This book analyses selected algorithms for probabilistic or deterministic statistical phenomena in the following areas: sampling theory, estimation theory, tests of hypotheses and significance, curve-fitting, regression and correlation, analysis of variance, nonparametric tests, and analysis of time series, in addition to the presentation of my “Complex Probability Paradigm” applied to Monté Carlo Methods and to the Central Limit Theorem. As such, the book will be of interest to all scholars, researchers, and undergraduate and graduate students in mathematics, statistics, computer science, and science in general.
1. Who are you, in a few lines?
I have been teaching for many years and I have a passion for researching and teaching mathematics. I am currently an Associate Professor of Mathematics and Statistics at Notre Dame University-Louaizé (NDU), Lebanon, where I have worked since 2005. I hold three PhDs in Applied Mathematics, Computer Science, and in Applied Statistics and Probability, completed at Bircham International University through a distance learning program. I also hold two PhDs in Mathematics and Prognostics from the Lebanese University, Lebanon, and Aix-Marseille University, France. My broad research interests are in the field of applied mathematics, and I have published 23 international journal articles and six contributions to conference proceedings, in addition to three books on prognostics, on applied mathematics and computer science. I am currently developing a novel branch of pure and applied mathematics known as 'the complex probability paradigm', which joins probability theory with complex variables and analysis. Aside from my research, my greatest pleasure is sharing my knowledge with others. I firmly believe that mathematics is a gateway to our deepest mysteries, and I am devoted to contributing, however modestly, to the illustrious field of mathematics, hoping to follow in the footsteps of history's greatest mathematicians.
2. A perfect day starts with? And ends with?
A perfect day starts with an original theorem on my mind and it ends by a successful proof and simulation of this novel theorem.
3. Could you tell us how you started writing?
I started writing during my early years at school. I master three languages which are: my native language which is Arabic, French, and English. In my youth, I wanted to study literature and to become a writer till I discovered mathematics and science in general, with their extremely powerful methods of discovering and proving relative and absolute truth.
4. Do you think that the writer has a special role in our society?
I believe that history is made by men of literature, scientists, and philosophers who have conquered across all times all societies on the whole globe. They were the precursors of all revolutions that mankind has known since the dawn of humanity.
5. Your latest book is "The Analysis of Selected Algorithms for The Statistical Paradigm", published in two volumes. What is the message you want to convey to the readers?
Each time I work on the field of mathematics and statistics I find the pleasure to tackle the knowledge, the theorems, the proofs, and the applications of the theory of statistics and probability. In fact, each problem on statistics is like a riddle to be solved, a conquest to be won, and I become relieved and extremely happy when I reach the end of the solution. This verily proves two important facts: firstly, the power of mathematics and its models to deal with such kind of problems and secondly the power of the human mind that is able to understand such class of problems and to tame such a wild concept that is randomness, probability, stochasticity, uncertainty, chaos, chance, nondeterminism, and consequently statistics. I am truly astonished by the power of statistics and probability to deal with deterministic or random data and phenomena, and this feeling and impression never left me from the first time I was introduced to this branch of science and mathematics. I hope that in the present book I will convey and share this feeling with the reader. I hope also that he will discover and learn about the concepts and applications of its paradigm.
6. Why is it important to analyze algorithms?
The book develops methods for simulating simple or complicated processes or phenomena. If the computer can be made to imitate an experiment or a process, then by repeating the computer simulation with different data, we can draw statistical conclusions. Thus, a simulation of a wide spectrum of statistical processes on computers was done. The result and accuracy of all the algorithms are truly amazing and delightful; hence, this confirms two complementary accomplishments: first the triumphs of the theoretical calculations already established using different theorems and second the power and success of modern computers to verify them.
7. What are the key features of an algorithm?
What is original in this work, like the title of the book suggests, is firstly the analysis of a large array of statistical problems and secondly the seventy-two algorithms written for this array of applications. Both are my creation and they illustrate how statistical theory can be applied to solve and understand random or deterministic phenomena existent in innumerable branches of science and pertaining to different disciplines of knowledge. Though, this was not certainly possible without the help of all the books, websites, and encyclopedias that provided me with a very rich source of hints, information, and mathematics. The algorithms written are completely the result of a personal effort. The work was done using Microsoft Visual C++ due to its excellent well-definedness, modularity, portability, and efficiency. Moreover, they were executed on a workstation computer with parallel microprocessors to acquire a suitable speed and efficiency needed for these numerical and computational methods.
8. What does this book mean to you?
This book is entitled The Analysis of Selected Algorithms for the Statistical Paradigm and it includes the analysis of selected algorithms for probabilistic or deterministic statistical phenomena in the following areas: sampling theory, estimation theory, tests of hypotheses and significance, curve-fitting, regression and correlation, analysis of variance, nonparametric tests, and analysis of time series, in addition to the presentation of my “Complex Probability Paradigm” applied to Monté Carlo Methods and to the Central Limit Theorem. Why algorithms and why statistics? My background is a Ph.D. in Computer Science and a Ph.D. in Applied Mathematics, so I combined my knowledge in computers and Applied Mathematics with statistics and I wrote this manuscript. Eager to learn and discover more as well as to apply my knowledge in mathematics and computer science, I embarked on this new research on statistical theory.
9. How was the publishing experience like? Describe Generis Publishing in a few words.
Generis Publishing is a very professional publisher giving the chance to any writer on the globe to publish his work and to share his findings with all kind of readers. I found my publishing experience with Generis very pleasant and I will repeat without any doubt this experience with other publications in the future.