On the frequentist coverage of Bayesian credible intervals for lower bounded means

For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-\alpha)$ Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space. Various new properties are obtained. Namely, we identify precisely where the minimum coverage is obtained and we show that this minimum coverage is bounded between $1-\frac{3\alpha}{2}$ and $1-\frac{3\alpha}{2}+\frac{\alpha^2}{1+\alpha}$; with the lower bound $1-\frac{3\alpha}{2}$ improving (for $\alpha \leq 1/3$) on the previously established ([9]; [8]) lower bound $\frac{1-\alpha}{1+\alpha}$. Several illustrative examples are given.Comment: Published in at http://dx.doi.org/10.1214/08-EJS292 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluating Discharge Regimes of Karst Aquifer

Karst springs are typical for abrupt changes of discharge immediately following recharge events. Monitored discharges of springs are used to determine quantitative variability over the period of time, showing their reliability as dependable water sources. Karst aquifers also exhibit (at least) dual ground-water flow regimes, that is, fast (conduit-dominated) flow and slow (diffuse) flow. This is something that can be observed in nature as the fast change of water amount outflowing from the groundwater source, or described by rapidly responding hydrographs, recording water levels or discharges. Selection of proper investigative techniques characterizing discharge regime properties of a karst aquifer is therefore important in order to identify possible theoretical background models describing this behaviour. On this basis, we can also find a particular method of hydrograph separation into flow components linked to the fast-flow regime, slow-flow regime, or intermediate regimes as well. With this point in mind, several quantitative methods that might be particularly useful in hydrograph analysis of water outlets from the karst aquifer system are briefly discussed here