50 Matching Annotations
  1. Oct 2020
    1. How this phenomenon translates into absolute, rather than relative, risk, however, is a bit thorny. A large study published in 2018, for instance, found that among women who had children between 34 and 47, 2.2 percent developed breast cancer within three to seven years after they gave birth (among women who never had children, the rate was 1.9 percent). Over all, according to the American Cancer Society, women between 40 and 49 have a 1.5 percent chance of developing breast cancer.

      The rates here are so low as to be nearly negligible on their face. Why bother reporting it?

    1. This result of Erd ̋os [E] is famous not because it has large numbers of applications,nor because it is difficult, nor because it solved a long-standing open problem. Its famerests on the fact that it opened the floodgates to probabilistic arguments in combinatorics.If you understand Erd ̋os’s simple argument (or one of many other similar arguments) then,lodged in your mind will be a general principle along the following lines:if one is trying to maximize the size of some structure under certain constraints, andif the constraints seem to force the extremal examples to be spread about in a uniformsort of way, then choosing an example randomly is likely to give a good answer.Once you become aware of this principle, your mathematical power immediately increases.
  2. Sep 2020
  3. Aug 2020
    1. Ray, E. L., Wattanachit, N., Niemi, J., Kanji, A. H., House, K., Cramer, E. Y., Bracher, J., Zheng, A., Yamana, T. K., Xiong, X., Woody, S., Wang, Y., Wang, L., Walraven, R. L., Tomar, V., Sherratt, K., Sheldon, D., Reiner, R. C., Prakash, B. A., … Consortium, C.-19 F. H. (2020). Ensemble Forecasts of Coronavirus Disease 2019 (COVID-19) in the U.S. MedRxiv, 2020.08.19.20177493. https://doi.org/10.1101/2020.08.19.20177493

  4. Jul 2020
  5. Jun 2020
    1. Winman, A., Hansson, P., & Juslin, P. (2004). Subjective Probability Intervals: How to Reduce Overconfidence by Interval Evaluation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30(6), 1167–1175. https://doi.org/10.1037/0278-7393.30.6.1167

  6. May 2020
  7. Apr 2020
    1. Therefore, En=2n+1−2=2(2n−1)

      Simplified formula for the expected number of tosses (e) to get n consecutive heads (n≥1):

      $$e_n=2(2^n-1)$$

      For example, to get 5 consecutive heads, we've to toss the coin 62 times:

      $$e_n=2(2^5-1)=62$$


      We can also start with the longer analysis of the 5 scenarios:

      1. If we get a tail immediately (probability 1/2) then the expected number is e+1.
      2. If we get a head then a tail (probability 1/4), then the expected number is e+2.
      3. If we get two head then a tail (probability 1/8), then the expected number is e+2.
      4. If we get three head then a tail (probability 1/16), then the expected number is e+4.
      5. If we get four heads then a tail (probability 1/32), then the expected number is e+5.
      6. Finally, if our first 5 tosses are heads, then the expected number is 5.

      Thus:

      $$e=\frac{1}{2}(e+1)+\frac{1}{4}(e+2)+\frac{1}{8}(e+3)+\frac{1}{16}\\(e+4)+\frac{1}{32}(e+5)+\frac{1}{32}(5)=62$$

      We can also generalise the formula to:

      $$e_n=\frac{1}{2}(e_n+1)+\frac{1}{4}(e_n+2)+\frac{1}{8}(e_n+3)+\frac{1}{16}\\(e_n+4)+\cdots +\frac{1}{2^n}(e_n+n)+\frac{1}{2^n}(n) $$

  8. Jan 2020
    1. My friend Marc again to the rescue. He suggested that since there was 10,000+ people RT'ing and following, I could just pick a random follower from my current total follower list (78,000 at this point), then go to their profile to check if they RT'd it and see. If they didn't, get another random follower and repeat, until you find someone. With 78,000 followers this should take about ~8 tries.

      Technically he said it would be random among those who retweeted, but he's chose a much smaller subset of people who are BOTH following him and who retweeted it. Oops!

  9. Dec 2019
    1. the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.
    1. Many people luck out like me, accidentally. We recognize what particular path to mastery we’re on, long after we actually get on it.

      Far too many people luck out this way and we all perceive them as magically talented when in reality, they're no better than we, they just had better circumstances or were in the right place at the right time.

  10. Mar 2019
    1. Special Complexity Zoo Exhibit: Classes of Quantum States and Probability Distributions 24 classes and counting! A whole new phylum of the Complexity kingdom has recently been identified. This phylum consists of classes, not of problems or languages, but of quantum states and probability distributions. Well, actually, infinite families of states and distributions, one for each number of bits n. Admittedly, computer scientists have been talking about the complexity of sampling from probability distributions for years, but they haven't tended to organize those distributions into classes designated by inscrutable sequences of capital letters. This needs to change.
  11. Feb 2019
    1. n they will share similar genes, but it 18is the phenotype –upon which selection acts –which is crucia

      There two important things to note.

