nhaliday + motivation   70

What's the expected level of paper for top conferences in Computer Science - Academia Stack Exchange
Top. The top level.

My experience on program committees for STOC, FOCS, ITCS, SODA, SOCG, etc., is that there are FAR more submissions of publishable quality than can be accepted into the conference. By "publishable quality" I mean a well-written presentation of a novel, interesting, and non-trivial result within the scope of the conference.

...

There are several questions that come up over and over in the FOCS/STOC review cycle:

- How surprising / novel / elegant / interesting is the result?
- How surprising / novel / elegant / interesting / general are the techniques?
- How technically difficult is the result? Ironically, FOCS and STOC committees have a reputation for ignoring the distinction between trivial (easy to derive from scratch) and nondeterministically trivial (easy to understand after the fact).
- What is the expected impact of this result? Is this paper going to change the way people do theoretical computer science over the next five years?
- Is the result of general interest to the theoretical computer science community? Or is it only of interest to a narrow subcommunity? In particular, if the topic is outside the STOC/FOCS mainstream—say, for example, computational topology—does the paper do a good job of explaining and motivating the results to a typical STOC/FOCS audience?
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june 2019 by nhaliday
probability - Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? - Cross Validated
The confidence interval is the answer to the request: "Give me an interval that will bracket the true value of the parameter in 100p% of the instances of an experiment that is repeated a large number of times." The credible interval is an answer to the request: "Give me an interval that brackets the true value with probability pp given the particular sample I've actually observed." To be able to answer the latter request, we must first adopt either (a) a new concept of the data generating process or (b) a different concept of the definition of probability itself.

http://stats.stackexchange.com/questions/139290/a-psychology-journal-banned-p-values-and-confidence-intervals-is-it-indeed-wise

PS. Note that my question is not about the ban itself; it is about the suggested approach. I am not asking about frequentist vs. Bayesian inference either. The Editorial is pretty negative about Bayesian methods too; so it is essentially about using statistics vs. not using statistics at all.

wut

http://stats.stackexchange.com/questions/6966/why-continue-to-teach-and-use-hypothesis-testing-when-confidence-intervals-are
http://stats.stackexchange.com/questions/2356/are-there-any-examples-where-bayesian-credible-intervals-are-obviously-inferior
http://stats.stackexchange.com/questions/2272/whats-the-difference-between-a-confidence-interval-and-a-credible-interval
http://stats.stackexchange.com/questions/6652/what-precisely-is-a-confidence-interval
http://stats.stackexchange.com/questions/1164/why-havent-robust-and-resistant-statistics-replaced-classical-techniques/
http://stats.stackexchange.com/questions/16312/what-is-the-difference-between-confidence-intervals-and-hypothesis-testing
http://stats.stackexchange.com/questions/31679/what-is-the-connection-between-credible-regions-and-bayesian-hypothesis-tests
http://stats.stackexchange.com/questions/11609/clarification-on-interpreting-confidence-intervals
http://stats.stackexchange.com/questions/16493/difference-between-confidence-intervals-and-prediction-intervals
q-n-a  overflow  nibble  stats  data-science  science  methodology  concept  confidence  conceptual-vocab  confusion  explanation  thinking  hypothesis-testing  jargon  multi  meta:science  best-practices  error  discussion  bayesian  frequentist  hmm  publishing  intricacy  wut  comparison  motivation  clarity  examples  robust  metabuch  🔬  info-dynamics  reference  grokkability-clarity 
february 2017 by nhaliday
general topology - What should be the intuition when working with compactness? - Mathematics Stack Exchange
http://math.stackexchange.com/questions/485822/why-is-compactness-so-important

The situation with compactness is sort of like the above. It turns out that finiteness, which you think of as one concept (in the same way that you think of "Foo" as one concept above), is really two concepts: discreteness and compactness. You've never seen these concepts separated before, though. When people say that compactness is like finiteness, they mean that compactness captures part of what it means to be finite in the same way that shortness captures part of what it means to be Foo.

--

As many have said, compactness is sort of a topological generalization of finiteness. And this is true in a deep sense, because topology deals with open sets, and this means that we often "care about how something behaves on an open set", and for compact spaces this means that there are only finitely many possible behaviors.

--

Compactness does for continuous functions what finiteness does for functions in general.

If a set A is finite then every function f:A→R has a max and a min, and every function f:A→R^n is bounded. If A is compact, the every continuous function from A to R has a max and a min and every continuous function from A to R^n is bounded.

If A is finite then every sequence of members of A has a subsequence that is eventually constant, and "eventually constant" is the only kind of convergence you can talk about without talking about a topology on the set. If A is compact, then every sequence of members of A has a convergent subsequence.
q-n-a  overflow  math  topology  math.GN  concept  finiteness  atoms  intuition  oly  mathtariat  multi  discrete  gowers  motivation  synthesis  hi-order-bits  soft-question  limits  things  nibble  definition  convergence  abstraction  span-cover 
january 2017 by nhaliday
pr.probability - What is convolution intuitively? - MathOverflow
I remember as a graduate student that Ingrid Daubechies frequently referred to convolution by a bump function as "blurring" - its effect on images is similar to what a short-sighted person experiences when taking off his or her glasses (and, indeed, if one works through the geometric optics, convolution is not a bad first approximation for this effect). I found this to be very helpful, not just for understanding convolution per se, but as a lesson that one should try to use physical intuition to model mathematical concepts whenever one can.

More generally, if one thinks of functions as fuzzy versions of points, then convolution is the fuzzy version of addition (or sometimes multiplication, depending on the context). The probabilistic interpretation is one example of this (where the fuzz is a a probability distribution), but one can also have signed, complex-valued, or vector-valued fuzz, of course.
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january 2017 by nhaliday
soft question - Why does Fourier analysis of Boolean functions "work"? - Theoretical Computer Science Stack Exchange
Here is my point of view, which I learned from Guy Kindler, though someone more experienced can probably give a better answer: Consider the linear space of functions f: {0,1}^n -> R and consider a linear operator of the form σ_w (for w in {0,1}^n), that maps a function f(x) as above to the function f(x+w). In many of the questions of TCS, there is an underlying need to analyze the effects that such operators have on certain functions.

Now, the point is that the Fourier basis is the basis that diagonalizes all those operators at the same time, which makes the analysis of those operators much simpler. More generally, the Fourier basis diagonalizes the convolution operator, which also underlies many of those questions. Thus, Fourier analysis is likely to be effective whenever one needs to analyze those operators.
q-n-a  math  tcs  synthesis  boolean-analysis  fourier  👳  tidbits  motivation  intuition  linear-algebra  overflow  hi-order-bits  insight  curiosity  ground-up  arrows  nibble  s:*  elegance  guessing 
december 2016 by nhaliday
Reflections on the recent solution of the cap-set problem I | Gowers's Weblog
As regular readers of this blog will know, I have a strong interest in the question of where mathematical ideas come from, and a strong conviction that they always result from a fairly systematic process — and that the opposite impression, that some ideas are incredible bolts from the blue that require “genius” or “sudden inspiration” to find, is an illusion that results from the way mathematicians present their proofs after they have discovered them.
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may 2016 by nhaliday

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