  In this document I aim to give an informal treatment of automatic Backward
Filtering Forward Guiding, a general algorithm for conditional sampling from a
Markov process on a directed acyclic graph. I'll show that the underlying ideas
can be understood with a basic background in probability and statistics. The
more technical treatment is the paper Automatic backward filtering forward
guiding for Markov processes and graphical models (Van der Meulen and Schauer,
2021). I specifically assume some background knowledge on likelihood based
inference and Bayesian statistics. The final sections are more demanding and
assume familiarity with continuous-time stochastic processes constructed from
their infinitesimal generator.
  Clearly, all work discussed here is the result of research carried out over
the past decade together with various collaborators, most importantly Moritz
Schauer (Chalmers University of Technology and University of Gothenburg,
Sweden). Section 8 is based on joint work with Marcin Mider (Trium Analysis
Online GmbH, Germany) and Frank Sch\"afer (University of Basel, Switzerland) as
well.

Computation;Probability