Bayesians vs Frequentists(aka sampling theorists)

This is a long standing debate/argument and like most polarized arguments, both sides have some valid and good reasons for their stand. (There goes the punchline/ TLDR). I’ll try to go a few levels deeper and try to explain the reasons why I think this is kind of a fake argument. (Disclaimer: am just a math enthusiast, and a (willing-to-speculate) novice. Do your own research, if this post helps as a starting point for that, I’d have done my job.)

  • As EY writes in this post about how bayes theorem is  a law that’s more general and should be observed over whatever frequentist tools we have developed?
  • If you read the original post carefully, he doesn’t mention the original/underlying distribution, guesses about it or confidence interval(see calibration game)
  •  He points to a chapter(in the addendum) here.
  • Most of the post otherwise is about using tools vs using a general theory and how the general theory is more powerful and saves a lot of time
  •  My first reaction to the post was but obviously there’s a reason those two cases should be treated different. They both have the same number of samples, but different ways of taking the samples. One sampling method(one who does sample till 60% success) is a biased way of gathering data .
  • As a different blog and some comments point out, if we’re dealing with robots(deterministic algorithmic data-collector) that precisely take data in a rigourous deterministic algorithmic manner the bayesian priors are the same.
  • However in real life, it’s going to be humans, who’ll have a lot more decisions to make about considering a data point or not. (Like for example, what stage of the patient should be when he’s considered a candidate for the experimental drug)
  • The point I however am going to make or am interested in making is related to known-unknowns vs unknown-unknowns debate.
  • My point being even if you have a robot collecting the data, if the underlying nature of the distribution is unknown-unknown(or for that matter depends on a unknown-unknown factor, say location, as some diseases are more widespread in some areas)  mean that they can gather same results, even if they were seeing different local distributions.
  • A contiguous point is that determining the right sample size is a harder problem in a lot of cases to be confident about the representativeness of the sample.
  • To be fair, EY is not ignorant of this problem described above. He even refers to it a bit in his 0 and 1 are not probabilities post here. So the original post might have over-simplified for the sake of rhetoric or simply because he hadn’t read The Red queen.
  • The Red queen details about a bunch of evolutionary theories eventually arguing that the constant race between parasite and host immune system is why we have sex  as a reproductive mechanism and we have two genders/sexes.
  • The medicine/biology example is a lot more complex system than it seems so this mistake is easier to make.
  • Yes in all of the cases above, the bayesian method (which is simpler to use and understand) will work, if the factors(priors) are known before doing the analysis.
  • But my point is that we don’t know all the factors(priors) and may not even be able to list all of them, let alone screen, and find the prior probability of each of them.

With that I’ll wind this post down. But leave you with a couple more posts I found around the topic, that seem to dig into more detail. (here and here)

 

P.S: Here’s a funny Chuck Norris style facts about Eliezer Yudkowsky.(Which I happened upon when trying to find the original post and was not aware of before composing the post in my head.) And here’s an xkcd comic about frequentists vs bayesians.

UPDATE-1(5-6 hrs after original post conception): I realized my disclaimer doesn’t really inform the bayesian prior to judge my post. So here’s my history/whatever with statistics. I’ve had trouble understanding the logic/reasoning/proof behind standard (frequentist?) statistical tests, and was never a fan of rote just doing the steps. So am still trying to understand the logic behind those tests, but today if I were to bet I’d rather bet on results from the bayesian method than from any conventional methods**.

UPDATE-2(5-6 hrs after original post conception):  A good example might be the counter example. i.e: given the same data(aka in this case frequency of a distribution, nothing else really, i.e: mean, variance, kurtosis or skewness) show that bayesian method gives different results based on how it(data) was collected and frequentist doesn’t. I’m not sure it’s possible though given the number of methods frequentist/standard methods use.

UPDATE-3 (a few weeks after original writing): Here’s another post about the difference in approaches between the two.

UPDATE-4 (A month or so after): I came across this post with mentions more than two buckets, but obviously they are not all disjoint sets(buckets).

UPDATE-5(Further a couple of months after): There’s a slightly different approach to splitting the two cultures from a different perspective here.

UPDATE-6: A discussion in my favourite community can be found here.
** — I might tweak the amount I’d bet based on the results from it .

A rule to avoid black swans

In fact, any time anybody offers you anything with a big commission and a 200-page prospectus, don’t buy it. Occasionally, you’ll be wrong if you adopt “Munger’s Rule”. However, over a lifetime, you’ll be a long way ahead—and you will miss a lot of unhappy experiences that might otherwise reduce your love for your fellow man.

https://old.ycombinator.com/munger.html

Elementary Worldly Wisdom

The great lesson in microeconomics is to discriminate between when technology is going to help you and when it’s going to kill you. And most people do not get this straight in their heads. But a fellow like Buffett does.

For example, when we were in the textile business, which is a terrible commodity business, we were making low-end textiles—which are a real commodity product. And one day, the people came to Warren and said, “They’ve invented a new loom that we think will do twice as much work as our old ones

https://old.ycombinator.com/munger.html

Advice to new Doctors starting practice

Hi all,

Please read the Disclaimers at the end of the post first, if you’re easily offended.

