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Like Three Diag in his very good answer let's consider this a binomial problem with p being the probability of each single member of the list being dead and having cast a vote. The Bayesian question would be how to estimate our best guess of that probability and for binomial problems that is expecially easy because we can use a conjugated, in this case a ...


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Let us say you have a large list of supposedly dead voter, you pick one at random and check whether they are actually dead and actually voted, in which case you mark a one, otherwise there must be a mistake in the list and you mark it with a zero. This is a bernoulli variable: $$ X_i = \begin{cases} 0, \text{with prob. }\ p \\ 1, \text{ with prob.}\ 1-p \end{...


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Is it not simply the ratio of the PDFs at the newly sampled value? Or more specifically.. P(sex=male|height) = PDF_male(height)/[PDF_male(height)+PDF_female(height)]


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$\newcommand{\convp}{\stackrel{\text p}{\to}}$By assumption we have $\sqrt n(G_n - \theta) \implies Y$ for some random variable $Y$. If $\gamma \neq 0$ and we have a consistent estimator $\hat\gamma_n$ of $\gamma$, so $\hat\gamma_n \convp \gamma$, then $$ \frac{\sqrt n (G_n - \theta)}{\sqrt{\hat\gamma_n}} \implies \frac{Y}{ \sqrt \gamma} $$ by a combination ...


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While you could use different periods for different stocks, results that are extrapolated from this data could be misleading, since the data does not account for one-off events in different time periods. For example, if one of your time periods is $2006-2012$ while another time period is $2011-2015$, the latter time period may account less of the $2008$ ...


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I think this sounds like an interesting and important question. Whether it's a valid approach - I don't know. Typically, I have always seen causal analyses correspond to some variable that's one is able to externally fix. This is of course not the case with race, gender, etc. However, any variable can have an effect that's obscured by confounders, and you ...


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you can use vcov(model) in R to find the covariance matrix. a = rnorm(100) b = rnorm(100,1,1) c = rnorm(100,2,2) y = rnorm(100,3,1) m1 = lm(y~a+b+c) Assume you have a linear model $y = \beta_1 \cdot a + \beta_2 \cdot b + \beta_3 \cdot c+\epsilon$ where $a, b, c$ are the regressors, then you can use the above code to fit the model. Then simply type vcov(m1),...


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For the linear regression, rather than the residuals, one usually assumes that the errors (the random unseen fluctuations in the response) are normal (and independent). Then, the residuals, and the estimated regression coefficients, will have normal sampling distributions as a consequence, and the inference machinery works exactly, not asymptotically. That ...


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The CLT allows to talk about the asymptotic distribution of the mean, which is useful for providing inference on it. For example, that an experiment has led to a change in the mean of group A vs group B. It is true that for right-tailed distribution it is more convenient (IMHO) to talk about the median instead, but making inference on the median is harder (e....


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You can use both because they're the same: $$\begin{align}\hat{\operatorname{var}(\bar X)}&=\frac{\sum (x_i-\bar x)^2}{n^2}=\frac{\sum x_i^2-2\sum x_i\bar x+\sum\bar x^2}{n^2}\\&=\frac{\sum x_i-2\hat p\sum x_i+n\hat p^2}{n^2}=\frac{n\hat p-2\hat p n \hat p+n\hat p^2}{n^2}\\&=\frac{\hat p-\hat p^2}{n}=\frac{\hat p (1-\hat p)}{n}\end{align}$$ Note ...


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The $X_{1},...,X_{n}$ variables coming from the $Bernoulli(p)$ and the $x_{1},...,x_{n}$ are realizations of those variables. The main question is to check how well your $\hat{p}$ estimates the true parameter $p$. Most frequently we want to check what happens to such assumptions asymptotically as $n\rightarrow \infty$. So, you define an estimator of the ...


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