For those interested in the theory of point processes, Mohamed Karray, uploaded some lecture slides, which are based on the book manuscript:
- 2024 – Baccelli, Błaszczyszyn, and Karray – Random Measures, Point Processes, and Stochastic Geometry.
I have written about this manuscript in a previous post.
Although both the slides and manuscript lean heavily on the side of mathematical rigour, applications are the driving motivation. For example, the third set of slides cover Palm calculus, which hinges upon the important concept of conditioning on a point (of the random point process) existing at a specific location. This idea is frequently used in mathematical models of wireless telecommunication networks based on stochastic geometry. (Unfortunately the Wikipedia article on Palm calculus is sorely lacking and only looks at the temporal, not spatial, setting.)
Karray, a researcher at Orange Labs in Paris, also has slides and (mostly forthcoming) manuscripts on machine learning and statistics, which take a rather rigorous route. It’s a French touch, mathematically, as measure theory appears.
Thank you, Paul, for sharing these lecture slides. As mentioned, they are derived from the upcoming manuscript “2024 – Baccelli, Błaszczyszyn, and Karray – Random Measures, Point Processes, and Stochastic Geometry.” While the manuscript leans towards mathematical rigor, we always emphasize applications. The Palm calculus slides, for instance, delve into conditioning on the existence of a point at a specific location – a vital concept for modeling telecommunication networks using stochastic geometry. I also have other slides and manuscripts (mostly forthcoming) on machine learning and statistics, taking a similar mathematically rigorous path.
-Mohamed Karray, Orange Labs
You’re very welcome, Mohamed. Rigour and applications abound.
Dear Paul, Dear Colleagues, I am pleased to announce the availability of my new lecture titled “Stationary Random Measures and Point Processes: Palm Theory in the Stationary Framework” on my website https://mohamedkadhem.com/point-processes/.
I invite you to explore the lecture and engage with the material. Your feedback and insights would be greatly appreciated as we continue to advance our understanding of this important area in stochastic processes.
Best regards,
Mohamed Kadhem
#StationaryRandomMeasures #StationaryPointProcesses #PalmTheory #MathematicsResearch #StatisticalModeling #AppliedMathematics #DataScienceInsights
Dear Paul, Dear Colleagues,
I’m pleased to announce the availability of my new lecture, “Stationary Random Measures and Point Processes: Marks in the Stationary Framework,” on my website: https://mohamedkadhem.com/point-processes/
This lecture provides a comprehensive overview of how to incorporate “marks” into the study of stationary random measures and point processes. We explore the theoretical foundations and applications of marks, covering topics such as Palm theory, mark-dependent thinning, and transformations based on marks.
I invite you to explore the material and engage with its concepts. Your feedback and insights would be greatly appreciated.
Best regards,
Mohamed Kadhem
#StationaryRandomMeasures #StationaryPointProcesses #MarkedPointProcesses #PalmTheory #StochasticGeometry #SpatialStatistics #MathematicsResearch #StatisticalModeling