The statistical description and modeling of volatility plays a prominent role in econometrics, risk management and finance. GARCH and stochastic volatility models have been extensively studied and are routinely fitted to market data, albeit providing a phenomenological description only. In contrast, the field of econophysics starts from the premise that modern economies consist of a vast number of individual actors with heterogeneous expectations and incentives. In turn explaining observed market statistics as emerging from the collective dynamics of many actors following heterogeneous, yet simple, rather mechanistic rules. While such models generate volatility dynamics qualitatively matching several stylized facts and thus illustrate the possible role of different mechanisms, such as chartist trading, herding behavior etc., rigorous and quantitative statistical fits are still mostly lacking. Here, we show how Stan, a modern probabilistic programming language for Bayesian modeling, can be used to fit several models from econophysics. In contrast to the method of moment matching, which is currently popular, our fits are purely likelihood based with many advantages, including systematic model comparison and principled generation of model predictions conditional on the observed price history. In particular, we investigate models by Vikram & Sinha and Franke & Westerhoff, and provide a quantitative comparison with standard econometric models.