      1. If the same genetic programme leads to two phenotypes because of the environment, this falls in the category of epigenetics. Epigenetic processes are usually not tree-like, hence, poorly modelled by inferring a tree.

      2. You implicitly assume (via your R-script) that homoiologies (in a strict sense, i.e. parallelism) are rare and not beneficial (neutral). But if the homoiology is beneficial (i.e. positively selected for), it will be much more common in a clade of close relatives than the primitive phenotype (the symplesiomorphy). We can further assume that beneficial homoiologies will accumulate in the most-derived, advanced, specialised taxa, in the worst case (from the mainstream cladistic viewpoint) mimicking or even outcompeting synapomorphies. A simply thought example: let's say we have a monophylum (fide Hennig) with two sublineages, each sublineage defined by a single synapormorphy. Both sublineages radiate and invade in parallel a new niche (geographically separated from each other) and fix (evolve) a set of homoiologies in adaptation to that new niche. The members of both sublineages with the homoiologies will be resolved as one clade, a pseudo-monophylum, supported by the homoiologies as pseudo-synapomorphies. And the actual synapomorphies will be resolved as plesiomorphies or autapomorphies.

      Without molecular (and sometime even with, many molecular trees are based on plastid in plants and mitochondria in animals, and both are maternally inherited, hence, geographically controlled) or ontological-physiological control it will be impossible to make a call what is derived (hence a potential homoiology) and what ancestral in a group of organisms sharing a relative recent common origin and a still similiar genetic programme.

  12. Oct 2018
    1. In contrast to his concept of a simple circular orbit with a fixed radius, orbitals are mathematically derived regions of space with different probabilities of having an electron.

      In this case, the QM model allows for probabilistic radii, not fixed radii, and the quantization is the energy level. An electron with principal quantum number n = 2 will always have quantized energy corresponding to \( E = R(1/n^2) \), but the exact minimal and maximal radial distance from the nucleus is not specified as in the Bohr model of the atom. Similar to the Bohr model though, the most probable radial distance is quantifiable, and that is the radius the electron is most likely to inhabit, however it will be found elsewhere at other times.

  13. Sep 2017
    1. Terrorist use of an actual nuclear bomb is a low-probability event

      Low probability and high impact but not a black swan

  14. Feb 2017
    1. These two qualities, therefore, PROBABILITY and PLAUSIBILITY

      This is an important set of terms to think through in terms of come to think about and with rhetoric.

    2. CHAPTER VI

      Chapter VII: General Audience Awareness

      But, really, Mere Rhetoric has a nice (I'm assuming she's mostly on point here) summary of some of the concepts to follow.

  15. Jan 2017
    1. Hume considers the possibility that there is, indeed, complete relativism in this matter. But his purpose is to find ways to reduce or eliminate disagreement, to set a standard

      A rhetorical concern dating back to at least Aristotle: how to decide upon things in the realm of the probable rather than the absolute.

  16. Nov 2016
    1. Finally, by assuming the non-detection of a species to indicate absence from a given grid cell, we introduced an extra level of error into our models. This error depends on the probability of false absence given imperfect detection (i.e., the probability that a species was present but remained undetected in a given grid cell [73]): the higher this probability, the higher the risk of incorrectly quantifying species-climate relationships [73].

      This will be an ongoing challenge for species distribution modeling, because most of the data appropriate for these purposes is not collected in such a way as to allow the straightforward application of standard detection probability/occupancy models. This could potentially be addressed by developing models for detection probability based on species and habitat type. These models could be built on smaller/different datasets that include the required data for estimating detectability.

  17. Jul 2016
  18. Feb 2016
    1. Great explanation of 15 common probability distributions: Bernouli, Uniform, Binomial, Geometric, Negative Binomial, Exponential, Weibull, Hypergeometric, Poisson, Normal, Log Normal, Student's t, Chi-Squared, Gamma, Beta.

  19. Jan 2016
    1. P(B|E) = P(B) X P(E|B) / P(E), with P standing for probability, B for belief and E for evidence. P(B) is the probability that B is true, and P(E) is the probability that E is true. P(B|E) means the probability of B if E is true, and P(E|B) is the probability of E if B is true.
    1. paradox of unanimity - Unanimous or nearly unanimous agreement doesn't always indicate the correct answer. If agreement is unlikely, it indicates a problem with the system.

      Witnesses who only saw a suspect for a moment are not likely to be able to pick them out of a lineup accurately. If several witnesses all pick the same suspect, you should be suspicious that bias is at work. Perhaps these witnesses were cherry-picked, or they were somehow encouraged to choose a particular suspect.

  20. Oct 2015
    1. Nearly all ap­pli­ca­tions of prob­a­bil­ity to cryp­tog­ra­phy de­pend on the fac­tor prin­ci­ple (or Bayes’ The­o­rem).

      This is easily the most interesting sentence in the paper: Turing used Bayesian analysis for code-breaking during WWII.

  21. Oct 2013