We present the highest resolution and sensitivity $\sim$$1.4\,$GHz continuum observations of the Eridanus supergroup obtained as a part of the Widefield Australian Square Kilometer Array Pathfinder (ASKAP) L-band Legacy All-sky Blind surveY (WALLABY) pre-pilot observations using the ASKAP. We detect 9461 sources at 1.37 GHz down to a flux density limit of $\sim$$0.1$ mJy at $6.1''\times 7.9''$ resolution with a median root mean square of 0.05 mJy beam$^{-1}$. We find that the flux scale is accurate to within 5 % (compared to NVSS at 1.4 GHz). We then determine the global properties of eight Eridanus supergroup members, which are detected in both radio continuum and neutral hydrogen (HI) emission, and find that the radio-derived star formation rates (SFRs) agree well with previous literature. Using our global and resolved radio continuum properties of the nearby Eridanus galaxies, we measure and extend the infrared-radio correlation (IRRC) to lower stellar masses and inferred SFRs than before. We find the resolved IRRC to be useful for: (1) discriminating between active galactic nuclei and star-forming galaxies; (2) identifying background radio sources; and (3) tracing the effects of group environment pre-processing in NGC 1385. We find evidence for tidal interactions and ram-pressure stripping in the HI, resolved spectral index and IRRC morphologies of NGC 1385. There appears to be a spatial coincidence (in projection) of double-lobed radio jets with the central HI hole of NGC 1367. The destruction of polycyclic aromatic hydrocarbons by merger-induced shocks may be driving the observed WISE W3 deficit observed in NGC 1359. Our results suggest that resolved radio continuum and IRRC studies are excellent tracers of the physical processes that drive galaxy evolution and will be possible on larger sample of sources with upcoming ASKAP radio continuum surveys.

We demonstrate that the Bayesian evidence can be used to find a good approximation of the ground truth likelihood function of a dataset, a goal of the likelihood-free inference (LFI) paradigm. As a concrete example, we use forward modelled sky-averaged 21-cm signal antenna temperature datasets where we artificially inject noise structures of various physically motivated forms. We find that the Gaussian likelihood performs poorly when the noise distribution deviates from the Gaussian case, for example, heteroscedastic radiometric or heavy-tailed noise. For these non-Gaussian noise structures, we show that the generalised normal likelihood is on a similar Bayesian evidence scale with comparable sky-averaged 21-cm signal recovery as the ground truth likelihood function of our injected noise. We therefore propose the generalised normal likelihood function as a good approximation of the true likelihood function if the noise structure is a priori unknown.