Questions tagged [self-study]

A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

A routine exercise designed to test one's knowledge; often, but not exclusively, from a textbook, course, or test used for a class or self-study.

The following guidelines are for those who are asking and those who would answer self-study questions.

They are rooted in two principles:

  • It is okay to ask about homework. Homework is included in this self-study tag. This site exists to help people learn and provide a standard repository for questions in statistics and machine learning, both simple and complex, and this includes helping students.

  • Providing an answer that doesn't help a student learn is not in the student's own best interest. Therefore, you should choose to treat self-study questions differently than other questions in order to avoid substituting for the student.

Asking about self-study questions

  • Make a good faith attempt to solve the problem yourself first. Showing a genuine attempt will help keep your question active. This can be demonstrated by a detailed description of your failed or incomplete or incorrect attempt(s).

  • Ask about specific problems you have encountered in your initial efforts. If you can't do that yet, try some more of your own work first or searching for more general help.

  • Be honest about the source of the question. Do this by adding the self-study tag and mentioning whether it is for some class in the question text. Provide reference to the book or material whenever available.

  • Quote the homework question exactly. If you try to paraphrase it, you might fail to paraphrase it correctly.

  • Be aware of school policy (if relevant). If your school has a policy regarding outside help on homework, make sure you are aware of it before you ask for/receive help here. If there are specific restrictions (for example, you can receive help, but not full solutions), include them in the question so that those providing assistance can keep you out of trouble. In particular, pay attention to plagiarism policy and plagiarism software when writing your own answer in order to avoid disciplinary consequences.

  • Only use suggestions you understand. It definitely won't help you later (after school, in later assignments, on tests, etc.), and it could be, at best, very embarrassing if you are asked to explain what you turned in. You can also comment on your own questions and answers to your questions, regardless of your reputation, so feel free to use comments to ask for additional clarification (after making an honest attempt at understanding). You may always ask further questions once you have tried and failed to understand points in some answers.

Answering self-study questions

  • Try to provide explanations that will lead the asker in the correct direction. Genuine understanding is the real goal for students, but trying to provide that is seldom unappreciated for any question. Give references that may help with the lack of background of the OP.

  • It's usually better to provide an incomplete solution (or code sample) if you believe it would help the student, using your best judgment. You can use pseudo-code and general descriptions first. In the spirit of creating a resource, you may come back after a suitable amount of time and edit your response to include more details, if the question seems like such information will have lasting value.

  • Don't downvote others who answer coursework-related questions in good faith, even if they break these guidelines. It is a better idea to suggest editing the response in a comment.

  • Leave positive comments. A student may be in the process of learning something obvious or is developing the good habits you'd expect from an expert. Add a respectful comment or answer that points them towards best practices and better style, but also point out the missing background necessary for the understanding of the question and its solution.

  • Don't downvote a homework question that follows the guidelines and was asked in good faith. CV explicitly accepts homework questions that follow the guidelines. Consider making helpful suggestions for improving the question instead.

  • The self-study tag should only be added by the one asking the question. If there's any room for doubt at all, it's best to leave it as is. Instead, always add a comment first, requesting that the asker clarify the situation.

(Adapted from an SO post by Joel Coehoorn as suggested in a meta discussion).

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Books for self-studying time series analysis?

I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself. Does anybody have a recommendation for a textbook on time series analysis that's suitable for self-study?
CuriousMind
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An example: LASSO regression using glmnet for binary outcome

I am starting to dabble with the use of glmnet with LASSO Regression where my outcome of interest is dichotomous. I have created a small mock data frame below: age <- c(4, 8, 7, 12, 6, 9, 10, 14, 7) gender <- c(1, 0, 1, 1, 1, 0, 1, 0, 0) bmi_p <-…
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7 answers

Find expected value using CDF

I'm trying to solve the following problem: Let $X$ have the CDF $F(x) = 1 - x^{-\alpha}, x\ge1$ . Find $E(X)$ for those values of $\alpha$ for which $E(X)$ exists. How can I determine which values of $\alpha$ exist? What do I do with the CDF? There…
styfle
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Interview question: If correlation doesn't imply causation, how do you detect causation?

I got this question: If correlation doesn't imply causation, how do you detect causation? in an interview. My answer was: You do some form of A/B testing. The interviewer kept prodding me for another approach but I couldn't think of any, and he…
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Visually interesting statistics concepts that are easy to explain

I noticed on Math Stack Exchange a terrific thread which highlighted a number of very visually interesting math concepts. I would be curious to see graphics/gifs which anyone has that very clearly illustrate a statistics concept (particularly those…
David Veitch
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What is the derivative of the ReLU activation function?

What is the derivative of the ReLU activation function defined as: $$ \mathrm{ReLU}(x) = \mathrm{max}(0, x)$$ What about the special case where there is a discontinuity in the function at $x=0$?
Tom Hale
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4 answers

Taking the expectation of Taylor series (especially the remainder)

My question concerns trying to justify a widely-used method, namely taking the expected value of Taylor Series. Assume we have a random variable $X$ with positive mean $\mu$ and variance $\sigma^2$. Additionally, we have a function, say, $\log(x)$.…
51
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5 answers

McFadden's Pseudo-$R^2$ Interpretation

I have a binary logistic regression model with a McFadden's pseudo R-squared of 0.192 with a dependent variable called payment (1 = payment and 0 = no payment). What is the interpretation of this pseudo R-squared? Is it a relative comparison for…
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Derivation of change of variables of a probability density function?

In the book pattern recognition and machine learning (formula 1.27), it gives $$p_y(y)=p_x(x) \left | \frac{d x}{d y} \right |=p_x(g(y)) | g'(y) |$$ where $x=g(y)$, $p_x(x)$ is the pdf that corresponds to $p_y(y)$ with respect to the change of the…
49
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Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1?

The denominator of the (unbiased) variance estimator is $n-1$ as there are $n$ observations and only one parameter is being estimated. $$ \mathbb{V}\left(X\right)=\frac{\sum_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}{n-1} $$ By the same token I…
48
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8 answers

Pitfalls in time series analysis

I am just starting out self-learning in time series analysis. I have noticed that there are a number of potential pitfalls that are not applicable to general statistics. So, building on What are common statistical sins? , I would like to ask: What…
naught101
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Why does the variance of the Random walk increase?

The random walk that is defined as $Y_{t} = Y_{t-1} + e_t$ , where $e_t$ is white noise. Denotes that the current position is the sum of the previous position + an unpredicted term. You can prove that the mean function $\mu_t = 0 $ , since…
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What's the difference between logistic regression and perceptron?

I'm going through Andrew Ng's lecture notes on Machine Learning. The notes introduce us to logistic regression and then to perceptron. While describing Perceptron, the notes say that we just change the definition of the threshold function used for…
43
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3 answers

How to take derivative of multivariate normal density?

Say I have multivariate normal $N(\mu, \Sigma)$ density. I want to get the second (partial) derivative w.r.t. $\mu$. Not sure how to take derivative of a matrix. Wiki says take the derivative element by element inside the matrix. I am working with…
user1061210
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