No evidence for persistent natural plague reservoirs in historical and modern Europe.

Caused by Yersinia pestis, plague ravaged the world through three known pandemics: the First or the Justinianic (6th-8th century); the Second (beginning with the Black Death during c.1338-1353 and lasting until the 19th century); and the Third (which became global in 1894). It is debatable whether Y. pestis persisted in European wildlife reservoirs or was repeatedly introduced from outside Europe (as covered by European Union and the British Isles). Here, we analyze environmental data (soil characteristics and climate) from active Chinese plague reservoirs to assess whether such environmental conditions in Europe had ever supported "natural plague reservoirs". We have used new statistical methods which are validated through predicting the presence of modern plague reservoirs in the western United States. We find no support for persistent natural plague reservoirs in either historical or modern Europe. Two factors make Europe unfavorable for long-term plague reservoirs: 1) Soil texture and biochemistry and 2) low rodent diversity. By comparing rodent communities in Europe with those in China and the United States, we conclude that a lack of suitable host species might be the main reason for the absence of plague reservoirs in Europe today. These findings support the hypothesis that long-term plague reservoirs did not exist in Europe and therefore question the importance of wildlife rodent species as the primary plague hosts in Europe.

Jackknife approach to the estimation of mutual information.

Quantifying the dependence between two random variables is a fundamental issue in data analysis, and thus many measures have been proposed. Recent studies have focused on the renowned mutual information (MI) [Reshef DN, et al. (2011) Science 334:1518-1524]. However, "Unfortunately, reliably estimating mutual information from finite continuous data remains a significant and unresolved problem" [Kinney JB, Atwal GS (2014) Proc Natl Acad Sci USA 111:3354-3359]. In this paper, we examine the kernel estimation of MI and show that the bandwidths involved should be equalized. We consider a jackknife version of the kernel estimate with equalized bandwidth and allow the bandwidth to vary over an interval. We estimate the MI by the largest value among these kernel estimates and establish the associated theoretical underpinnings.

Estimation and tests for power-transformed and threshold GARCH models.

Consider a class of power-transformed and threshold GARCH ( p , q ) (PTTGRACH ( p , q ) ) model, which is a natural generalization of power-transformed and threshold GARCH(1,1) model in Hwang and Basawa [2004. Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes. Statistics & Probability Letters 68, 209-220.] and includes the standard GARCH model and many other models as special cases. We first establish the asymptotic normality for quasi-maximum likelihood estimators (QMLE) of the parameters under the condition that the error distribution has finite fourth moment. For the case of heavy-tailed errors, we propose a least absolute deviations estimation (LADE) for PTTGARCH ( p , q ) model, and prove that the LADE is asymptotically normally distributed under very weak moment conditions. This paves the way for a statistical inference based on asymptotic normality for heavy-tailed PTTGARCH ( p , q ) models. As a consequence, we can construct the Wald test for GARCH structure and discuss the order selection problem in heavy-tailed cases. Numerical results show that LADE is more accurate than QMLE for heavy-tailed errors. Furthermore, the theory is applied to the daily returns of the Hong Kong Hang Seng Index, which suggests that asymmetry and nonlinearity could be present in the financial time series and the PTTGARCH model is capable of capturing these characteristics. As for the probabilistic structure of PTTGARCH ( p , q ) model, we give in the appendix a necessary and sufficient condition for the existence of a strictly stationary solution of the model, the existence of the moments and the tail behavior of the strictly stationary solution.

Cumulative effects of air pollution on public health.

Cumulative effect is an important way through which the pollutants affect public health. However, few existing dynamical models are well enough understood and documented to detect or quantify the cumulative effects and to answer pertinent questions posed by the World Health Organization (WHO): 'Is there a threshold below which no effects of the pollutants on health are expected to occur in all people?' and 'What averaging period (time pattern) is the most relevant from the point of view of health?'. Using a new semi-parametric time series modelling approach, which incorporates non-linearity and latent cumulative variables, we show that the cumulative effects on health due to continual exposure to environmental pollutants can be very serious even at levels below the national ambient air quality standards of America (NAAQS). The situation is especially worrying for chronic sufferers. Our study suggests that different pollutants may require different cumulative periods (on average) to impact on health but they share a similar functional form in respect of their impact. We also suggest some possible revision of the ambient air quality standards.

Smoothing for spatiotemporal models and its application to modeling muskrat-mink interaction.

For a set of spatially dependent dynamical models, we propose a method for estimating parameters that control temporal dynamics by spatial smoothing. The new approach is particularly relevant for analyzing spatially distributed panels of short time series. The asymptotic results show that spatial smoothing will improve the estimation in the presence of nugget effect, even when the sample size in each location is large. The proposed methodology is used to analyze the annual mink and muskrat data collected in a period of 25 years in 81 Canadian locations. Based on the proposed method, we are able to model the temporal dynamics which reflects the food chain interaction of the two species.