Top new questions this week:
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A friend from Italy pointed me to a nice Probability Theory book written in Italian by G. Dall’Aglio, a well-known Italian probabilist; Original title: Calcolo delle Probabilità, terza edizione, …
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I’m trying to solve this problem: Let $X$ be a single sample from Geo($p$) where $p ∈ (0, 1)$. Find a minimax estimator for $p$ under the loss $L(p, δ(x)) = (p−δ(x))^2/ p(1−p)$ . I’m trying to put …
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In machine learning approaches to classification, practitioners sometimes upweight the minority class to achieve a 50-50 balance, claiming that this results in improved classification performance. …
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I have a dataset with information belonging to medical patients (e.g. age, gender, height, etc.). Suppose that the response variable is whether or not the patient has a specific disease or not – thus, …
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A classical result in statistical theory is the Neyman-Pearson lemma, which not only shows the existence of tests with the most power that return a pre-specified level of Type I error, but also a way …
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This issue may be a little trivial, but I really want to get some inspiration. I know the formula of logistic regression, but have no idea how it is deduced. How can I deduce this formula from more …
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Consider two independent random variables $V$ and $Z$. Assume that $Z$ is standard normal. We only assume that $E[|V|]<\infty$ and $E[V]=0$. Now consider the following optimization problem: \begin{…
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Greatest hits from previous weeks:
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Fitting a logistic regression using lme4 ends with Error in mer_finalize(ans) : Downdated X’X is not positive definite. A likely cause of this error is …
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For a prediction interval in linear regression you still use $\hat{E}[Y|x] = \hat{\beta_0}+\hat{\beta}_{1}x$ to generate the interval. You also use this to generate a confidence interval of $E[Y|x_0]$….
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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 am trying to do a scatterplot to see the relationship between literacy and baby mortality. How do I know if literacy is my X axis and baby mortality is my Y axis, or the reverse? How do I …
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I have plotted this after I did a Shapiro-Wilk normality test. The test showed that it is likely that the population is normally distributed. However, how to see this “behaviour” on this plot? …
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Recently I have been reading about deep learning and I am confused about the terms (or say technologies). What is the difference between Convolutional neural networks (CNN), Restricted Boltzmann …
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Data analysis cartoons can be useful for many reasons: they help communicate; they show that quantitative people have a sense of humor too; they can instigate good teaching moments; and they can help …
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Can you answer these questions?
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In longitudinal experimental trials, where typically (relatively) small sample number of participants are examined, two solutions are proposed to address two kinds of issues: robust estimator of the …
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Suppose we have two groups of students: A and B. We want to look at the distribution of these two groups of students in each …
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I am pretty familiar with linear regression analysis, but not about how to generate plots using it (aside from residuals, etc.). I’d like to create a scatter plot of two variables, say depression and …
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