# Bibliography

Monography Chapter

### Bayesian approach to collaborative inference in networks of agents

,

**: **Cooperative and graph signal processing, p. 131-145
, Eds: Djurić Petar M., Richard Cédric

**: **GA16-09848S, GA ČR

**: **Distributed estimation,
diffusion network,
information diffusion

**: **10.1016/B978-0-12-813677-5.00004-3

**: **http://library.utia.cas.cz/separaty/2018/AS/dedecius-0493396.pdf

**(eng): **Bayesian inference has become a standard tool in the modern statistical signal processing theory, particularly due to the probabilistically consistent representation of the available knowledge about the variables of interest, and the amount of the uncertainty contained in this knowledge. Unlike in the 'standard' theory, the underlying inferential principles are generally applicable to virtually any inference task, from linear models to nonlinear, mixture, or hierarchical models. Furthermore, the rapid development of the modern devices with high computational performance finally eliminated the major drawback of the Bayesian theory: the frequent analytical intractability of the posterior distributions. This chapter studies the possible implementation of the Bayesian inference in networks of collaborating agents. In particular, we focus on the diffusion networks, where the agents may share information (measurements and/or estimates) with their adjacent neighbors, and incorporate it into own knowledge about the unknown variables of interest. There are several ways how to perform this incorporation in an optimal way according to a convenient user-selected information criterion, and under certain conditions where the model belongs to the exponential family of distributions and the prior distributions are conjugate, the results are analytically tractable. The celebrated Kalman filter serves as an illustrative example demonstrating the straightforward application of the abstractly described principles to a particular problem. It is reformulated for the collaborative estimation task in networks where both the neighbors' observations and posterior distributions are available to each agent. Naturally, the analyticity of the resulting filter is preserved.

**: **BC

**: **20205