JOB #3 For Monday October 3rd, 5pm: Sections 15.2 and 15.3 of W&H: MCMC in DLMs with parameter learning, and extending DLMs to mixtures of DLMs. Read and digest section 15.2 - focus mainly on the general setup for MCMC in DLMs and then heavily on the (key) forward-filtering, backward sampling (FFBS) algorithm of section 15.2.3 - this just uses the one-step back/retrospective analysis in a simulation context Read and digest section 15.3 which extends the AR DLM analysis to allow for learning about a latent AR process in a general DLM, or simply just an AR process observed with noise. Develop code to implement the MCMC with FFBS for the AR(p) in noise of section 15.3. There are lots of details, including general questions of storage of samples and also details of conditional posterior sampling specific to the AR DLM - covered in subsection 15.3.2 - that need clear understanding. The goal is then to develop the analysis and experiment in analysing the SOI time series from the STA 214 web site. The analysis format should mirror that of the isotope series presented as the example in section 15.3.4. Hand-in completed assignment as usual (in Mike W's Duke Statistics mailbox in room 211 Old Chem) before 5pm on Monday 3rd October. This is a big assignment - get started soon. BUT the assignment is not expected or intended to lead to a publishable paper nor final, fully battle-tested code and "final" data analysis of the SOI series. It IS intended to (completely) immerse you in AR component DLMs, reinforce your facility with manipulation of models and the implied conditional posteriors, and get started on real data analysis in a broadly useful class of TSDLMs context. And you have a lot of time to do this. Last year's STA 214 developed this in detail in simple stochastic volatility models - you can build on that and the code developed there. Those that did'nt take STA 214 should borrow from those that did - who will be happy to discuss and share old code (that's part of the assignment). If you can partner appropriately for projects, then the few of you that skipped STA 214 last year should partner with someone that did'nt.