Top new questions this week:
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As someone who started by studying classical statistics where the Central Limit theorem is key to making inferences, and only later now am studying Bayesian statistics, I was late to realize that the …
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Consider two random variables $Y,V$ where $Y$ is discrete and $V$ is continuous. Is it true that $$ \Pr(Y=y)=\int \Pr(Y=y|V=v) f(v) dv, $$ where $f$ is the probability density function of $V$? I am …
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In survival analysis, is it appropriate to have a time to event value of zero for a subject(s). For example, the subject experiences the event on the same date as their date of entry. Does this cause …
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The goal is to find out if the frequency difference of a word “X” in two texts/corpora is significant. We have a $2\times 2$ contingency table of observed and expected frequencies. To find …
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In a PCA, the loadings can be understood as the weights for each original variable when calculating the principal component, or “how much each variable influence a principal component”. Thus,…
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I have been working with beta-bernoulli posteriors recently. Is it true that if $X,Y$ are independent rvs with $X \sim Beta(a_1+1,b_1+1)$ and $Y \sim Beta(a_2+1,b_2+1)$ then $\mathbb{P}(X>Y)>0.5$…
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For two random variables $X$ and $Y$, does it hold that the median of $\frac{X}{Y}$ is approximately equal to the median of $X$ divided by the median of $Y$: $$ F_{X/Y}^{-1}(0.5) \approx \frac{F_{X}^{-…
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Greatest hits from previous weeks:
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In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can’t we just simply take the absolute …
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I am lost in normalizing, could anyone guide me please. I have a minimum and maximum values, say -23.89 and 7.54990767, respectively. If I get a value of 5.6878 how can I scale this value on a scale …
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Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix …
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My understanding was that descriptive statistics quantitatively described features of a data sample, while inferential statistics made inferences about the populations from which samples were drawn. …
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What are principal component scores (PC scores, PCA scores)?
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Need to understand the working of ‘Embedding’ layer in Keras library. I execute the following code in Python …
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I understand that the basic definition of endogeneity is that $$ X’\epsilon=0 $$ is not satisfied, but what does this mean in a real world sense? I read the Wikipedia article, with the supply and …
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Can you answer these questions?
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Let’s assume I want to test a paired differences between two samples. Or, equivalently, to check, if the paired mean of differences is statistically non zero. Now I want to calculate the sample size. …
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Disclaimer : not a strong background in Bayesian statistics. I gather from questions such as this one and this one that in the context of VAEs, we suppose that we know the (form of the ?) prior $p(z)$ …
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I have an array of where each columns represents the probability of being in a certain state and rows represent time indexes. Each one of the rows sum up to one (we always are in one state). \begin{…
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