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0answers
7 views

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 ...
1
vote
0answers
11 views

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 ...
1
vote
1answer
25 views

Distribution for simulating machine learning algorithm errors

I want to simulate machine learning algorithm, that solves binary classification problem. This algorithm should output not just $\{0, 1\}$ labels, but probability of class $1$ (that of course is in $[...
1
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0answers
14 views

Can I use subset of a time series if OLS assumptions are failing?

My OLS model build on full data has heteroscedasticity of residuals. Is it allowed to use a subset of the time series to get around this issue? What are the possible implications?
1
vote
1answer
9 views

One year of historical data with yearly and daily seasonality

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 ...
1
vote
0answers
4 views

One or two structural equation models if DVs are not theoretically related?

I have four DVs and 3 IVs. The IVs predict all DVs. The DVs are split into two pairs. That is, DV1 is theoretically related to DV2 and DV3 and theoretically related to DV4, but there is no theoretical ...
3
votes
1answer
32 views

linear combination and univariate normal

Show that $(X_1,X_2)$ has a bivariate normal distribution with means $\mu_1, \mu_2$, variances $\sigma _1^2 $ and $\sigma _2^2$, and correlation coefficient $\rho $ if and only if every linear ...
1
vote
1answer
23 views

What does it mean “a conditional expectation given a stochastic process”?

Let $(\Omega,\mathscr{F},P)$ be a probability space. Let $X,Y$ be random variables on $\Omega$. Then, we say $Z\sim X|Y$ iff (i) $\int_{Y^{-1}(A)} X dP = \int_{Y^{-1}(A)} Z dP$ and (ii) $Z$ is $\...
1
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1answer
24 views

Bivariate normal distribution from independent random variables

Let $X_1$ and $X_2$ random variables such that $X_1+X_2$ and $X_1-X_2$ have independent standard normal distributions. Show that $x=(X_1, X_2)$ has a bivariate normal distribution. My work: Since $...
1
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0answers
10 views

How to treat low frequency continuous variable in machine leanring

Hello I am working on machine learning model for count data, and I have various features that are highly skewed. The frequency table for one of the feature is given below. ...
1
vote
1answer
23 views

What probability or weight should I assign to X so that it has a Y% chance of being one of the 6 items selected out of a population of 12?

I have a population of 12 items, let's call them A through L. I'm going to be drawing 6 of those items out of the population without replacement. So you can't choose the same item twice. What I know ...
1
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0answers
20 views

Expected value for f(x) [on hold]

I am reading an article and trying to extend their case to a multivariate case. I have the function $f_{i} (x)=\frac{1}{|Σ|}f_{0}((x-μ_{i})'Σ^{-1}(x-μ_{i}))$, and I am trying to find $∫xf_i^2 (x)dx$ ...
1
vote
1answer
18 views

MLE of shifted Gamma

Let $X = (X_1,\dots, X_n)$ and $X_1,\dots, X_n$ be i.i.d Gamma($p,a,A$) random variables where $p$ and $a$ are known. Find the MLE of $\theta =A$. We have \begin{align*} f_{\theta}(x) &=\...
7
votes
1answer
255 views

Why does the likelihood function of a binomial distribution not include the combinatorics term?

So the likelihood function for a binomial distribution is: Why is the likelihood function above not multiplied by a combinatorics term: n! / (x! * (n - x)!) If the likelihood function is ...
1
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0answers
7 views

“nested” time-series comparison

Hope you can help me with a methodological issue. I want to compare two sets of observations made in two independent groups (15 subjects per group) over time. The two groups are cell cultures derived ...
1
vote
1answer
21 views

In a large extended family somehow only my sister was born in October. What are the odds of that?

The are 45 people in my extended family. Only my sister was born in October. What are the odds of that occuring?
1
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0answers
12 views

Why is Knuth's definition of random sequence (R4) too weak?

Knuth's $R4$ definition of a random sequence is called "too weak" and he presents an example of why --- second paragraph after the definition on the previous link. Definition $R4$. A $[0..1)$ ...
1
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0answers
17 views

Regression: How to account for grouping among dependent variables [on hold]

updated to clarify what I'm asking... I have a data set where each respondent provided a "rating" on multiple objects (i.e 50). There are also attributes measured for each respondent (i.e. Age, ...
2
votes
0answers
24 views

Joint distribution of sample means from multivariate normal

Suppose $\mathbf{Z_1}, \dots, \mathbf{Z}_n$ be iid random vectors of normal distribution s.t. $\mathbf{Z}_i \sim N(\boldsymbol{\mu},\boldsymbol{\Sigma})$ where $\mathbf{Z}_i = (X_i, Y_i)^T$, $\...
2
votes
0answers
12 views

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 ...
1
vote
1answer
14 views

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 ...
1
vote
1answer
13 views

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 ...
1
vote
1answer
19 views

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 ...
0
votes
0answers
7 views

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 ...
1
vote
0answers
10 views

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 ...
2
votes
0answers
17 views

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 ...
1
vote
1answer
13 views

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 ...
1
vote
0answers
23 views

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 ...
0
votes
0answers
16 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
0answers
6 views

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', ...
0
votes
1answer
29 views

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)...
0
votes
1answer
29 views

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 ...
1
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0answers
25 views

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 ...
1
vote
2answers
23 views

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. ...
1
vote
0answers
31 views

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 ...
0
votes
0answers
7 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
0answers
12 views

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 ...
1
vote
1answer
19 views

Bayes and Naive Bayes code implementations

I know that Bayes classifier assigns the new data point $\pmb{x}$ to the class $\omega_j, \ j=1,\dots,M$, when $p(\omega_j \mid \pmb{x}) = \max_{q=1,\dots,M}p(\omega_q \mid \pmb{x})$, where $p(\...
0
votes
0answers
11 views

Finite grid approximation to the Bayesian filtering problem

I need some hints for solving Ecercise 4.4 from Bayesian Filtering & Smoothing by Simo Särkkä: Select a finite interval in the state space, say, $x \in [-10, 10]$ and discretize it evenly to N ...
1
vote
1answer
19 views

Advise for two non gaussian distribution group

I have a dataset which test the introduction of a new measure of a luggage checking a local small airport, the aim is to conclude whether the new measure reduce the luggage checking time. My dataset ...
0
votes
0answers
19 views

What distribution can be predicted more accurately?

I am working on simple statistical prediction. However, whatever i did, i come up with a high range. I have used standard deviation and also percentile. Yes they work well in the given data but the ...
0
votes
0answers
23 views

Compute the Risk function

Suppose we are given $(X_1,...,X_n)$ random variables which are iid. from $\mathcal{N}(\mu,\theta)$ and finite variance. Let $Y=\frac{1}{n}\sum_{i=1}^n(X_i-\overline X)^2$ and define a loss function $...
1
vote
2answers
33 views

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 ...
0
votes
0answers
15 views

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 $p(\mathcal I_{t,0})$? ...
0
votes
0answers
7 views

“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. ...
0
votes
0answers
13 views

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+...
1
vote
0answers
12 views

Modelling resource selection in savanna ungulates

I am amidst an analysis of an 8 year data set that was collected from wildlife surveys over an 8 year period for my MSc thesis. 2 surveys were conducted each season for the three discernible seasons ...
0
votes
1answer
18 views

Conditional variance of a random variable conditioned on its own value

Suppose that $X$ is a random variable. Does it hold that $\mathbb{V}ar[X|X]=0$? What is the proof/intuition behind this?

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