Nested Sampling for Uncertainty Quantification and Rare Event Estimation

Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The main idea of Nested Sampling is to replace a high-dimensional likelihood integral over parameter space with an integral over the unit line by employing a push-forward with respect to a suitable transformation. Practically, a set of active samples ascends the level sets of the integrand function, with the measure contraction of the super-level sets being statistically estimated. We justify the validity of this approach for integrands with non-negligible plateaus, and demonstrate Nested Sampling's practical effectiveness in estimating the (log-)probability of rare events.Comment: 24 page

Nested Sampling for Uncertainty Quantification and Rare Event Estimation

Nested sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The main idea of nested sampling is to replace a high-dimensional likelihood integral over parameter space with an integral over the unit line by employing a push-forward with respect to a suitable transformation. Practically, a set of active samples ascends the level sets of the integrand function, with the measure contraction of the superlevel sets being statistically estimated. We justify the validity of this approach for integrands with nonnegligible plateaus and demonstrate nested sampling’s practical effectiveness in estimating the (log-)probability of rare events

Staff costs of hospital-based outpatient care of patients with cystic fibrosis

BACKGROUND: This study identified per patient resource use and staff costs at a cystic fibrosis (CF) outpatient unit from the health care provider's perspective. METHODS: Personnel cost data were prospectively collected for all CF outpatients (n = 126) under routine conditions at the Charité Medical School Berlin in Germany over a six month study period. Patients were grouped according to age, sex and two severity categories. Ordinary least squares regression analysis was performed to determine the impact of various independent variables on personnel costs. RESULTS: The mean staff costs were €142.3 per patient over six months of outpatient service. Services provided by physicians were the biggest contributor to staff costs. Patient age correlated significantly and negatively with mean total costs per patient. CONCLUSIONS: Age of patient is a significant determinant of staff costs for CF outpatient care. For a cost-covering remuneration of outpatient treatment it seems plausible to create separate reimbursement rates for two or three age groups and to consider additional costs due to tasks carried out by physicians without direct patient contact. The relatively low staff costs identified by our study reflect a staffing level not sufficient for specialist CF outpatient care