The algorithmic family that in general seems called for is "sequential monte carlo" or "particle filtering". While often this is presented for models and proble

The algorithmic family that in general seems called for is "sequential monte carlo" or "particle filtering". While often this is presented for models and problems where the latent dimension is small and the problem is about how something evolves over time, the "sequential" part of it can just be about the order in which data are received (I think this traces to "A Sequential Particle Filter Method for Static Models", N Chopin, 2002). On the PPL side, I think SMC has often been a secondary target, but there has been good work on getting good, efficient inference be more turn-key. I think this has often focused on being able to automatically provide better/adaptive proposal distributions. For example, "SMCP3: Sequential Monte Carlo with Probabilistic Program Proposals" by Lew et al 2023 (Stuart Russell is among the contributors).