Alright, here’s my take on documenting my Gibbs sampling game log, kinda like a blog post. I’m diving into the trenches, detailing how I wrestled with it.
So, I was messing around with Gibbs sampling the other day, trying to get it to work for this funky Bayesian model I cooked up. Let me tell you, it wasn’t exactly a walk in the park. Started off feeling confident, like “yeah, I got this,” and ended up staring blankly at my screen for a solid hour.
First things first, I had to actually write down the model. No skipping steps! Spent a good chunk of time just figuring out what the conditional distributions actually were. This is where things started to get hairy. My original model, the one I thought was so clever, had some seriously ugly conditionals. Think integrals that look like they were designed by a math goblin.
Realized that my initial model was a total bust. Simplified! Went back to the drawing board and tweaked the model to get those conditionals into something manageable. Basically, I wanted something I could actually code. Think conjugate priors – that’s the ticket. Saved myself a whole heap of trouble. Ended up with something a bit less “realistic,” but hey, it’s about learning, right?
Next up, the coding. Chose Python, ’cause that’s what I’m comfy with. NumPy is my best friend here. Started by initializing all the variables. This is important! If you don’t give the sampler a good starting point, it’ll wander around like a lost tourist for ages. I tried a few different initialization schemes. Turns out, starting near the true values (if you know them from simulated data) is, unsurprisingly, a good idea.
Then comes the actual Gibbs sampling loop. This is where you iteratively sample each variable from its conditional distribution, given the current values of all the other variables. For each variable, I wrote a little function to do the sampling. This kept the main loop nice and tidy. The sampling itself was just a matter of plugging the current values into the formulas I had derived earlier and using NumPy’s random number generators.
The real pain was debugging. Getting the sampler to converge was a nightmare. I’d run it, and the samples would just bounce around all over the place, never settling down. Turns out, I had a couple of stupid errors in my conditional sampling functions. Like, off-by-one errors, missing a factor of two – the kind of stuff that drives you crazy.
Finally! After hours of tweaking and debugging, I got it to work! The samples started to look reasonable, and the estimated parameters were close to the true values. Huge sigh of relief. Plotted the trace plots (the values of the samples over time) to check for convergence. They looked nice and stationary, not all wiggly and chaotic.
- Learned that simplifying the model is sometimes the best way to go.
- Double-check your conditional distributions. Then check them again.
- Good initialization matters!
- Plotting is your friend. Look at those trace plots!
It was a bit of a slog, but in the end, I learned a lot about Gibbs sampling and Bayesian modeling in general. Plus, I now have a working sampler that I can use as a template for other projects. Not bad for a day’s work!
