Tomographic three-dimensional 21 cm images from the epoch of reionization contain a wealth of information about the reionization of the intergalactic medium by astrophysical sources. Conventional power spectrum analysis cannot exploit the full information in the 21 cm data because the 21 cm signal is highly non-Gaussian due to reionization patchiness. We perform a Bayesian inference of the reionization parameters where the likelihood is implicitly defined through forward simulations using density estimation likelihood-free inference (DELFI). We adopt a trained 3D Convolutional Neural Network (CNN) to compress the 3D image data into informative summaries (DELFI-3D CNN). We show that this method recovers accurate posterior distributions for the reionization parameters. Our approach outperforms earlier analysis based on two-dimensional 21 cm images. In contrast, an MCMC analysis of the 3D lightcone-based 21 cm power spectrum alone and using a standard explicit likelihood approximation results in inaccurate credible parameter regions both in terms of the location and shape of the contours. Our proof-of-concept study implies that the DELFI-3D CNN can effectively exploit more information in the 3D 21 cm images than a 2D CNN or power spectrum analysis. This technique can be readily extended to include realistic effects and is therefore a promising approach for the scientific interpretation of future 21 cm observation data.
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