Coherent frequentism

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalize

Probabilistic Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.Comment: 26 pages. A preliminary version appeared in Proc. 9th Conference on Theoretical Aspects of Rationality and Knowledge (TARK'03

Improving the quality of care of children in community clinics: an intervention and evaluation in Bangladesh.

Community health care providers (CHCPs) in 40 rural community clinics of Comilla district, Bangladesh, were trained using a newly developed case-management job aid based on the World Health Organization Integrated Management of Childhood Illness and a communication guide.To assess 1) the change in knowledge of the CHCPs after training; 2) the absolute quality of care provided by the CHCPs (determined as the proportion of children aged <5 years [under-fives] correctly diagnosed, treated and referred); and 3) the consultation behaviour of the CHCPs.Change in knowledge was assessed by tests pre-and post-training. The quality of care was determined by reassessments at the clinic exit by a medical officer, without a baseline comparison. Consultation behaviour was assessed through direct observation. The study was performed during 2014-2015.The mean standard knowledge score of the CH-CPs increased from 19 to 25 (P < 0.001). Of 1490 under-fives examined, 91% were correctly diagnosed, 86% were correctly treated and 99.5% received a correct referral decision. The CHCPs performed well on most of the measures of good communication, although one third did not explain the diagnosis and treatment to patients.The training was effective in changing knowledge. The CHCPs applied the knowledge gained and provided good quality care. Following these results, the Bangladesh Ministry of Health and Family Welfare has scaled up the training nationwide. The lessons learnt should be useful for other countries

Barriers to hospital and tuberculosis programme collaboration in China: context matters

Background: In many developing countries, programmes for ‘diseases of social importance’, such as tuberculosis (TB), have traditionally been organised as vertical services. In most of China, general hospitals are required to report and refer suspected TB cases to the TB programme for standardised diagnosis and treatment. General hospitals are the major contacts of health services for the TB patients. Despite the implementation of public–public/private mix, directly observed treatment, short-course, TB reporting and referral still remain a challenge. Objective: This study aims to identify barriers to the collaboration between the TB programme and general hospitals in China. Design: This is a qualitative study conducted in two purposefully selected counties in China: one in Zhejiang, a more affluent eastern province, and another in Guangxi, a poorer southwest province. Sixteen in-depth interviews were conducted and triangulated with document review and field notes. An open systems perspective, which views organisations as social systems, was adopted. Results: The most perceived problem appeared to be untimely reporting and referral associated with non-standardised prescriptions and hospitalisation by the general hospitals. These problems could be due to the financial incentives of the general hospitals, poor supervision from the TB programme to general hospitals, and lack of technical support from the TB programme to the general hospitals. However, contextual factors, such as different funding natures of different organisations, the prevalent medical and relationship cultures, and limited TB funding, could constrain the processes of collaboration between the TB programme and the general hospitals. Conclusions: The challenges in the TB programme and general hospital collaboration are rooted in the context. Improving collaboration should reduce the potential mistrust of the two organisations by aligning their interests, improving training, and improving supervision of TB control in the hospitals. In particular, effective regulatory mechanisms are crucial to alleviate the negative impact of the contextual factors and ensure smooth collaboration

An almost sure limit theorem for super-Brownian motion

We establish an almost sure scaling limit theorem for super-Brownian motion on $\mathbb{R}^d$ associated with the semi-linear equation $u_t = {1/2}\Delta u +\beta u-\alpha u^2$, where $\alpha$ and $\beta$ are positive constants. In this case, the spectral theoretical assumptions that required in Chen et al (2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in $\mathbb{R}^d$.Comment: 14 page

Stable non-standard imprecise probabilities

Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [8] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered "practically impossible" but not "logically impossible"