Generalists(general medicine):

  1. Get extremely unbeatable at 20 Questions(rationality link). It’ll help you make your initial diagnoses(ones based on questions about symptoms) faster and more accurate.
  2. Understand probability, bayes theorem and how to apply it** This will help you interpret the test results, you ordered based on the 20 questions.
  3.  Understand base rate fallacy, and how to avoid  being over confident.
  4. Practice enough of systems thinking in your diagnoses and prognoses thought-experiments. May be even try it in other domains to check your skill level. And for extra credits learn some of the basics of dynamical sytems***, as the human body is one.
  5. Understand the upsides and downsides of the drugs you prescribe. Know the probabilities of fatal and adverse side-effects and update them with evidence(Bayes’ theorem mentioned above) as you try out different brands and combinations.
  6. Know the costs and benefits of any treatment and help the patient make a good decision based on the cost-benefit analysis of treatment combined with the probabilities of outcome.
  7. Ask and Keep a history of medical records and allergies of the patient and till their grand parents.*
  8. Be willing and able to judge, when a patient is better off with a specialist. Try to keep in touch with Doctors nearby and hopeful all types of specialists.
  9. Explain the treatment options and pros and cons in easy language to the patients. It’ll reduce misunderstandings and eventually dis-satisfaction with the treatment.
  10. Resist the urge to treat patients as NPCs. Involve them in the treatment process.
  11. Meditate
  12. Find a hobby, that you can keep improving on till the end of life.
  13. Be aware of the conflict of interest between the patient and the pharmaceutical companies.
  14. Have enough research skills to form opinions on base rates/probabilities in different diseases and treatment methods as needed.
  15. If you’re in a big hospital setup, make sure you’ve the best hospital administration, if not find ways to improve or find better big hospital.
  16. Medical expertise is only relevant once you see the patient. Your ability to judge the evidence requires getting access to it; this means you need to be able to correctly send requests, get the data back, and keep all this attached to the correct patient.Scheduling, filing and communication. Lacking these, medical expertise is meaningless.
  17. Be aware of cognitive biases humans are liable to make.

Specialists:

Basically the same skill sets as above. One difference is in the skill level and you should customize that as needed.

  1. For ex: You would need to be able to explain the treatment options and the probabilistic nature of the outcomes to your patients.
  2. As for research, keep a track of progress in your area in treatment methods and different outcomes on the “quality of life” for the patients after the treatment.
  3. Better applied Bayesian skills. In the sense of figuring out independent variables and their probabilities affecting the outcome.

Some controversial ideas(Better use your common-sense before trying out):

  1.  Experiment a little with your bio-chemistry and see how they affect your thought-processes.  To be safe, stick to biologically produced ones. For ex: injecting self with a small adrenalin dose and monitoring bodily response can help keep your thinking clear in emergency situations.
  2. Know your self biology better. For ex: male vs female differences mean the adrenalin response is different and peaks later in females.  If you think that’s wrong, please go back and check your course work. Also watch this 2 hour video and come back with objections after reading the studies he quotes.
  3. Keep regularly(whatever frequency your practice and nature of work demands) checking your(for ex; hormone levels) blood states, so that you  can start regulating your self for optimal decision-making skills.
  4. If you’re a woman, you’ll customize practice on some of the skill sets above differently. For ex: Mastery over emotions might need more practice, while empathizing/connecting with the patient might be easier.

Disclaimers:

  1. Most of what follows is based on my experiences(either as a patient myself or a concerned relative) with Indian Doctors. Some of it may be trivial, to others, but most of it is skills a doc will need and ignored in school.
  2.  I’ve split it in two (specialists and generalists) but there’s a fair amount of overlap.
  3. These are fairly high standards, but worth shooting for and I’ve kept the focus on smart rather than hard work.
  4. I’ve stayed from a few topics like: bedside manners/social skills, specific medical treatments and conditions(obviously, I’m not a Doctor after all) and a few others, you can add/delete(also specify/pick levels) as you see fit.
  5. Pick the skill-levels as demanded by your client population and adjust.
  6. I’m assuming generalists, don’t have to deal with emergency cases, but in some parts, that’s not likely then pick common emergency categories and follow specialist advice.
  7. My qualifications are basic mechanical engineering plus a master’s in cognitive science. By their nature, I’ve a very shallow knowledge/overview of the topics involved, but too little certainty for me to give any specific advice.
  8. I wrote this based on my experiences and with humans in mind, but veterinary Doctors may find some useful too.
  • — I understand this is difficult in Indian circumstances, but I’ve seen it being done manually(simply leaves of prescriptions organized alphabetically, link to dr.rathinavel) , so it’s possible and worth the effort unless, you practice in area of highly migratory population.(for example rural vs urban areas).

**– If you’re trying to compete on availability for consultation, you’ll need to be able to do this after being woken in the middle of the night.

*** — Please don’t take this literally. Though I’m optimistic that dynamical system tools may be enough to describe the human body, it might turn out human body is more dynamic than them. In other words, use your judgement, and make sure you can apply the dynamical systems theory to say “three-body problem

Notes/Thoughts from waiting at the labour ward.

  1. Child-birth or labour involves physical trauma, but it is expected to happen (for say 9 months)… that complicates things???? (It definitely breeds paranoia and worry-downward-spiral)
  2. However, the fact that it is expected and the fact that it is linked to species survival has facilitated a lot of research. I tend to think expected and predictable events get a bit over-researched and over-operationalized* in general. Is the fact that it is linked to reproduction causes too much(harmful) research or not?? Interesting question, but may not be answerable…
  3. The choice of word “labour” is interesting. It has marxist/communist connotations in most contexts, but in this, not really…. coincidence???
  4. The blanket ban of “no males in labour ward”** might be useful and valid, but it hardly is without exception and definitely allows for more follow-the-process decisions, encouraging a ignorance of context..
  5. Even after about 30 hours of partial sleep and adrenaline surge*** I could feel that jump in heart beat on looking at my daughter..
  6. P.S: every note above(except 5th) was written before the adrenaline surge.

* — to the point of over-engineering that risks violating the “do-no-evil”

**–in India

***–which was another story, i’ll write after my lymbic system settles down(aka down-regulating-lymbic-system for that memory), suffice it to say, i became more convinced of gender-difference (aka sexist)
Context location: