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Exploring Monte Carlo Methods
BOOKS AND MEDIA
Q&A
Exploring Monte Carlo Methods
Prof Jackie Ying
This book presents an introduction to Monte Carlo methods with some coverage of applications in radiation transport. It serves, in the main, as an introduction to these techniques at the graduate and undergraduate level.
A*Star | Editor-in Chief, Nano Today
Prof Jackie Ying is the Editor-in-Chief of our sister publication, Nano Today, as well as a leading light within the nanotech arena. Materials Today caught up with Jackie at the recent Nano Today Conference. MT: Can you and tell us about your background? JY: I’m the editor-in-chief of Nano Today and I’m also the Executive Director of the Institute of Bioengineering and Nanotechnology (IBN) in Singapore. MT: Can you tell us a little about your research? JY: My research interests are rather broad. We are working on a number of areas involving nanocomposite materials; in particular, we are looking at designing biomaterials for cell culture and for drug delivery. We try and create nanocomposites that lead to unique functionalities by exploiting the synergies between different types of components. MT: So, just what is the Institute of Bioengineering and Nanotechnology? JY: The institute was founded in 2003, and it’s a national research institute under Singapore’s Agency for Science, Technology and Research. We have about 170 staff, including around 30 graduate students. MT: In your opinion, what are the “hot” topics in nanotechnology right now? JY: Certainly nano medicine is a really hot area, as well as nano energy. We are very hopeful that with the advances that have been made recently in nano science and nano technology, that people will have more and more tools that will allow us to tailor materials and systems for specific functionalities and applications. At the end of the day, people want to see how we can generate useful devices that can be applied in everyday life, varying from energy all the way to medicine, and in between there are a variety of different possibilities as well.
To hear more from Jackie, as well as a plethora of speakers from academia and industry, visit our podcast page at www.materialstoday.com/podcasts or search for Materials Today on iTunes. To find out more about our sister publications Nano Today and Nano Energy, visit www.elsevier.com.
Ajay Jasra | [email protected] Monte Carlo techniques are broadly methods designed to approximate high-dimensional integrals, which appear in a wide variety of real applications including engineering, statistics, physics, and finance. Their use is wide-spread both in academia and industry for their (supposed) ability to deal with the curse of dimensionality. This is only true in some cases; however, it is certainly preferable, in most scenarios, to deterministic numerical techniques. The literature on Monte Carlo methods has become quite mature in both physics and statistics. The book provides a simple introduction to various Monte Carlo methods for the first eight chapters. Afterward, reflecting the background of the authors as nuclear engineers, the book focuses for two chapters, upon applications in radiation transport. Specifically, the book provides an introduction to Monte Carlo methods, starting with the motivation (Chapter 1), a theoretical justification (2) (i.e., the strong law of large numbers and the central limit theorem), and then moving towards the simulation of random variables. In this direction the authors follow the logical route of describing pseudo random number generators (3), inversion, and rejection sampling (4). This is followed by some ideas on variance reduction (4), such as importance sampling and stratified sampling. The authors then move onto more advanced techniques such as Markov chain Monte Carlo (6), inverse Monte Carlo (7), and techniques for linear operator equations (8). The final two chapters are on applications, first describing neutral particle methods (9) and the application of Monte Carlo in this field (10). There is also an appendix giving some details on probability distributions, the strong law of large numbers and the central limit theorem. The authors also include some Monte Carlo codes for particle transport. In terms of the book providing an introductory account to Monte Carlo methods, it achieves this goal. However, there are many books which also do this (e.g., Monte Carlo Statistical Methods by C. Robert and G. Casella) and at a level which is both accessible and which are substantially more technically accurate. While the authors’ aim is to present a book which emphasizes
“practical implementations of Monte Carlo rather than on strict mathematical rigor”, the latter element is a little too lax. As an example, in Chapter 6, the authors discuss ergodic Markov chains, with a description that is not correct. If a reader is to understand anything about Markov chain Monte Carlo, an accurate description of this concept is a prerequisite. While one can certainly understand the method (if not how it actually works work), it is unlikely that a non-expert reader would fully grasp the concept without reference to another text. On this basis, the book does not manage to be a self-contained introduction to Monte Carlo methods. In addition, it is a little disappointing that the authors do not describe particle filtering methods, also known as Sequential Monte Carlo (Sequential Monte Carlo Methods in practice, A. Doucet, N. De Freitas, N. Gordon), which would be useful in nuclear engineering. More positively, the book provides non-technical students/researchers, who are less familiar with probability and statistics, with some ideas on how to use Monte Carlo methods and this is the strength of the book. The additions of Chapters 9 and 10 undoubtedly help Monte Carlo William L. Dunn & J. Kenneth Shultis Exploring Monte Carlo Methods Elsevier • 2011 • 398 pp ISBN: 978-0-444-51575-9 $ 121.00
to come alive for researchers and students in neutral particle transport. In addition, the code appendices are very useful resources. There is also some content which may not be familiar to all expert researchers in Monte Carlo methods such as inverse Monte Carlo. In addition, the coverage of the applications of Monte Carlo to the solution of linear differential equations is most welcome and illuminating. To my knowledge, these issues are seldom covered in Monte Carlo text-books (at least in statistics and probability) and this helps the book towards its ambitious objective of being useful to a broad wide audience. However, in my opinion, this latter goal is not achieved due to the imprecise nature of parts of the text.
