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It has been claimed and disputed that World War II has been followed by a `long peace', an unprecedented decline of war. We conduct a full changepoint analysis of well-documented, publicly-available battle deaths datasets, using new techniques that enable the robust detection of changes in the statistical properties of such heavy-tailed data. We first test and calibrate these techniques. We then demonstrate the existence of changes, independent of data presentation, at around 1910 and 1950 CE, bracketing the World Wars, and around the 1830s and 1994 CE. Our analysis provides a methodology for future investigations and an empirical basis for political and historical discussions., 24 pages, 11 figures

Circadian rhythms coordinate endogenous events with external signals, and are essential to biological function. When environmental contaminants affect these rhythms, the organism may experience fitness consequences such as reduced growth or increased susceptibility to pathogens. In their natural environment plants may be exposed to a wide range of industrial and agricultural pollutants. Here, we investigate how the addition of various metal salts to the environment can impact plant-circadian rhythms, via the promoter:luciferase system. The consequences of these environmental changes were found to be varied and complex. Therefore, in addition to Fourier-based analyses, we apply novel wavelet-based spectral hypothesis testing and clustering methodologies to organize and understand the data. We are able to classify broad sets of responses to environmental contaminants, including pollutants which increase, or decrease, the period, or which induce a lack of precision or disrupt any meaningful periodicity. The methods are general, and may be applied to discover common responses and hidden structures within a wide range of biological time series data.

The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical global autocorrelations can give misleading answers. This article introduces two estimators of the local partial autocorrelation function and establishes their asymptotic properties. The article then illustrates the use of these new estimators on both simulated and real time series. The examples clearly demonstrate the strong practical benefits of local estimators for time series that exhibit nonstationarities.

Rhythmic processes are found at all biological and ecological scales, and are fundamental to the efficient functioning of living systems in changing environments. The biochemical mechanisms underpinning these rhythms are therefore of importance, especially in the context of anthropogenic challenges such as pollution or changes in climate and land use. Here we develop and test a new method for clustering rhythmic biological data with a focus on circadian oscillations. The method combines locally stationary wavelet time series modelling with functional principal components analysis and thus extracts the time-scale patterns arising in a range of rhythmic data. We demonstrate the advantages of our methodology over alternative approaches, by means of a simulation study and real data applications, using both a published circadian dataset and a newly generated one. The new dataset records plant response to various levels of stress induced by a soil pollutant, a biological system where existing methods which assu...

Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display nonstationary behaviour, as is common in many biological systems, the established methodologies may be misleading. Therefore, there is a real need for new methodology that enables the formal comparison of nonstationary processes. As circadian behaviour is best understood in the spectral domain, here we develop novel hypothesis testing procedures in the (wavelet) spectral domain, embedding replicate information when available. The data are modelled as realisations of locally stationary wavelet processes, allowing us to define and rigorously estimate their evolutionary wavelet spectra. Motivated by three complementary applications in circadian biology, our new methodology allows the identification of three specific types of spectral difference. We demonstrate the advantages of our methodology over alternative approaches, by means of a comprehensive simulation study and real data applications, using both published and newly generated circadian datasets. In contrast to the current standard methodologies, our method successfully identifies differences within the motivating circadian datasets, and facilitates wider ranging analyses of rhythmic biological data in general.

Time series that arise on a graph or network arises in many scientific fields. In this paper we discuss a method for modelling and prediction of such time series with potentially complex characteristics. The method is based on the lifting scheme first proposed by Sweldens, a multiscale transformation suitable for irregular data with desirable properties. By repeated application of this algorithm we can transform the original network time series data into a simpler, lower dimensional time series object which is easier to forecast. The technique is illustrated with a data set arising from an energy time series application.

The limited availability of livers donated by deceased donors for transplantation means that not everyone who might benefit from the procedure can receive a graft, so any selection and allocation system must have clearly defined goals. The United Kingdom, in common with many other countries, has adopted a minimum benefit criterion of a greater than 50% probability of survival 5 years after transplantation. We investigated the impact of changing this minimum benefit criterion on a case mix of listed patients. The analysis was based on 5330 adult elective patients who underwent transplantation with livers from donation after brain death donors between January 1994 and December 2007. We examined the impact of balancing the number of registrations on the list with the number of available donor livers while allowing a 10% mortality rate and found that this would require a survival threshold of at least 74% at 5 years. According to historical data, the application of this more stringent criterion would significantly reduce the eligibility of older and nonwhite patients and patients with hepatocellular carcinoma or hepatitis C virus infections. Thus, if such undesirable restrictions on access to liver transplantation are to be avoided, we must consider alternative strategies such as the acceptance of higher transplant list mortality. Liver Transpl, 2012. © 2012 AASLD.