# Questions tagged [bounds]

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### Changing only one point of a discrete distribution to maximize variance augmentation

X has a discrete distribution with support $x1, x2, ...$ in ${]}0,1{[}$. You have the right to change only one of the $xi$ to lead to the highest increase in variance (or, at least, a systematic ...
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### Can mean plus one standard deviation exceed maximum value?

I have mean 74.10 and standard deviation 33.44 for a sample that has minimum 0 and maximum 94.33. My professor asks me how can mean plus one standard deviation exceed the maximum. I showed her ...
56 views

### Why is the lower bound of the confidence interval of a model's error relatively constant compared to the upper bound? [closed]

I am interested in studying the effect of increasing data samples for a regression model on train error and test error. For this I have used 95% confidence intervals for different values of a sample ...
13 views

### Bounds on Ratio of Likelihood to Marginal?

Bayesian inference tells us that the posterior over parameters $\theta$ given data $X$ is given by: $$p(\theta|X) = \frac{p(X|\theta)}{p(X)} p(\theta)$$ Are there any known bounds on the ratio of the ...
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146 views

### Bounding sum of quartic deviations from sample mean

[Cross-posted here with no answers for a few days] I came - to the very best of my knowledge from reading the source - across the following statement in The Jackknife and Bootstrap, Shao and Tu, p. 87:...
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### Lower bounding the sum of product of two sub-Gaussian variables where one follows an AR(1) process

Suppose we have the sum $$\sum_{t=2}^{n}\epsilon_{t-1}u_t$$ where $\epsilon_t$ and $u_t$ are both sub-Gaussian variables. Further suppose that while $u_2,\cdots,u_n$ are i....
256 views

### Detecting outliers in binary data using Mahalanobis distance

I have a binary vector $X_i$, $i=1...N$ of independent Bernoulli variables with parameters $p_i, \mu_i = p_i, \sigma_i^2 = p_i(1-p_i)$ (which is known) and I'm looking for some sort of tail bound to ...
40 views

### Predicting limits of bounded dependent variable in Random Forest

I am new to machine learning and trying to use Random Forest to predict a bounded dependent variables (percentage from 0 - 100). The majority of the training data points (~80%) are at the limits of ...
75 views

### What does knowing two pairwise copulas tell us about the third

Say we have three random variables, which are all standard uniforms: $$X \sim U(0,1), \\ Y \sim U(0,1), ~\text{and}~~~ Z ~ U(0,1)$$ If we know two of the pairwise copulas, $C_{XY}$ and $C_{YZ}$, ...
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### Bounding the norm of the difference between two related probability densities

Suppose we have a continuous random variable $X$ and two continuous functions $f$ and $g$ such that $f(X)$ and $g(X)$ are continuous random variables. Let $p_A$ be the probability density function of ...
29 views

### What is a common-sensical approach to setting the boundaries of an interval?

As I am trying to present my results to a non-expert audience, I am wondering about what the most commonly used boundaries are for intervals. I mean specifically, which of the four versions explained ...
57 views

### How to bound a regressor function?

I've seen similar questions on here, but none seem to quite apply to my use case. I want to predict Metacritic scores bases on a number of features. Metacritic scores are bounded to a 0-100 scale, ...
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### Positive or negatively bounded CDFs [closed]

If $X\in\mathbb{R}^n$ is a continuous random variable whose cumulative distribution function is ordinarily $$F_X(x) = \int_{-\infty}^{\infty} f_X(x) dx$$ what is the meaning of F_X(x) = \int_{0}^{\...
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### How to deal with training models on data where the examples are highly dependent on each other?

Say you have a dataset of products sold at a store with the special condition that each day there is only one of each product in stock. That is, if there are multiple orders for a given product on a ...
I know that many results exist for making an argument about the tail of a distribution, i.e., for a random variable $X$, one can find a bound $\epsilon$ such that $\Pr[X \geq a]<\epsilon$. Some ...