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    A propositional logic question

    Actually, I have several questions: 1) Why are axiom schemas the way they are? What do they represent? I know that infinitely many axioms can be written using the axiom schema form. However, what's the formal definition of axioms in predicate calculus? I've heard that the formal definition of...
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    Statistical models and likelihood functions

    Homework Statement I have a couple of notation interpretation questions: 1) What does f_X(x|θ) represent in this case? The realization function of of our random vector X for some value x and a parameter θ (so that if our random vector has n random variables, its realization vector will be a...
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    Likelihood functions

    As far as I know, the definition of likelihood functions is the probability of a given random variable result given some parameter (please correct me if I'm wrong). What kind of parameters are usually handled by likelihood functions? Population parameters? Statistical model parameters? Both?
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    Any good statistics glossaries out there?

    I'm looking for a statistical glossary - an organized and detailed list of concepts which constitute the field of statistics. I've already checked the glossaries of some statistics books; however, many of the said glossaries seem to use very general terms to define each glossary terms - they...
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    Please judge my statistics knowledge based on the following mind map

    How bad is my statistics knowledge based on the following mind map? Any concepts which aren't bold are the concepts that I know; the bold ones are the ones I'm currently learning. The mind map in question: What should I learn next based on my current...
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    Mathematical logic and statistics

    Let's say that a treatment A has been proven to have an impact on the levels of B with a given confidence interval. Let's also say that we know that the treatment C causes the treatment A to be imposed on our sample. Before the testing on the effects of C has been done, which statistical models...
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    News Should smoking in all the public places (indoors and outdoors) be banned?

    In your opinion, should smoking in all the public places, including streets, parks and even rivers be banned? In my opinion, it should. Not only have smoking bans been proven to be highly effective in reducing the overall mortality rate and the incidence of various diseases (Source...
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    News What's the difference between many human rights violation accusations and

    What's the difference between many human rights violation accusations and baseless conspiracy theories? For example, I often encounter human rights violations accusations against the Russian government - that it supposed abused the legal system and the state TV system to discredit and jail...
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    Bayesian statistics learning materials

    Does anyone here know any good Bayesian statistics, Bayesian hypothesis testing, Bayesian inference, etc. learning materials (preferably online)?
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    News Should the church be taxed?

    In my opinion, the church shouldn't be subject to any tax exemptions at all. It should be taxed, and the taxes should be reinvested on noble causes, such as health care, education, scientific and technological development, resource and environmental protection, housing security and food...
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    Bayesianism vs frequentism: which one is better for science?

    Which interpretation of probability is better for testing scientific hypotheses, and for scientific modeling in general: Bayesianism or frequentism, and why?
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    Medical What are some scientifically valid ways to increase your life expectancy?

    As the title says, what are some scientifically valid ways to increase your life expectancy? That is, which practices (ex: diet, exercise, etc.) have been shown to increase the average life expectancy in experimental studies?
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    Do the premises of a theory have to be empirical?

    Since there's no board dedicated to the methodology of science, I thought that this board would be the best fit. Here's my question: Do the premises and elements of a theory have to be empirical? Or do they not have to be, as long as the theory is consistent with the observed data? By...
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    How is causality proven when it's impossible to change the IV?

    How is causality usually proven when it's impossible to change the independent variable? Also, why is correlation often treated as a very reliable hint to causation, even in various respected journals? Here's an example...
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    The line between insane conspiracy theories and credible human rights violatio

    What is the formal definition of the line between insane conspiracy theories and credible human rights violations? What usually distinguishes the two, and makes some rational, and others not? For example, 9/11 conspiracy theories don't seem to be credible nor believable at all. However, US...
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    The fields of applied mathematics

    What kind of mathematical disciplines/fields take part in what's called "applied mathematics"? As far as I know, it's Differential Equations, Calculus, Statistics and Linear Algebra. What other fields are there? I'm sure there are some others.
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    Transform a set into an ascending order sequence

    Homework Statement Let's say that I have a set called M, which is a subset of real numbers. Let's say that I want to create a sequence {s_1, s_2, ..., s_3} with all of the members of M, which would be ordered in an ascending (increasing) order. For example, if M = {4, 5, 1, 3, 2}, then s_0 = 1...
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    What's the difference between trends and regression lines?

    What's the difference between trends and regression lines (linear and non-linear) which minimize the residual sum of squares?
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    Estimating the unreliability of extrapolations

    Are there any methods for estimating the unreliability of extrapolations? Obviously doing so is highly unreliable itself. However, I'm sure there are some factors, such as for how long a given trend persisted - if it persisted for a very long time, the future short-term extrapolations based on...
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    Determining the second order polynomial from the intersection points

    Homework Statement Let's say that we have a second order polynomial function, and we know all of the points where it intersects with the x and y axis. Ex: (-2; 0), (0; 2), (1; 0) How does on determine the ax^2+bx+c polynomial form based on that? Homework Equations - The Attempt at...
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    Mathematical logic & its branches

    What branches of mathematical logic are there? I've taken formal logic (that is, the logic where one has various operators, like conjunction, disjunction, etc). What other fields of logic should I take to become better at mathematical logic? Which fields of logic are the most useful and essential?
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    Any good books on empiricism and the scientific method?

    Do you know any good books which explain the scientific method and empiricism in detail? If so, please share.
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    Which branch of statistics and mathematics deals with extrapolations?

    Which branch of statistics and mathematics deals with extrapolations and trend analysis? That is, where one can estimate various trends (be they exponential, linear, etc.) that apply to our data and draw a trend which could extrapolate the future variation. Am I referring to the time series...
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    How to get the distance traveled from the force and mass functions?

    Homework Statement I have two functions: F(t) - where F(t) is the force at a given time t m(t) - where m(t) is the mass of the object in question at a given time t Let's say that some force (in a thrust form) is applied to the object for "b" seconds. The function F(t) specifies in what...
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    Hydrogen + oxygen model rockets

    Homework Statement Could one expect to get a good thrust off oxygen and hydrogen fuel in a gaseous form, pumped at ~60 PSI into a 2 liter container? How much (in terms of mass) oxygen and hydrogen would be in the said container at such a pressure, assuming we have a 2/1 hydrogen/oxygen ratio in...
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    Economics: Elasticity of substitution between capital and labor

    Homework Statement Am I right or wrong on the following? The more capital is needed to replace one unit of labor to attain the same production level, the lower the elasticity of substitution between capital and labor. It can measure how productive the capital in question is, and/or how...
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    Sign convention and vectors

    Homework Statement What is sign convention, and how is it applied to vectors? I was reading an economics paper when I came across this term. There's a ":" sign between the vector in question and an entry, which is all supposed to output a real number. What exactly is sign convention, and how...
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    A linear algebra question

    Homework Statement Is a set of n-tuples which must respect the conditions of closure under addition and closure under scalar multiplication a vector space or a vector subspace? That is, in a 3-dimensional space, are planes which pass by the origin considered to be subspaces of the 3-dimensinal...
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    Natural log derivatives

    Homework Statement What does it mean when the derivative of a function f(x) is in the form: d ln f(x) / d ln x ? Is it the logarithmic scale derivative, or something? Homework Equations d ln f(x) / d ln x The Attempt at a Solution Googling.
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    A notation question

    Homework Statement What does the following notation mean, assuming that I is a set, and i is a member of the set i, and x is an endowment of a member i, and is a vector? Assuming x is (1, 2, 3) for each i, and I = {1, 2, 3, 4} Does mean (1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3) ...