2.1 Sufficient statistics. Classically, a " statistic " is a measurable function of the observations , say f (X 1 ,. .. , X n). The concept of " statistic " differs from that of " random variable " in that a random variable is defined on a probability space, so that one probability measure is singled out, where for statistics we have in mind a family of possible probability measures, R. A. Fish...

We outline in this paper a suite of methods, and illustrate their use, to empirically determine food self-sufficiency at a relatively small (Local Health Areas) level of geography. Further we have, after identifying regions of lowest food self-sufficiency in British Columbia (BC) superimposed these on regions whose populations have relatively poor dietary ill health. Approximately one third of ...

The common form of a mathematical theorem consists in that "the truth of some properties for some objects is necessary andlor sufficient condition for other properties to hold for other objects". To formalize this, one happens to resort to Kripke modal logic K which, having in the syntax the notions of 'property' and 'necessity', appears to provide a reliable metamathematical fundament. In this...

Many countries are facing a challenging transition toward more sustainable energy systems, which produce more renewables and consume less energy. The latter goal can only be achieved through a combination of efficiency measures and changes in people’s lifestyles and routine behaviors (i.e., sufficiency). While research has shown that acceptance of technical efficiency is relatively high, there ...

Sampling the full diversity of interactions in an ecological community is a highly intensive effort. Recent studies have demonstrated that many network metrics are sensitive to both sampling effort and network size. Here, we develop a statistical framework, based on bootstrap resampling, that aims to assess sampling sufficiency for some of the most widely used metrics in network ecology, namely...

1 2 Transportation planning has been playing a critical role in shaping the economic health and 3 quality of life. It not only provides insight into the mobility of people and goods, but also 4 influences patterns of growth and economic activity. Metropolitan transportation planning is a 5 challenging transportation topic due to the lack of future traffic information, such as evaluation 6 of th...

In this paper, we prove the stochastic version of the Positive Real Lemma (PRL), to study the stability problem of nonlinear systems in Lur’e form with stochastic uncertainty. We study the mean square stability problem of systems in Lur’e form with stochastic parametric uncertainty affecting the linear part of the system dynamics. The stochastic PRL result is then used to study the problem of s...

During pregnancy and lactation, mothers require significant amounts of calcium to pass on to the developing fetus and suckling neonate, respectively. Given the dependence of adult calcium concentrations and bone metabolism on vitamin D, one might anticipate that vitamin D sufficiency would be even more critical during pregnancy and lactation. However, maternal adaptations during pregnancy and l...