One can seldom consider mathematics-heavy books as exciting page-turners. Yet, Bayesian methods in the search for MH370 is so far the best one I have encountered that could stand up to such a description. Published by Springer in its “Briefs in Electrical and Computer Science Engineering” series, this short book (110 pages) describes in detail how statistical methods have been applied to help address the mystery of the disappearance of flight MH370, a Malaysian Airlines Boeing 777 bound for Beijing from Kuala Lumpur that disappeared from radar in March 2014, with 227 passengers and 12 crew members on board. This summary of the full report provided by the Flight Path Reconstruction group, which included experts from Inmarsat, Thales, Boeing, the US National Transportation Safety Board, and the UK Air Accidents Investigation Branch, under the supervision of the Australian Transport Safety Bureau, reads almost like a thriller. The book comprises 11 short chapters, each focused on one of the aspects of the flight that were relevant to help best delimit, in probabilistic terms, the search zone for the rescue efforts.

After a short introduction and a factual description of the accident, chapter 3 briefly presents the Bayesian approach that will inform the rest of the book. Because analytical solutions are not feasible in such a complex setting, a particle filter technique will be used to perform the numerical simulations that will end up providing the precise posterior probability density function (PDF) describing the distribution of the aircraft location, taking into account the few available measurements regarding the flight route (the initial, well-known aircraft movements are described in chapter 4). The goal of chapter 5 is to describe the various types of (sparse) data that were collected during the flight. This Boeing 777 was indeed equipped with an Inmarsat Classic Aero system that uses satellite communication to relay automatically emitted signaling messages between the airplane and a ground receiving station in Perth, Australia (another one in Burum, Netherlands, is also involved, by providing reference information); in addition, two telephone calls were initiated from the doomed plane. The peculiarities of this communication system located on a moving aircraft are the key ingredients to help track it: data is sent, usually once per hour, in bursts characterized by a burst timing offset (BTO), which accounts for the propagation delay between the satellite and the ground, and a burst frequency offset (BFO), which handles Doppler effects. The BTO can be used to assess the distance from the satellite position, while the BFO compounds the effects of the satellite and aircraft movements. The logging of this arcane information is, interestingly, a recent evolution in the aviation industry, and a consequence of the Air France 447 Rio-Paris crash.

Making sense of the communication data requires a precise modeling of aircraft dynamics. Two dynamic modes have been considered: (1) a cruise condition (chapter 6), in which only speed and control angles with respect to either magnetic or true north are modeled as so-called Ornstein-Uhlenbeck processes, in which random perturbations are introduced, but the values are forced to revert to predefined set points (here consistent with the logged data), and (2) a maneuvering condition (chapter 7), in which both the number and the amplitudes of heading changes are taken into account. As mentioned, simulating routes is only possible using computers; here, the particle filter approach, in which swarms of points are evolved over time in a manner consistent with the maneuvering statistics, has been chosen. Such a simulation approach, described in chapter 8, has been validated by using six flight logs recorded before the tragedy on both the accident aircraft and other similar ones. The correlations between the actual routes and the ones predicted by the model are impressive, providing strong evidence regarding the validity of its application to MH370. Chapter 10 is the climax of the book: applying all the previously introduced theoretical and practical machinery to the Malaysian Airlines plane, the best location for the crash site is revealed to be a 100,000 square kilometer rectangular area centered at 38 degrees South and 88 degrees East. The (minimal) impact of recent developments, such as the discovery of a flaperon on Reunion Island more than a year after the accident, on the aircraft location PDF is discussed in chapter 11. A one-page brief conclusion ends the book.

I enjoyed every moment of reading this book, which is pedagogical, informative, and full of suspense. The writing is crisp and to the point, illustrating the depth and complexity of current aviation accident investigation techniques and the skills of the experts in this field. I advise both statisticians and aviation enthusiasts to have a look at this book; they won’t regret it. A basic knowledge of probability will help, but even nonspecialists will get something out of this reading.