I can't find an example of how to use Bayesian statistics with some real data and when to use it.
If I have a bunch of IV curves from a bunch of devices, in my calculation of R using Ohm's law V = IR should I be using a Bayesian approach to calculate the uncertainty of measurement? Or is Bayesian something else to be used for esoteric academic cases??
I wrote a whole book on this topic! There's lots of applied examples, and entire chapter dedicated to the Bayesian workflow. Happy to answer any questions
"Should" you be using Bayesian statistics? That simply comes down to personal preference. I like to use it because it makes it really easy to reason about uncertainty in downstream applications. It's also useful when I have strong prior knowledge about an estimate or am updating it from a previous measurement. Its also especially useful when the data generating process has multiple stages or subpopulations and the particular application can make use of those component measurements.
You can totally use Bayesian statistics to measure V = IR... You could also just bootstrap `V/I`.
Bayesian statistics gets tonnes of practical use. Software packages like STAN-MC get lots of use in traditional stats/econometric circles, while probabilistic programming languages like Turing, Edward, and PyMC get plenty of use elsewhere. Developing algorithms to sample from or solve for the posterior distribution given an arbitrary prior and likelihood is an active area of research. If you want stuff to google, relevant families of algorithms are Variational Inference, Approximate Bayesian Computation, Markov Chain Monte Carlo, and Particle Filters / SMC. However there’s a few newer families of algorithms that have popped up in recent years.
Also worth pointing out that Bayesian methods are the only good option when performing data assimilation into large scale simulators (like epidemic models) which are typically statistically under identified by available data. So this stuff is very relevant!
I lead a platform where we've built a market mix model as a product (SaaS) using Bayesian stats. It allows us to:
- Have a prior based on industry benchmarks to constrain the outputs reasonably
- Calibrate the model using AB test results (aka incrementally)
If I have a bunch of IV curves from a bunch of devices, in my calculation of R using Ohm's law V = IR should I be using a Bayesian approach to calculate the uncertainty of measurement? Or is Bayesian something else to be used for esoteric academic cases??