The funny thing is, I imagine I'd fail this, and a lot of other "interview" questions. (Not fizzbuzz incidentally :P)
Why? Because my brain just doesn't seem to work in the way people expect "experts" brains to work in our world of tests/qualifications.
Now for context, I don't consider my self some wishy washy "Oh I have a different KIND of intelligence" making-excuses dumb as nails nancy. I've worked several years now for my nation's statistics agency. I've written programs to calculate things professional statisticians couldn't (indeed that seems to be one of the reasons I get to keep my job :P) and just about every useless bloody stat there is, I've written my own probabilistic data linking software, finished in the top 10% of unrelated competitions on kaggle, and my formal qualifications are in economics. I don't think I'm the greatest thing ever, but if i might be so blunt, I feel I'm at the stage where I can confidently claim to have "proven my capabilities".
But I haven't memorized Bayes theorem (or any other probability or math-formulas), despite having applied it about 100 gazillion times. And despite being an economist, I haven't memorized "the relationship between bond prices and interest rates". Now, I could try to reason these things out from scratch in front of you, but I imagine most people in our world would see that as a "weakness" or trying to hide the fact that I couldn't answer the question.
With the probability one, I'd start going down the various interpretations of probability and whether your notion of probability is internally consistent/justified, etc etc etc. I doubt I could write the math on the white board of the top of my head in an interview (and i know several statisticians who couldn't also), but I could probably outperform most of the candidates who could in its application in the real world (speaking from experience), or be able to question whether there is a better tool for the job in the real world.
With the bond one, I know there's an answer that you expect me to give from rote during my education. But i won't. I haven't memorized it (because from experience, memorising these types of things is bad form, conditions you into erroneous thinking when they eventually turn out not to be universally true, and is far worse than reasoning, questioning or thinking about problems). So i'll ask you to describe your idea of a bond to me. I'll ask you to describe your idea of interest rates. Why are the interest rates rising? Maybe then, depending on what answers YOU give, I'll say "well then obviously bond prices must move inversely to interest rate movements", but there's just as much chance i'll pick up on some mistake you've made and never reach that point.
Now I'm not attacking you specifically. I don't know you, or what we think of each other, or how we'd interview each other. But from my experience, most people/recruiters/employers/interviewers would take my behaviour as a negative sign. A sign of "stalling" or "evading the question". Questioning, or reasoning, or skeptically interrogating things or mulling over questions for long periods of time, especially if they consider the answer "known", is a "bad sign".
And the rote learner, who'd just happened to memorise a particular formula or spent most of their time in one particular context, or bought the book on interview questions for said industry will get a big fat tick.
Moral of the story: Please don't use "interview questions" :P
* The person suggesting the question says that this is trivial for people suited to the job in mind;
* You say you couldn't do this question;
* You also say that you would be suitable to do the job.
Given that the proposer of the question is the one that understands the job, I'm having a hard time understanding why you claim you would be suitable for it, given that you couldn't do the question. Please understand that I'm not attacking you specifically, I'm just having a hard time understanding your reasoning.
Well, I'd disagree with at least two of your premises:
1) That the proposer of the question often understands the job. (by which i mean, in real world interviews. I'm not commenting on the specific poster).
2) I am not saying that I couldn't do the question, per se.
On the contrary, my professional work shows not only that I can do the question, but that I've probably done it innumerable times and to the standard of (and sometimes greater than) other professionals.
The subtext of my response to the bond question shows that, in an absolute juvenile sense, I "know" the answer that's being looked for because I've notionally been trained as en economist. Which is to say, I am aware of the rote learned current models/theory.
I'm saying that I probably couldn't answer it in the interview environment in the way that most interviewers would deem "acceptable" or "right".
Why? Because I both haven't memorized Bayes theorem, and wouldn't accept there as being a simple probabilistic interpretation applicable to real world problems. Now its true, I could probably attempt to re-derive it there in the interview from some even more basic understandings of probability, but is that what interviewers want? I'd almost certainly offer the answer of "Can i look at the two sides of the coin?" or "the probability is either 0 or 1". And then we'd go down the path of probability interpretations, and then only after they made it clear that they wanted a Bayesian approach, we could start heading in that direction. Is that what they're looking for? I don't think it is. But they are all valid responses.
I think they want someone who has remembered Bayes and its application recently and then just applied it. I think in the bond question, they want someone who has rote learnt some economic/finance theory. And I think the worst aspect is that the stronger candidate, who pauses, who thinks, who questions, and who doesn't just go down the regurgitated answer will probably, in real life, be marked as the weaker candidate.
And I'm also saying this as someone who is already employed, being paid and and working professionally on things the questions are supposed to be screening for. So while the original poster is in a position of authority to speak of such things, so am I.
Are you familiar with Project Euler? I've completed many of those problems as well, but I would never expect myself or some other candidate to be able to do them spontaneously in said interview, or think worse of them if they couldn't. And if they could do them, I don't think that would be an indicator of very much more than the fact that they happened to be working on said problem recently, had just taken a course on said problem, or had just been doing interview questions for my field.
What sorts of questions or tests were posed to you in interviews for jobs you ended up accepting? Or if you've never been in that situation, can you propose some interview techniques that would give the interviewer a good idea of your abilities?
Lets break down the role of interviews into two parts. The first part: To ensure the candidate is sufficiently-socialised and isn't a dangerous toxic mouth-breather. For this, current interviews can work relatively well. An hour or so, face to face, just talking back and forth mulling over problems/theory with an authority in the field or people they're working with.
