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Englerophytum and Synsepalum are two closely related genera of trees and shrubs from the African tropics. Previous molecular studies have shown that these genera collectively form a clade within the subfamily Chrysophylloideae (Sapotaceae). However, little is known about the inter-relationships of the taxa within the Englerophytum-Synsepalum clade. In this study, nuclear ribosomal DNA and plastid trnH-psbA sequences were used to estimate the phylogeny within the clade. Results indicate that the clade consists of six major lineages, two composed solely of taxa from the genus Englerophytum and four composed of taxa from the genus Synsepalum. Each lineage can be distinguished by suites of vegetative and floral characters. Leaf venation patterns, calyx fusion, style length and staminodal structure were among the most useful characters for distinguishing clades. Some of the subclades within the Englerophytum-Synsepalum clade were also found to closely fit descriptions of former genera, most of which were described by Aubréville, that have since been placed in synonymy with Englerophytum and Synsepalum. The clade with the type species of Englerophytum also contains the type species of the genera Wildemaniodoxa and Zeyherella, which are confirmed as synonyms. © Trustees of the Royal Botanic Garden Edinburgh (2019).

Introduction The maximum likelihood framework set out in Part ONE is now applied to estimating and testing regression models. This chapter focusses on linear models, where the conditional mean of a dependent variable is specified to be a linear function of a set of exogenous variables. Extensions to this basic model are investigated in Chapter 6 (nonlinear regression), Chapter 7 (autocorrelation) and Chapter 8 (heteroskedasticity). Single equation models include the linear regression model and the constant mean model. For single equation regression models, the maximum likelihood estimator has an analytical solution that is equivalent to the ordinary least squares estimator. The class of multiple equation models includes simultaneous equation models with multiple dependent and exogenous variables, seemingly unrelated systems and recursive models. In this instance, the maximum likelihood estimator is known as the full information maximum likelihood (FIML) estimator because the entire system is used to estimate all of the model parameters jointly. The FIML estimator is related to the instrumental variable estimator commonly used to estimate simultaneous models and, in some cases, the two estimators are equivalent. Unlike linear single equation models, analytical solutions of the maximum likelihood estimator for systems of linear equations are only available in certain special cases. Many of the examples considered in Part ONE specify the distribution of the observable random variable, y t . Regression models, by contrast, specify the distribution of the unobservable disturbance, u t , which means that maximum likelihood estimation cannot be used directly because this method requires evaluating the log-likelihood function at the observed values of the data.

Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalised least squares and full information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, y t . Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of y t is known. (2) The specifications of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, θ. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of y t is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalised method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12).

Introduction In most of the models previously discussed, the dependent variable, y t , is assumed to be a continuous random variable. There are a number of situations where the continuity assumption is inappropriate and alternative classes of models must be specified to explain the time series features of discrete random variables. This chapter reviews the important class of discrete time series models commonly used in microeconometrics namely the probit, ordered probit and Poisson regression models. It also discusses some recent advances in the modelling of discrete random variables with particular emphasis on the binomial thinning model of Steutel and Van Harn (1979) and the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998), together with some of its extensions. Motivating Examples Recent empirical research in financial econometrics has emphasised the importance of discrete random variables. Here, data on the number of trades and the duration between trades are recorded at very high frequencies. The examples which follow all highlight the need for econometric models that deal with discrete random variables by preserving the distributional characteristics of the data. Example 21.1 Transactions Data on Trades Table 21.1 provides a snapshot of transactions data recorded every second, on the United States stock AMR, the parent company of American Airlines, on 1 August 2006. Three examples of discrete random variables can be obtained from the data in Table 21.1.

This book provides a general framework for specifying, estimating and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalised method of moments estimation, nonparametric estimation and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

The 2003 Comprehensive Peace Agreement (CPA) and the ensuing two-year-long National Transitional Government of Liberia (NTGL), which brought together two rebel forces, the former government and members of civil society, justifiably had many critics but also one positive and possibly redeeming feature. In spite of, or perhaps because of, the realpolitik nature of the CPA and the barely disguised gross corruption of the members of the coalition government, the protagonists in the second Liberian civil war (2000–03) complied with the agreement and the peace process held. The culmination of this sequence of events was the 11 October 2005 national elections, the 8 November presidential run-off and the 16 January 2006 inauguration. In several ways, this was the African post-conflict election that broke the mould, but not just in that a woman, Ellen Johnson-Sirleaf, won the presidential race, and a football star, George Weah, came second. The virtual absence of transformed rebel forces or an overbearing incumbent in the electoral races, partially as a result of the CPA and NTGL, gave these polls extraordinary features in an African setting.

For the best part of seven years, an increasing number of warring factions fought a vicious civil war for control of the West African state of Liberia. In August 1996, the fourteenth peace accord led to presidential and parliamentary elections in July of the following year. Charles Taylor and his National Patriotic Party (NPP), formed out of the original invasion force, emerged victorious with a landslide 75 per cent of the vote. Given the international reputation of Taylor as a brutal warlord whose sole aim had never wavered from the capture of power in Monrovia, Taylor's across-the-board victory appears difficult to explain. Having concluded that, despite problems and allegations, the election did seem more free and fair than not, the article examines the factors that probably influenced the electorate's choices. The results of this research show an election heavily dependent on an uncertain security situation. However, it suggests that, although a former ‘warlord’ has been rewarded, the voting was a reasoned ploy by the electorate to maximise the possibility of improved living conditions.

1. Introduction Donald Kelley and David Harris Sacks 2. Example and truth: Deggory Wheare and the ars historica J. H. M. Salmon 3. Truth, lies and fiction in sixteenth-century Protestant historiography Patrick Collinson 4. Thomas More and the English Renaissance: history and fiction in Utopia Joseph Levine 5. Ancestral and antiquarian: Little Crosby and early modern historical culture Daniel Woolf 6. Murder in Faversham: Holinshed's impertinent history Richard Helgerson 7. Foul, his Wife, the Mayor, and Foul's Mare: anecdote in Tudor historiography Annabel Patterson 8. Thomas Hobbes' Machiavellian moments David Wooton 9. The background of Hobbes' Behemoth Fritz Levy 10. Leviathan, mythic history, and natural historiography Patricia Springborg 11. Adam Smith and the history of private life Mark Phillips 12. Protesting fiction, constructing history Paul Hunter 13. Contemplative heroes and Gibbon's historical imagination Patricia Craddock 14. Experience, truth, and natural history in early English gardening books Rebecca Bushnell.