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Petros G. Malakyan, PhD

associate professor of Leadership Studies, Center for Life Calling and Leadership, Indiana Wesleyan University

Dr. Edgar Elliston’s book, "Introduction to Missiological Research Design," has been an effective tool which has shaped the research of hundreds of doctoral students at Fuller Theological Seminary’s School of Intercultural Studies. It not only directs the reader step-by-step through the process of missiological research, it also gives the reasoning behind each process. Elliston has also included four essays written by preeminent scholars with each providing their perspective on research in their respective disciplines. In addition, several appendices give instruction on pre- and post-text issues, and common research errors. Exhaustive is the one word that comes to mind when describing the range of material contained in this book. After almost two decades of development, "Introduction to Missiological Research Design" is definitive. It will be an invaluable resource and a must-buy for anyone wishing to pursue missiological inquiry.

John Timothy Kauffman, PhD Intercultural Studies, ThM Missiology

Dr. Edgar (Eddie) J. Elliston has recently revised his classic work, "Introduction to Missiological Research Design," which was an invaluable guide to hundreds of us who, over the past fifteen years since its first publication, struggled to understand the inscrutable maze often surrounding missiological research, whether at the MA, ThM, PhD or post-doctorate level. Elliston’s book is an invaluable tool in the hands of novice and experienced researchers alike as he leads us through a step-by-step approach to credible research. He provides examples, exercises, checklists, a much-needed glossary of terms, and an up-to-date bibliography for in-depth investigation of specific issues. Perhaps most valuable is Elliston’s exploration of the ethical issues and errors that are inherent in missiological research. Elliston’s book is a refreshing, much-needed guide for those of us who still see research toward trustworthy findings and conclusions as decidedly necessary to mission integrity and effectiveness.

C. Neal Johnson, JD, PhD

former dean at Belhaven University and currently an international legal and missiological consultant

Part II Contributions from Other Disciplines

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by: Reg Reimer (Author)

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In 1975, Vietnam, united under communism, fell behind a bamboo curtain. Many feared the worst for churches there. But fifteen years later, churches, especially among Vietnam’s ethnic minority mountain peoples, suddenly exploded in number and vitality.

I have been waiting for this book. What a tantalizing mystery Vietnam is. The long heritage of the people. The trauma of war. Today’s hot economy. The continuing legacy of Marxist persecution. And, through it all, the church of Jesus Christ. What does it mean to be a Christian in this land? How have believers inside and outside the country offered wise witness, service, and advocacy? This book tells the story in solid context. Details never before revealed come to light.

In this section we complement the previous analysis by employing a copula approach to study the structure of dependence between GHGs and global temperature anomalies. A copula-based methodology is particularly useful to analyse the probability of joint multivariate extremes while it allows the use of different classes of probability distributions of events, that is, “those in which events are accompanied by well behaved, mild variations (e.g., Gaussian or thin tails), and those where small probabilities are associated with large variations that have no characteristic scale (fat tails)” (Taleb et al. CLARKS Womens Helina Alessia Flat Black CpDXB
, p. 5).

The concept of dependence embedded in copula functions is more general than standard correlation as it allows a specific modelling of different types of dependence structures. In particular, here we will examine the dependence structures in terms of types of copulas that have the best fit for our data and assess the hypothesis of a joint extreme event of (high) GHG emissions and temperature anomalies.

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Scatterplots of marginal standard normal distributions that are combined with (i) a Gaussian copula, (ii) a Student copula, (iii) a Clayton copula, (iv) a Gumbel copula and (v) a Frank copula (from left to right). All bivariate distributions have a Kendall’s tau correlation measure of roughly 0.6

$$ F\left( {\mathbf{x}} \right) = C\left( {F_{1} \left( {x_{1} } \right),F_{2} \left( {x_{2} } \right), \ldots ,F_{n} \left( {x_{n} } \right)} \right),\quad {\mathbf{x}} \in {\mathbf{R}}^{n} , $$

Here we restrict ourselves to bivariate copulas, \( C\left( {u_{1} , u_{2} } \right) \) , analysing the dependence structure of temperature anomalies ( \( u_{1} \) ) and emissions ( \( u_{2} \) ). The focus is not on a specific modelling of the marginal and joint distributions, but on the calibration of various copulas to see which has the best fit. Hence only the dependence structure (copula) is analysed and not the joint distribution function as such.

The Gaussian copula is the copula that is implied by a Gaussian distribution. The Student t copula is the copula that is implied by a Student t distribution. In contrast to the Gaussian copula it displays tail dependence. This means that it assigns a higher probability to joint extreme events than does the Gaussian copula. The lower the parameter \( \nu \) (“degrees of freedom”) the higher the tail dependence. If \( \nu \) is large, the Student t copula resembles a Gaussian copula. In fact, the Gaussian copula is a special case of the Student t copula, where \( \nu \to \infty \) . The Clayton copula displays lower tail dependence but no upper tail dependence. Loosely speaking, this means that there is a comparably high probability of joint extreme low realisations and a comparably low probability of joint extreme high realisations. The Gumbel copula displays upper tail dependence but no lower tail dependence. The Frank copula does not display tail dependence. Actually, the Frank copula assigns a lower probability to joint extreme events than does the Gaussian copula.

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