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Bayesian statistics for confused data scientists
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Re: Bayesian statistics for confused data scientists
#32Earlier quoted context omitted.
Not true. In frequentist statistics, from the perspective of Bayesians, your prior is a point distribution derived empirically. It doesn't have the same confidence / uncertainty intervals but it does have an unnecessarily overconfident assumption of the nature of the data generating process.
Not true. In frequentist statistics, from the perspective of Bayesians and non-Bayesians alike, there are no priors. —- Dear ChatGPT, are there priors in frequentist statistics? (Please answer with a single sentence.) No — unlike Bayesian statistics, frequentist statistics do not use priors, as they treat parameters as fixed and rely solely on the likelihood derived from the observed data.
There's always priors, they're just "flat", uniform priors (for maximum likelihood methods). But what "flat" means is determined by the parameterization you pick for your model. which is more or less arbitrary. Bayesians would call this an uninformative prior. And you can most likely account for stronger, more informative priors within frequentist statistics by resorting to so-called "robust" methods.
Re: Bayesian statistics for confused data scientists
#33I went through grad school in a very frequentist environment. We “learned” Bayesian methods but we never used them much. In my professional life I’ve never personally worked on a problem that I felt wasn’t adequately approached with frequentist methods. I’m sure other people’s experiences are different depending on the problems you gravitate towards. In fact, I tend to get pretty frustrated with Bayesian approaches b…
In clinical settings and situations where probabilities really matter, its a better fit.
I studied stats at Duke which is a Bayesian academy. Almost every problems come from regimes with small sample sizes. Given that Duke houses the largest academic clinical research organization globally, having a stats and biostats department with this bent is useful: samples are tiny in clinical trials compared to most big data settings.
The biggest problem with the whole Bayesian regime IMO is that as the data gets larger its selling point vanishes. If your data is big or is normal (mean-based statistics), a frequentest/bootstrapped CI approximates the Bayesian CI anyway.
Furthermore, many us work in settings where we're trying to sell toothpaste: we don't need the Bayesian guarantees that an insurer might.
Re: Bayesian statistics for confused data scientists
#34[flagged]
I would argue the opposite is true. It takes a long time to beat the Bayesian thinking out of students when presenting them with a confidence interval: https://link.springer.com/article/10.3758/s13423-013-0572-3
Re: Bayesian statistics for confused data scientists
#35Re: Bayesian statistics for confused data scientists
#36Re: Bayesian statistics for confused data scientists
#37Nice writeup. Something that clicked for me reading this is how much the prior/likelihood/posterior dynamic mirrors transfer learning in deep learning. The prior is basically your pre-trained weights: broad knowledge you bring to the table before seeing any task-specific data. The likelihood is your fine-tuning step. And the Bernstein-von Mises result at the end is essentially saying "with enough fine-tuning data, your pre-training washes out."
Obviously the analogy isn't perfect (priors are explicit and interpretable, pre-trained weights are not), but I think it's a useful mental model for anyone coming from an ML background who finds Bayesian stats unintuitive. Regularization being secretly Bayesian was the other thing that made it click for me. If you've ever tuned a Ridge regression lambda, you were doing informal prior selection.
Re: Bayesian statistics for confused data scientists
#38As a data scientist, I find applied Bayesian methods to be incredibly straightforward for most of the common problems we see like A/B testing and online measuring of parameters. I dislike that people usually first introduce Bayesian methods theoretically, which can be a lot for beginners to wrap their head around. Why not just start from the blissful elegance of updating your parameter's prior distribution with your…
can you explain what you're saying please?
Re: Bayesian statistics for confused data scientists
#39Nicely done.
I have the same challenge with Bayesian stats and usually do not understand why there is such controversy. It isn’t a question of either/or, except in the minds of academics who rarely venture out into the real world, or have to balance intellectual purity with getting a job done.
In the very first example, a practitioner would consciously have to decide (i.e. make the assumption) whether the number of side on the die (n) is known and deterministic. Once that decision is made, the framework with which observations are evaluated and statistical reasoning applied will forever be conditional on that assumption.. unless it is revised. Practitioners are generally OK with that, whether it leads to ‘Bayesian’ or ‘frequentist’ analysis, and move on.
Re: Bayesian statistics for confused data scientists
#40This article made me enthusiastic to dive into Bayesian statistics (again). A quick search led me to Think Bayes [1], which also introduces the concepts using Python, and seems to have a little more depth.