I am genuinely skeptical about whether people who don't know what they're talking about can actually hide that fact
from people who do know what they're talking about in such a situation. The secret of course is to basically ignore qualifications/status and do it as a conversation. Perhaps in such a scenario, five minutes in me and the original poster would be getting onto ridiculous questions of trading/probability with great big smiles on our faces and forgetting all about whether one can remember bayes off the top of their head.
The second part: Assessing the technical ability of the candidate at hand. And for this I think current interview culture is horribly toxic.
I do not work for Facebook, nor do I believe that such techniques are not without their flaws, and are difficult/expensive to implement, but I think techniques aimed at "actually get the candidate to do the task involved in the job, and see how they go" has merit. Forget your preconceptions about what is required. Give them a real world task you'd expect them to do in the job, the time it would be expected of someone in the job. The resources of the job. See how they go.: See http://www.kaggle.com/c/facebook-recruiting-iii-keyword-extr... for example.
Not perfect, but better than 5 minute "interviewer questions of the year".
Funnily enough, I got into my current organisation answering questions in the interview on analyzing health statistics. Something I knew nothing about. A senior executive then snatched/let me move across to his area in the more technical side of things without a subsequent interview after I made it known I'd be interested, and after working with their guys for a bit on another project. Swings and roundabouts :P
> But from my experience, most people/recruiters/employers/interviewers would take my behaviour as a negative sign.
The negative sign is your stubborn conviction about the lack of value of rote memorization.
The stereotypical "rote learner" you describe in your before-last paragraph is just as one-sided as the opposite.
Of course neither extremes really exist and you probably have rote-memorized more things than you realize. You don't work out everything from scratch every time you encounter a medium hard problem.
Unless you actually do, in which case someone reasonably clever who does not stubbornly refuse to learn a few formulas will beat you by speed. Which is a reason to hire them over you.
That's the the point. You may be very smart and capable doing it this way, but learning a few basics (such as Bayes, in the context of statistics) doesn't really cost you anything. Memorizing a few things isn't hard. You won't actually run into problems like "erroneous thinking" because you're smart enough and knowing the conditions under which something holds is easy enough when you understand the thing. Additionally you get the knowledge when a particular important theorem does not hold, which is higher level knowledge that you just can't get when you reason from scratch every time (positive vs negative knowledge).
Memorizing a few of the basic important theorems and formulas in your field is such low-hanging fruit to improve yourself that a potential employer might ask why you're not doing it, even if you're so very capable without doing it.
Finally, there's communication with your peers. Maybe you can figure that stuff out by yourself easily, but when your colleagues say "ah, so we just use Bayes and poof", you'll be lagging behind figuring that out, and in reverse when you do these things from scratch, I'm assuming you'll be doing them much quicker, speeding through your ad hoc methods, leaving your team mates confused and wondering "why don't he just use Bayes?" (which may or may not be what you are in fact doing, but you lack the knowledge to tell them as much).
I'm sure you do a very good job at what you're doing now, the way you're doing it. I'm just pointing out that there are various well-justified reasons why employers can be wary of your refusal to memorize some basic field-knowledge, even when you're perfectly capable figuring out that stuff when you need it.
Why? Because my brain just doesn't seem to work in the way people expect "experts" brains to work in our world of tests/qualifications.
Now for context, I don't consider my self some wishy washy "Oh I have a different KIND of intelligence" making-excuses dumb as nails nancy. I've worked several years now for my nation's statistics agency. I've written programs to calculate things professional statisticians couldn't (indeed that seems to be one of the reasons I get to keep my job :P) and just about every useless bloody stat there is, I've written my own probabilistic data linking software, finished in the top 10% of unrelated competitions on kaggle, and my formal qualifications are in economics. I don't think I'm the greatest thing ever, but if i might be so blunt, I feel I'm at the stage where I can confidently claim to have "proven my capabilities".
But I haven't memorized Bayes theorem (or any other probability or math-formulas), despite having applied it about 100 gazillion times. And despite being an economist, I haven't memorized "the relationship between bond prices and interest rates". Now, I could try to reason these things out from scratch in front of you, but I imagine most people in our world would see that as a "weakness" or trying to hide the fact that I couldn't answer the question.
With the probability one, I'd start going down the various interpretations of probability and whether your notion of probability is internally consistent/justified, etc etc etc. I doubt I could write the math on the white board of the top of my head in an interview (and i know several statisticians who couldn't also), but I could probably outperform most of the candidates who could in its application in the real world (speaking from experience), or be able to question whether there is a better tool for the job in the real world.
With the bond one, I know there's an answer that you expect me to give from rote during my education. But i won't. I haven't memorized it (because from experience, memorising these types of things is bad form, conditions you into erroneous thinking when they eventually turn out not to be universally true, and is far worse than reasoning, questioning or thinking about problems). So i'll ask you to describe your idea of a bond to me. I'll ask you to describe your idea of interest rates. Why are the interest rates rising? Maybe then, depending on what answers YOU give, I'll say "well then obviously bond prices must move inversely to interest rate movements", but there's just as much chance i'll pick up on some mistake you've made and never reach that point.
Now I'm not attacking you specifically. I don't know you, or what we think of each other, or how we'd interview each other. But from my experience, most people/recruiters/employers/interviewers would take my behaviour as a negative sign. A sign of "stalling" or "evading the question". Questioning, or reasoning, or skeptically interrogating things or mulling over questions for long periods of time, especially if they consider the answer "known", is a "bad sign".
And the rote learner, who'd just happened to memorise a particular formula or spent most of their time in one particular context, or bought the book on interview questions for said industry will get a big fat tick.
Moral of the story: Please don't use "interview questions" :P