Observational constraints using Bayesian Statistics and deep learning in Kaniadakis holographic dark energy

In this paper, we present the Kaniadakis holographic dark energy (KHDE) model with hybrid expansion law, which describes the Universe accelerating expansion in the flat Friedmann-Lema$\tilde{i}$tre-Robertson-Walker Universe. The deceleration parameter obtained in the KHDE model depicts the expansion of the universe from decelerating to an accelerating phase. The KHDE model’s equation of state (EoS) parameter reproduces the Cosmos’ rich behaviour, such as the phantom division line spanning the quintessence era ($\omega >-1$). We include the statefinder pair $(r,s)$, which emulates the $\Lambda$ CDM model in the future. Bayesian Statistics and 57 Hubble data points, 6 baryonic acoustic oscillations $\left(BAO\right)$ data points, and 1048 Pantheon Type Ia supernovae $\left(SNIa\right)$ data points are used to extract model constraints. Bayesian and $ANN$ findings are also compared. CoLFI, an ANN-based parameter estimation approach is employed. CoLFI is more efficient for parameter estimation, especially for intractable likelihood functions or big, resource-intensive cosmological models. Some physical properties of the model are also discussed in detail.