Modus Ponens and Modus Tollens for Conditional Probabilities,and Updating on Uncertain Evidence

There are narrowest bounds for P(h) when P(e)  =  y and P(h/e)  =  x, which bounds collapse to x as y goes to 1. A theorem for these bounds – Bounds for Probable Modus Ponens – entails a principle for updating on possibly uncertain evidence subject to these bounds that is a generalization of the principle for updating by conditioning on certain evidence. This way of updating on possibly uncertain evidence is appropriate when updating by ‘probability kinematics’ or ‘Jeffrey-conditioning’ is, and apparently in countless other cases as well. A more complicated theorem due to Karl Wagner – Bounds for Probable Modus Tollens – registers narrowest bounds for P(∼h) when P(∼e) =  y and P(e/h)  =  x. This theorem serves another principle for updating on possibly uncertain evidence that might be termed ‘contraditioning’, though it is for a way of updating that seems in practice to be frequently not appropriate. It is definitely not a way of putting down a theory – for example, a random-chance theory of the apparent fine-tuning for life of the parameters of standard physics – merely on the ground that the theory made extremely unlikely conditions of which we are now nearly certain. These theorems for bounds and updating are addressed to standard conditional probabilities defined as ratios of probabilities. Adaptations for Hosiasson-Lindenbaum ‘free-standing’ conditional probabilities are provided. The extended on-line version of this article (URL: ) includes appendices and expansions of several notes. Appendix A contains demonstrations and confirmations of elements of those adaptations. Appendix B discusses and elaborates analogues of modus ponens and modus tollens for probabilities and conditional probabilities found in Elliott Sober’s “Intelligent Design and Probability Reasoning.” Appendix C adds to observations made below regarding relations of Probability Kinematics and updating subject to Bounds for Probable Modus Ponens.      

“I would do it again”: Past and present experiences of older lesbians

ABSTRACT

Few studies have asked older lesbians to reflect on the primary experiences of their life. The following provides the responses of a nationally representative sample of 221 lesbians over the age of 55 to an open-ended question on anything they wanted to share. Through triangulated data analysis, resulting themes include the importance of the Women’s Movement, coming out, as well as the role of discrimination. Underlying each of these were the importance of social connection and for some the increasing experience of disconnection. Implications for gerontology practice, policy, and future research are included.     

‘You've got to trust her and she's got to trust you’: children's views on participation in the child protection system

Participation by children in child protection remains a complex area of practice. This paper presents findings from a qualitative study exploring the views of 26 children, aged 6–17 years, about their participation in the child protection system in England. All of the children were subject to a child protection plan and were living at home at the time of interview. The children's understanding of the child protection process was categorized, and the majority of children, including the youngest, were found be at least partially aware of the child protection process, often struggling to make sense of the professional intervention in their families on the basis of partial information. It is argued that decisions about children's involvement should take into account not only children's age and understanding, but be seen in the context of wider family dynamics. Participation in formal processes such as child protection conferences was experienced as difficult and emotive. The child's relationship with their social worker was central to meaningful participation.     

Joint covariate selection and joint subspace selection for multiple classification problems

We address the problem of recovering a common set of covariates that are relevant simultaneously to several classification problems. By penalizing the sum of ℓ ₂ norms of the blocks of coefficients associated with each covariate across different classification problems, similar sparsity patterns in all models are encouraged. To take computational advantage of the sparsity of solutions at high regularization levels, we propose a blockwise path-following scheme that approximately traces the regularization path. As the regularization coefficient decreases, the algorithm maintains and updates concurrently a growing set of covariates that are simultaneously active for all problems. We also show how to use random projections to extend this approach to the problem of joint subspace selection, where multiple predictors are found in a common low-dimensional subspace. We present theoretical results showing that this random projection approach converges to the solution yielded by trace-norm regularization. Finally, we present a variety of experimental results exploring joint covariate selection and joint subspace selection, comparing the path-following approach to competing algorithms in terms of prediction accuracy and running time.     

Near-optimal control policy for loss networks

In this paper, the phenomenon of the optimal management of requests of service in general networks is formulated as a control problem for a finite number of multiserver loss queues with Markovian routing. This type of problem may arise in a wide range of fields, e.g., manufacturing industries, storage facilities, computer networks, and communication systems. Using inductive approach of dynamic programming, the optimal admission control can be induced to be the functions of the number of requested service in progress. However, for large-scale network, the computational burden to find optimal control policy may be infeasible due to its involvement of the states for all stations in the networks. Hence, the idea of bottleneck modeling is borrowed to compute the near-optimal admission control policy. We reduced the scale of loss network and decreased the difference between the original and reduced models by making compensation for system parameters. A novel method is proposed in this paper to compute the compensation. Numerical results show that the near-optimal control policy demonstrates close performance to the optimal policy.     

The Role of Openness to Experience and Sexual Identity Formation in LGB Individuals: Implications for Mental Health

Openness to experience has been shown to have a positive impact on mental health in the general population, but there is a dearth of information both about why this is the case and on LGB populations in this area. The present article explores the relationship between openness to experience, LGB identity development, and mental health. The results revealed a full mediation model, where the positive impact of openness to experience on mental health is fully mediated by positive LGB identity development. Limitations and implications are discussed.     

Patterns in autobiographical reminiscing among early adults: Implications for forgiveness and self‐compassion

The ways early adults recount autobiographical experiences are associated with adjustment. Most prior research on autobiographical reminiscing has taken a variable‐oriented approach to examine relations of reminiscing variables with outcomes. The present study takes a person‐oriented approach to (a) identify systematic within‐individual patterns of reminiscing across multiple autobiographical memories; and (b) examine whether these patterns of reminiscing are uniquely related to self‐compassion and forgiveness. Participants were early adults (18 to 24 years) from undergraduate (n = 221) and community (n = 145) contexts. Participants self‐reported forgiveness and self‐compassion and described three autobiographical memories about past challenges: (a) a time they hurt someone else; (b) a time they were hurt by someone; and (c) a time they experienced a personal setback. Each memory was rated for positive self‐meaning (personal growth) and distancing of the current self from the past event (subjective distancing). Cluster analyses showed three subgroup patterns for personal growth and five subgroup patterns for subjective distancing. Participants displaying a pattern of higher personal growth across memories reported the highest forgiveness. Findings point to meaningful heterogeneity in autobiographical reminiscing and support the utility of a person‐oriented approach in providing a holistic view of early adults’ approaches for recollecting lived experiences.     

Establishing auditory-tactile-visual equivalence classes in children with autism and developmental delays

The Analysis of Verbal Behavior - The current study sought to evaluate the efficacy of a stimulus equivalence training procedure in establishing auditory–tactile–visual stimulus classes...     

Happiness Vs Contentment? A Case for a Sociology of the Good Life

Despite the enormous growth in happiness research in recent decades, there remains a lack of consistency in the use of the terms happiness, satisfaction, contentment and well‐being. In this article I argue for a sociologically grounded distinction between happiness and contentment that defines the former as positive affect and the latter as positive reflection. Contentment is therefore understood as a fulfilling relationship with the self and society (to borrow from G.H. Mead's terminology) and happiness involves pleasurable experiences. There is a history of similar distinctions in philosophy and psychoanalysis, but much of the contemporary discourse fails to distinguish between individual and collective definitions of happiness. This article will argue that happiness and contentment ought not to be treated as competing approaches to the good life, but as complimentary forms of emotional experience. Further, I argue that the current interest in happiness can be linked to larger culture shifts involving neoliberalism and individualism.