JAN-FEB 2012 | VOLUME 15 | NUMBER 1-2
69
Q&A
Exploring Monte Carlo Methods
Prof Jackie Ying
This book presents an introduction to Monte Carlo methods with some coverage of applications in radiation transport. It serves, in the main, as an introduction to these techniques at the graduate and undergraduate level.
A*Star | Editor-in Chief, Nano Today
Prof Jackie Ying is the Editor-in-Chief of our sister publication, Nano Today, as well as a leading light within the nanotech arena. Materials Today caught up with Jackie at the recent Nano Today Conference. MT: Can you and tell us about your background? JY: I’m the editor-in-chief of Nano Today and I’m also the Executive Director of the Institute of Bioengineering and Nanotechnology (IBN) in Singapore. MT: Can you tell us a little about your research? JY: My research interests are rather broad. We are working on a number of areas involving nanocomposite materials; in particular, we are looking at designing biomaterials for cell culture and for drug delivery. We try and create nanocomposites that lead to unique functionalities by exploiting the synergies between different types of components. MT: So, just what is the Institute of Bioengineering and Nanotechnology? JY: The institute was founded in 2003, and it’s a national research institute under Singapore’s Agency for Science, Technology and Research. We have about 170 staff, including around 30 graduate students. MT: In your opinion, what are the “hot” topics in nanotechnology right now? JY: Certainly nano medicine is a really hot area, as well as nano energy. We are very hopeful that with the advances that have been made recently in nano science and nano technology, that people will have more and more tools that will allow us to tailor materials and systems for specific functionalities and applications. At the end of the day, people want to see how we can generate useful devices that can be applied in everyday life, varying from energy all the way to medicine, and in between there are a variety of different possibilities as well.
To hear more from Jackie, as well as a plethora of speakers from academia and industry, visit our podcast page at www.materialstoday.com/podcasts or search for Materials Today on iTunes. To find out more about our sister publications Nano Today and Nano Energy, visit www.elsevier.com.
Ajay Jasra | [email protected] Monte Carlo techniques are broadly methods designed to approximate high-dimensional integrals, which appear in a wide variety of real applications including engineering, statistics, physics, and finance. Their use is wide-spread both in academia and industry for their (supposed) ability to deal with the curse of dimensionality. This is only true in some cases; however, it is certainly preferable, in most scenarios, to deterministic numerical techniques. The literature on Monte Carlo methods has become quite mature in both physics and statistics. The book provides a simple introduction to various Monte Carlo methods for the first eight chapters. Afterward, reflecting the background of the authors as nuclear engineers, the book focuses for two chapters, upon applications in radiation transport. Specifically, the book provides an introduction to Monte Carlo methods, starting with the motivation (Chapter 1), a theoretical justification (2) (i.e., the strong law of large numbers and the central limit theorem), and then moving towards the simulation of random variables. In this direction the authors follow the logical route of describing pseudo random number generators (3), inversion, and rejection sampling (4). This is followed by some ideas on variance reduction (4), such as importance sampling and stratified sampling. The authors then move onto more advanced techniques such as Markov chain Monte Carlo (6), inverse Monte Carlo (7), and techniques for linear operator equations (8). The final two chapters are on applications, first describing neutral particle methods (9) and the application of Monte Carlo in this field (10). There is also an appendix giving some details on probability distributions, the strong law of large numbers and the central limit theorem. The authors also include some Monte Carlo codes for particle transport. In terms of the book providing an introductory account to Monte Carlo methods, it achieves this goal. However, there are many books which also do this (e.g., Monte Carlo Statistical Methods by C. Robert and G. Casella) and at a level which is both accessible and which are substantially more technically accurate. While the authors’ aim is to present a book which emphasizes
“practical implementations of Monte Carlo rather than on strict mathematical rigor”, the latter element is a little too lax. As an example, in Chapter 6, the authors discuss ergodic Markov chains, with a description that is not correct. If a reader is to understand anything about Markov chain Monte Carlo, an accurate description of this concept is a prerequisite. While one can certainly understand the method (if not how it actually works work), it is unlikely that a non-expert reader would fully grasp the concept without reference to another text. On this basis, the book does not manage to be a self-contained introduction to Monte Carlo methods. In addition, it is a little disappointing that the authors do not describe particle filtering methods, also known as Sequential Monte Carlo (Sequential Monte Carlo Methods in practice, A. Doucet, N. De Freitas, N. Gordon), which would be useful in nuclear engineering. More positively, the book provides non-technical students/researchers, who are less familiar with probability and statistics, with some ideas on how to use Monte Carlo methods and this is the strength of the book. The additions of Chapters 9 and 10 undoubtedly help Monte Carlo William L. Dunn & J. Kenneth Shultis Exploring Monte Carlo Methods Elsevier • 2011 • 398 pp ISBN: 978-0-444-51575-9 $ 121.00
to come alive for researchers and students in neutral particle transport. In addition, the code appendices are very useful resources. There is also some content which may not be familiar to all expert researchers in Monte Carlo methods such as inverse Monte Carlo. In addition, the coverage of the applications of Monte Carlo to the solution of linear differential equations is most welcome and illuminating. To my knowledge, these issues are seldom covered in Monte Carlo text-books (at least in statistics and probability) and this helps the book towards its ambitious objective of being useful to a broad wide audience. However, in my opinion, this latter goal is not achieved due to the imprecise nature of parts of the text.
JAN-FEB 2012 | VOLUME 15 | NUMBER 1-2
69