![]() ![]() Now I could have said: "Well that's easy, MCMC generates samples from the posterior distribution by constructing a reversible Markov-chain that has as its equilibrium distribution the target posterior distribution. When I presented a new Bayesian model to Quantopian's CEO, Fawce, who wasn't trained in Bayesian stats but is eager to understand it, he started to ask about the part I usually gloss over: "Thomas, how does the inference actually work? How do we get these magical samples from the posterior?". The beauty of probabilistic programming is that you actually don't have to understand how the inference works in order to build models, but it certainly helps. Where $\phi(.)$ is the standard normal pdf.When I give talks about probabilistic programming and Bayesian statistics, I usually gloss over the details of how inference is actually performed, treating it as a black box essentially. #Sd the emcee codeIn more formal terms, the code below sets up a basic_model having the following form: Our "dependent variable" is given by observed=data, where data is generated above and shown in the histogram. The likelihood function is chosen to be Normal, with one parameter to be estimated ( mu), and we use known $\sigma$ (denoted as sigma). Here, mu is defined as a stochastic variable (we want a chain of sampled values for this variable) and we provide a prior distribution and hyper-parameters for it. This is the model statement describing priors and the likelihood. We will start with our very simple one parameter model and then move to slightly more complicated settings: Today, we are going to focus on PyMC3, which is a very easy to use package now that we have a solid understanding of how posteriors are constructed. Python is the used a lot in many fields including physics and is strong in the big-data arena, more so than any of the other packages mentioned above. Maybe (in my view probably) also easier to code your own samplers than R as I really prefer python syntax to R. The libraries aren't as rich as R, but you might view Python as sitting between Matlab and R. ![]() I almost elected to teach this course in R. Also Jags, Rbugs and Open BUGS have been around for a long time. For a long time R was the de-facto standard and probably still is, with packages like R-stan which interfaces the STAN C Library. ![]() A decent set of packages, not used very much in the social sciences (maybe in the medical sciences?), but is well suited for big data. Matlab is for people who want to possibly tweak their own sampler code and who need the fastest possible computation. For example, there is a version of emcee that is implemented there (more on this later in the course). There are numerous user and Matlab written routines. To be honest, I have never heard of anyone using Stata for Bayesian Sampling Methods although I haven't really looked.
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