A routine question from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for self-study questions.

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1answer
24 views

Normal Distribution

I am a little bit confused about the correctness of the following statement. Could you check please, if my small "proof" is correct? Let $X_{1}, \ldots, X_{n}$ be a i.i.d sequence that follows a ...
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0answers
13 views

Lasso as an optimization problem

Following my previous question in this topic, I have two questions First: why my R code does not produce similar results to lasso? In this case I use an already developed package and find the ...
0
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0answers
15 views

How do I calculate the probability level in which I can rule something out?

The question asks "At what probability level can you rule out a 10% larger slope", given the data, with a measured uncertainty of 0.13 in the y. $$ \begin{array}{cc} x & y \\ 1.0 & 1.1 \\ 2.0 ...
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0answers
30 views

help me with this please [on hold]

Analyze the following statement: Michele watched videos of other soccer teams' plays, and she played better against those teams. Is the statement an example of correlation or causation? a:No ...
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0answers
9 views

How to find copula-based conditional probability P(U|V>=v)?

Using the Copula operator $C$, which for any (possibly dependent) RVs $U$ and $V$ represents the joint cumulative DF of their inverse probability transform. That is, $U^* = F^{-1}_U (U) \sim ...
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2answers
48 views

Covariance of two sample means

I am trying to derive the covariance of two sample means and get confused at one point. Given is a sample of size $n$ with paired dependent observations $x_i$ and $y_i$ as realizations of RVs $X$ and ...
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0answers
21 views

variational inference with KL

i am self-studying variational inference - and in Murphy's book "A probabilistic perspective on machine learning" it is discussed that minimizing the forward KL divergence (which is stated to be ...
1
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0answers
35 views

Calculating Odds Ratios from R output

I've fitted a GLM with a binomial link function in R, and need to interpret the result of the fit. How do I calculate the Odds Ratio for country 2 relative to country 1? Also, how do I calculate the ...
3
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1answer
44 views

Splines - basis functions - clarification

I have been reading the very helpful introduction on splines on http://freakonometrics.hypotheses.org/9184 and on http://www.stats.uwo.ca/faculty/braun/ss3859/chapters/splines/splines.pdf, as well as ...
0
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1answer
39 views

Difference between two lmer model

Can you please explain where is the difference between the following two models : ...
1
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0answers
30 views

Interpretation of various output of “lmer” function in R

library(lme4) fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy) The notation (Days | Subject) says to allow the ...
3
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1answer
24 views

Importance sampling - derivation

I am reading Kevin Murphy's explanation of importance sampling, and would like to test my understanding in three areas. The text states that importance sampling samples from any proposal $q(x)$, and ...
0
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0answers
26 views

probability distribution of complex Gaussian column vector and conditional probability of complex Gaussian column vector

I have column vector $\vec r=[r_1\ r_2]^T$. $$\vec r =hA\vec s +\vec n$$ where $h$ is a complex number , $\vec n \sim \mathcal{C} \mathcal{N}(\begin{bmatrix} 0 \\ 0 ...
0
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1answer
28 views

Are my correlations significant or non significant?

I have 4 Pearson's r correlation. I used cor.test in R. My p values are super high and I am having trouble interpreting significance. I would say there is no significance in ANY of my 4 correlations. ...
0
votes
1answer
18 views

Notation - gradients

i am reading Friedman's paper on stochastic boosting - and saw as per below the following set of formulas. purely from a notation perspective - why do we write $F(x)$ = $F_{m-1}(x)$ outside the ...
1
vote
1answer
14 views

Transforming models in order to use linear least squares estimations

As a pre-exam question, I found a question asking to consider the following three models $$ y = \beta_{0}(x_{1})^{\beta_{1}}(x_{2})^{\beta_{2}}\epsilon $$ $$ y = \frac{1}{\beta_{0} + \beta_{1}x + ...
1
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0answers
19 views

