between them are derived, and an example related to grain size distributions is presented. The geometry of the sample space of random compositions, known as Aitchison geometry of the simplex, is obtained as a particular case of the Hilbert space when the measures have discrete and finite support.     

Mental Health Consultation on the College Campus

Abstract

“Mild Hypertension: When and How to Treat,” NORMAN M. KAPLAN. “Early and aggressive” drug therapy for mild hypertension, now widely prescribed in the United States, may be inappropriate for many of the 30 million patients with this condition. Although all of these patients are at greater risks of premature cardiovascular disease, the risks are manifested neither quickly nor uniformly. Drug therapy has not proved beneficial for patients with a diastolic (D) BP reading below 100 mm Hg, particularly those patients who are otherwise at low risk. Those antihypertensive drugs that are available now carry risks along with their benefits. Therefore, persons with mild hypertension who are at low risk should be encouraged to use nondrug therapies for at least six to 12 monts. If their DBP remains below 100 mm Hg, they may be better off than if they were given drugs. The drug used in initial therapy has usually been a diuretic. For many patients, however, an adrenergic inhibitor may be a more appropriate choice.     

Essential Data Elements for Reporters of Elder Abuse

Most states' adult or elder protective services and aging agency personnel prepare annual reports about their protective services. These reports vary by state and have different terms for the reporter of abuse. Reviewing annual reports from 46 states and the District of Columbia, 248 different terms were used for the reporter of abuse. To develop essential data elements for reporters of abuse, a literature search, a compilation of state elder abuse annual report list of abuse reporters, and a sorting exercise were conducted. Eleven terms were recommended for the different reporters of abuse, encouraging all state administrators and caseworkers to reach consensus to standardize the language.     

Trends in Education for Social Work Practice with Groups

A survey study of groupwork educators in graduate schools of social work indicated that group process and group-work methods courses continue to attract large numbers of students despite movement by schools away from single-method concentrations. Experiential learning groups, groupwork process records, and videotape instruction are the most widely used teaching tools of groupwork faculty. Critical problems facing groupwork educators include lack of methodological specificity in groupwork, the knowledge explosion in the group methods, and poorly developed group-work courses in schools of social work. The problem exists of determining what to teach and how to teach group methods.     

Defining the Professional Foundation in Social Work Education

Abstract

This paper reports the results of a national study designed to identify preferred curriculum content important to the “professional foundation” in social work education. All BSW program directors were surveyed, using the Delphi Technique, to evaluate potential curriculum content The heavy response indicated a strong interest in this timely issue. The authors found that there is a high degree of consensus on curriculum material thought to be appropriate for a professional foundation.