Likelihood free particle filtering with approximate Bayesian computation for parameter estimation in cosmic ray air shower studies

Highly energetic particles called cosmic rays arrive at earth and interact with the atmosphere to cause other particles to emerge and fuel a chain interaction of particle production until the energy is dissipated. These cascades emerging from a highly energetic initial particle and producing secondary particles that spread over a large area at the ground are called Extensive Air Showers. These showers are studied to find anisotropy in their arrival direction and energy to unveil their source and production mechanisms in the universe. In this study we utilize the likelihood free particle filtering with Approximate Bayesian Computation to estimate the incident angle and energy of the primary particle. ABC method makes use of comparison between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood function of particle physics.