Simulating data from multilevel model

I am trying to simulate data from the following two-level model : $$Y_{ij}=\gamma_{00}+\gamma_{10}X_{ij}+\gamma_{01}Z_{j}+\gamma_{11}X_{ij}Z_j+u_{0j}+u_{1j}X_{ij}+e_{ij}$$ Three conditions are ...
2
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1answer
35 views

Gradient descent boosting

I am reading the useful Wikipedia entry on gradient boosting (https://en.wikipedia.org/wiki/Gradient_boosting), and try to understand how / why we can approximate the residuals by the steepest descent ...
2
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1answer
27 views

Adaboost - update of weights

i am self-studying AdaBoost - and reading the following useful article. http://www.inf.fu-berlin.de/inst/ag-ki/adaboost4.pdf . I am trying to understand, as per below, the following questions: 1) ...
0
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1answer
12 views

Poisson distribution exercises. Are my answers correct?

Suppose that a book contains an average of $\lambda$ misprints per page. (a) What is the probability that 10 pages will contain at most 1 misprint? (b) What is the probability that ...
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0answers
16 views

Calculating 95 % confidence interval for the mean [closed]

I need little help. If I have 30 random sample with mean of 52 and variance of 30 then how can i calculate the 95 % confidence interval for the mean with estimated and true variance of 30.
0
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1answer
15 views

Interpretation of “Same Slope” in Multilevel Modeling Example

An example of multilevel modeling : Consider an educational study with data from students in many schools,predicting in each school the students’ grades y on a standardized test given their scores on ...
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0answers
48 views
+50

Notation of Variance of Residuals in Multilevel Modeling

I am having some trouble to understand the notation of variance of residuals in multilevel modeling . In this paper "Sufficient Sample Sizes for Multilevel Modeling" , in p.87 below equation (3) , ...
3
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1answer
98 views

Proof of Simplification of Conditional Expectation of Product of Random Variables

Could someone please provide detailed steps to prove or disprove the following? $E[XY\mid XY>k] = E[XE[Y\mid XY>k]]$ Here, $X,Y$ are independent random variables that could be discrete or ...
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1answer
41 views

Generalised Least Square and Square Root of a Positive Definite Matrix

Consider a generalised least square problem as follows. $$ \mathbf y = \sigma \mathbf x + \mathbf e, $$ where $\mathbf x, \mathbf y\in \mathbb R^n, \sigma\in(0, \infty),\mathbf e \sim \mathscr N(0, ...
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0answers
31 views

Concept of fitting cubic splines

i am reading the elements of statistical learning, and the following diagram is included on page 262. i interpret the text (potentially incorrectly) that the fitted line $\mu(x)$ is a linear ...
1
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1answer
28 views

spike and slab models

Kevin Murphy discusses in this book (http://www.cs.ubc.ca/~murphyk/MLbook/index.html) the spike-and-slab model. I am struggling to understand the prior linked to this model. Why, if $\gamma$=0, and we ...
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1answer
33 views

Random Forest, dependent measurements

I have a following quiz: A random forest is used for classifying the disease state of patients based on measuring multiple genes. The dataset consists of 100 genes and 50 patients. However, ...
0
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1answer
21 views

Proof that Conditional Expectation of Sum is Sum of Conditional Expectations

\begin{eqnarray*} E\left[\left.\left(X+k\right)\right|\left(X+k\right)>0\right] & = & E\left[k\left|\left(X+k\right)>0\right.\right]+E\left[X\left|\left(X+k\right)>0\right.\right] ...
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1answer
33 views

Factor analysis and curved manifolds

I am self-studying Kevin Murphy's book, and one passage on factor analysis states that "the Factor Analysis model assumes that the data lives on a low dimensional linear manifold. In reality - most ...
1
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1answer
44 views

Hidden Markov model - formulas

I am self-studying Kevin Murphy's book, and trying to understand the math behind the HMM. I am struggling with the following derivation. Why can we in 17.46 cross out the $X_{1:t-1}$ term? my guess ...
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0answers
27 views

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 ...
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1answer
20 views

What are the different frameworks for solving regression problems in Machine Learning (like GLMs)?

