RadioSED II: discovering the peaked spectrum radio sources in Stripe 82

This paper is the second in a series presenting \textsc{RadioSED}, a Bayesian inference framework for constructing, modelling and classifying radio spectral energy distributions from publicly-available surveys. We focus here on the application of our framework to SDSS Stripe 82. Not only do we recover all eleven previously-published peaked spectrum sources from the literature within this region, but we increase the number of known peaked spectrum sources here by more than an order of magnitude. We investigate the variability properties of our peaked spectrum sample, and find that overall they exhibit a low degree of variability, consistent with previous samples of peaked spectrum active galactic nuclei. The multiwavelength properties of these sources reveal that we have selected a population comprising largely distant ($z \geq 1$), powerful active galaxies. We find that the most compact jets are located preferentially in quasar-type hosts, with galaxy-type hosts home to slightly more extended radio structures. We discuss these findings in the context of current and forthcoming large area radio surveys.