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Bayesian statistics for confused data scientists

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Re: Bayesian statistics for confused data scientists

#21

Post by fumeux_fume »

statskier wrote: post #3

I 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…

Given your bias, why bother making this point on a thread about using Bayesian methods where they are applicable? Just seems like unconstructive negativity.

Re: Bayesian statistics for confused data scientists

#22

Post by fumeux_fume »

As 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 observed data to magically get your parameter's estimate?

Re: Bayesian statistics for confused data scientists

#23

Post by _alternator_ »

getnormality wrote: post #9
nextos wrote: post #5

Earlier quoted context omitted.

> I’ve never personally worked on a problem that I felt wasn’t adequately approached with frequentist methods Multilevel models are one example of problem were Bayesian methods are hard to avoid as otherwise inference is unstable, particularly when available observations are not abundant. Multilevel models should be used more often as shrinking of effect sizes is important to make robust estimates. Lots of flashy res…

The evidence "actually supports the null" over what alternative? In a Bayesian analysis, the result of an inference, e.g. about the fairness of a coin as in Lindley's paradox, depends completely on the distribution of the alternative specified in the analysis. The frequentist analysis, for better and worse, doesn't need to specify a distribution for the alternative. The classic Lindley's paradox uses a uniform altern…

Thank you. The main problem with Bayesian statistics is that if the outcome depends on your priors, your priors, not the data determine the outcome.

Bayesian supporters often like to say they are just using more information by coding them in priors, but if they had data to support their priors, they are frequentists.

Re: Bayesian statistics for confused data scientists

#24

Post by kgwgk »

_alternator_ wrote: post #23
getnormality wrote: post #9

Earlier quoted context omitted.

The evidence "actually supports the null" over what alternative? In a Bayesian analysis, the result of an inference, e.g. about the fairness of a coin as in Lindley's paradox, depends completely on the distribution of the alternative specified in the analysis. The frequentist analysis, for better and worse, doesn't need to specify a distribution for the alternative. The classic Lindley's paradox uses a uniform altern…

Thank you. The main problem with Bayesian statistics is that if the outcome depends on your priors, your priors, not the data determine the outcome. Bayesian supporters often like to say they are just using more information by coding them in priors, but if they had data to support their priors, they are frequentists.

If they were doing frequentist inference they wouldn’t be using priors at all and there is nothing frequentist in using previous data to construct prior distributions.

Re: Bayesian statistics for confused data scientists

#25

Post by jb1991 »

jmalicki wrote: post #19
statskier wrote: post #3

I 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…

I feel like I'm a polyglot here but primarily a native frequentist thinker. I've found Bayesian methods shine in cases of an "intractible partition function". Cases such as language models, where the cardinality of your discrete probability distribution is extremely large, to the point of intractability. Bayesians tend to immediately go to things like Monte Carlo estimation. Is that fundamentally Bayesian and anti-fr…

When you are using something like Monte Carlo you’re probably using some method that’s more advanced than the Naïve Bayes, is that right?

Re: Bayesian statistics for confused data scientists

#26

Post by uoaei »

kgwgk wrote: post #24
_alternator_ wrote: post #23

Earlier quoted context omitted.

Thank you. The main problem with Bayesian statistics is that if the outcome depends on your priors, your priors, not the data determine the outcome. Bayesian supporters often like to say they are just using more information by coding them in priors, but if they had data to support their priors, they are frequentists.

If they were doing frequentist inference they wouldn’t be using priors at all and there is nothing frequentist in using previous data to construct prior distributions.

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.

Re: Bayesian statistics for confused data scientists

#27

Post by jrumbut »

The author makes a comparison to Haskell, which I think might be a little misleading.

Haskell is a little more complicated to learn but also more expressive than other programming languages, this is where the comparison works.

But where it breaks down is safety. If your Haskell code runs, it's more likely to be correct because of all the type system goodness.

That's the reverse of the situation with Bayesian statistics, which is more like C++. It has all kinds of cool features, but they all come with superpowered footguns.

Frequentist statistics is more like Java. No one loves it but it allows you to get a lot of work done without having to track down one of the few people who really understand Haskell.

Re: Bayesian statistics for confused data scientists

#28

Post by DeathArrow »

HawtAds wrote: post #11

I think it would be interesting if frequentist stats can come up with more generative models. Current high level generative machine learning all rely on Bayesian modeling.

Most ML algorithms, be it SVM, random forest or neural networks require parameter tuning. That in itself is using bayesian statistics.

Re: Bayesian statistics for confused data scientists

#29

Post by kgwgk »

uoaei wrote: post #26
kgwgk wrote: post #24

Earlier quoted context omitted.

If they were doing frequentist inference they wouldn’t be using priors at all and there is nothing frequentist in using previous data to construct prior distributions.

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.

Re: Bayesian statistics for confused data scientists

#30

Post by kgwgk »

jmalicki wrote: post #13
therobots927 wrote: post #8

Earlier quoted context omitted.

That’s Bayesian propaganda

Huh? Are there really any pure frequentists post Stein's paradox? At least ones that are aware of it and maintain objections to fusing the fields?

> Are there really any pure frequentists post Stein's paradox?

What does that have to do with anything? If one cares about that using a shrinkage estimator is an option which maintains the frequentist purity.

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