# All Questions

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### Deciding upon the important regressors for a SARIMA model

I have 14 months(01/07/2018 to 30/08/2019) of one minute data, which I have aggregated to 10 mins block. So I have a data of dimension "61056 * 350". From this I am using 12 months of data to train ...
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### distance formula between point estimated by gradient decent for a quadratic form at each iteration and the optimal value

Given a positive definite matrix $A$ and a function $f(x)=\frac{1}{2}x^TAx+bx+c$. We know that the hessian matrix of $f(x)$ is $A+A^T$ which is a constant and positive definite. Hence the stationary ...
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### Paired non-parametric test for a difference in variance

I have $N = 391$ paired data points $\mathbf a = a_1, \ldots a_N$ and $\mathbf b = b_1, \ldots b_N$. Both $\mathbf a$ and $\mathbf b$ are approximately normally distributed with a mean of zero. I ...
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### Mixed models basic

I am learning mixed models and while reading different materials I still have a couple of questions that I could not find answers. If I have 2 or more fixed effects and if the interaction is not ...
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### Controlling variables for interaction effects

I'm trying to understand what adding a 3rd covariate to a regression model does to the overall effects on interaction effects. I'll be using the mtcars dataset in R ...
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### parameter n in p.adjust function in R [on hold]

I'm quite confused about the n parameter in p.adjust function. p.adjust(p, method, n = length(p)) where n could be changed. but the default is length of p as stated in the documentation. So in my ...
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### Distribution to Examine Perceived Impact of Aircraft Flyovers [on hold]

I am attempting to model the impact of aircraft flyover noise and had a two question survey filled by students 1) The frequency of disruption of their study sessions per day 2) The perceived noise ...
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### Covariance Matrix for LDA

I have two classes of data: $X = (3,2),(2,3),(1,2),(2,1),(-2,-1),(-1,-2),(-3,-2),(-2,-3)$ $Y = 1,1,1,1,0,0,0,0$ Here, $Y$ is a binary label for each corresponding value of $X$. For example, the ...
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### Conjuage priors for linear combination

My knwoledge of statistics in general and Bayesian statistics in particular is limited. With that in mind, I would sincerely appreciate if somebody could help me with the following problem that I have ...
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### Maximum Likelihood: Bias and Efficiency

I have a basic question but I somehow can't wrap my head around it. It is said that Maximum Likelihood Estimation is unbiased and efficient in large samples. I am also aware that usually there is ...
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### How to discard the first spike after auto-correlation and handle sloping auto-correlation output

Disclaimer: I am not very mathematically inclined and am mostly looking to be pointed in the right direction. I have various signals that I am putting through an auto-correlation function that uses ...
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### ARIMA model on sales data [on hold]

I have a 'theory' question based on the ARIMA model. I have daily sales data for about 3 years, so I could apply ARIMA to the data. However, the data contains categorical variables. I can apply the ...
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### Selecting landmark in SVM [on hold]

I have difficulty to select landmarks l(i) in SVM. Suppose we have 3 features (m = 3), and we know that x(i) = l(i) (landmarks should be exactly the same as the training example), so which feature's ...
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### Which Naive Bayes Classifier fits best for categorical data? [on hold]

Which Naive Bayes Classifier would you choose to fit data with two categorical variables and a class variable? weather=['Sunny','Sunny','Overcast','Rainy','Rainy','Rainy','Overcast','Sunny','Sunny', ...
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### How do I approach this Bayesian question?

I am auditing a Bayesian Statistics course and I am facing problem in understanding the following question. Suppose you are given a coin and told that the coin is either biased towards heads (p = 0.6)...
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### Am I right in calculating confidence interval?

Task: In voting 20% of people among 1000 voted "yes", how many "yes" voted will be among 1 million responders? My approach: Ground truth is distributed normally with ...
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### Theoretically, does deep learning defeat all other statistical methods in predictive modeling?

I am a student of statistics/machine learning, just beginning to understand a bit about different methods and predictive modeling, but this question has been bothering me for a long time. We learn ...
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### 2-sample t-test VS Mann-Whitney test - one group is not normally distributed

I'm comparing two groups of data. One group has a sample size of 30, and the other a sample size of 45. The second group is not normally distributed, and thus this violates the normality assumption. ...
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### Estimating the bias and variance of an estimator

Suppose I have a vector of values generated by an estimator of $y$. I also have corresponding values of $y$ in another vector. Starting at the first observation, and adding the remaining observations ...
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### Calculate the inverse of the sum of an identity and a Kronecker product

Let $Q=\alpha\mathbb{I}+(S\otimes S)^T(S\otimes S)=\alpha\mathbb{I}+S^TS\otimes S^TS$, where $\mathbb{I}$ is $n^2\times n^2$ matrix, $S$ is an $m\times n$ binary matrix and $\otimes$ is a Kronecker ...
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### ALE plots on the log scale can be exponentiated to relative risks?

I'm using the ALE plot method for global interpretation of my gradient boosting model predictions. The model is trained on a dichotomic outcome and the predictions are on the probability scale. The ...
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### survreg predict default options

Given a suvreg model, for example, lfit <- survreg(Surv(time, status) ~ ph.ecog, data=lung) I get the same result if I ...
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### Clinical trials simple randomization scheme simulation [on hold]

I'm trying to do 1000 simulations for how to randomize 100 patients to two treatment groups (A and B) using simple randomization scheme (with probability 0.5) and figure out what is the chance of a ...
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### Marginal In Bayesian Optimization Expression

I am reading a paper and presentation on batch Bayesian optimization and came across the following formula. Question 1: Does the expression inside the redbox evaluate to $p(\mathcal I_{t,0})$? ...
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### “Nested” time-series comparison?

I'm Stick with a methodological problem and I'm not sure how to manage a possible solution. I want to compare two sets of observations made in two independent groups (15 subjects per group) over time. ...
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### Deriving the average and variance of number of runs in runs test

NIST states that the average and variance of a number of runs in the "runs above median" test as  \overline{R} = \frac{2n_a n_b}{n_a + n_b} + 1 \\ s^2 = \frac{2n_a n_b(2n_a n_b - n_a - n_b)}{(n_a+...
Suppose that $X$ is a random variable. Does it hold that $\mathbb{V}ar[X|X]=0$? What is the proof/intuition behind this?