I'm going through Andrew Ng's lecture notes on Machine Learning. The notes start with introducing linear regression and intuitively explaining what the cost function for the problem should be and how ...
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1answer
53 views

Is my understanding of Generalized Linear Models correct?

I'm going through Andrew Ng's lecture notes on Machine Learning & I just learnt about Generalized Linear Models there. I want to check if I know correctly what Generalized Linear Models are. ...
1
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1answer
14 views

Calculating new averages

I'm studying for a midterm in my basic stats course and came across a question that I'm confused with how it's solved. A manager at a local gas bar has 13 staff members. The average hourly wage for ...
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0answers
18 views

Mixtures of experts

I am trying to self-study and understand "mixture of expert" models, as desribed per below: . Is my intuition here correct that the $\rho(z_i|x_i,\theta)$ is a probability vector of length k, with ...
1
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0answers
19 views

How to compare a non-random sample with known population?

I'm currently working on my first substantial data project and I'm using stata (though I could probably just as well be using excel). The project deals with lobbying data and unfortunately I haven't ...
3
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1answer
36 views

Understanding a characterization of minimal sufficient statistics

I have some questions regarding the proof of the theorem below. First we need a definition: A statistic $T$ is minimal sufficient iff $T$ is a function of any other sufficient statistic. That ...
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0answers
6 views

reasons for using ARCH over transformation of the data

in using ARCH model, why is it that sometimes you dont transform your data and use an ARIMA model. is it always necessary to transform data with heteroscadasticity pattern.
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0answers
17 views

GLM - exponential form

i stumbled upon the following formula in Kevin Murphy's machine learning book: I am familiar wiht the following formula for the exponential family: $$ 1/Z(\theta) h(x) \exp \left( \theta^T ...
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0answers
11 views

Reference for Two-level Logistic Regression

I am an undergraduate student . In this level , we aren't taught Multilevel Logistic Regression. But my project topic is Multilevel Logistic Regression and I am ...
2
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0answers
28 views

Derivation of the BIC

i am trying to self-study / understand the derivation of the BIC. I have studied that: however - it is not quite clear to me how this leads to the formula below. I don't fully understand where the ...
1
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1answer
81 views

How to compute the residual standard deviation from `glmer()` function in R?

I want to extract standard deviation of residual from glmer() function in R . So I wrote : ...
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0answers
67 views

Reproducing table 3.3 from Elements of Statistical Learning

I am trying to reproduce a table 3.3 in Elements of statistical learning. Specifically, I am trying to get the coefficient estimates for ridge regression and lasso. I know that the estimate can be a ...
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0answers
38 views

Unable to figure out why 1/3=20 in this sample space question

I read a questiona and its answer also but unable to figure out why 1/3=20 is choosen? For ex- Q- Write the sample space S for the following random experiments. c.A customer arrives at a bank and ...
0
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1answer
35 views

Latent Dirichlet Allocation - definitions

I am self-studying the article on LDA by Blei, Ng and Jordan (https://www.cs.princeton.edu/~blei/papers/BleiNgJordan2003.pdf). at the start of the second section - the following definitions are given: ...
4
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0answers
50 views

Distribution of sum of order statistics

The question is from a problem I am trying to solve in Robert Hogg's introduction to Mathematical Statistics 6th version problem 7.2.9 in page 380. The problem is: We consider a random sample ...
1
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0answers
26 views

Bayesian decision theory - loss function

i am trying to learn bayesian decision theory. the book that i am using (Kevin Murphy: Machine Learning: A Probabilistic Perspective) - has the following introduction on the action a: however - ...
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0answers
21 views

gaussian process - missing data

One approach to deal with missing data is be to define a joint gaussian distribution / Gaussian process, and then define the (conditional) distribution of the unknown values on the known values. (e.g. ...