The book presents a general mathematical framework able to detect and to characterize, from a morphological and statistical perspective, patterns hidden in spatial data. The mathematical tool employed is a Gibbs point process with interaction, which permits us to reduce the complexity of the pattern. It presents the framework, step by step, in three major parts: modeling, simulation, and inference. Each of these parts contains a theoretical development followed by applications and examples.

Features:

• Presents mathematical foundations for tackling pattern detection and characterisation in spatial data using marked Gibbs point processes with interactions
• Proposes a general methodology for morphological and statistical characterisation of patterns based on three branches, probabilistic modeling, stochastic simulation, and statistical inference
• Includes application examples from cosmology, environmental sciences, geology, and social networks
• Presents theoretical and practical details for the presented algorithms in order to be correctly and efficiently used
• Provides access to C++ and R code to encourage the reader to experiment and to develop new ideas
• Includes references and pointers to mathematical and applied literature to encourage further study

The book is primarily aimed at researchers in mathematics, statistics, and the above-mentioned application domains. It is accessible for advanced undergraduate and graduate students, so could be used to teach a course. It will be of interest to any scientific researcher interested in formulating a mathematical answer to the always challenging question: what is the pattern hidden in the data?