# Questions tagged [calculus]

For statistical questions involving calculus. Please use also a more statistical tag. For purely mathemathical questions about the calculus, it is better to ask at math SE https://math.stackexchange.com/

40 questions
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### How to manually calculate odds ratio for continuous variables?

In school, long before learning about logistic models, I've been taught how to calculate odds ratios by hand. Formula was based on a contingency table, just like this: This is very easy to ...
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### Meaning of Jacobian of the transformation for pdf of function of random vectors

I am studying multivariate statistics and I don't understand the meaning of Jacobian of the transformation for pdf of function of random vectors. If I have a random vector, let's say bivariate, (X,Y)...
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### Simple Log-likelihood question

I've got a simple question about deriving log-likelihoods. I am stumped by the following--> If the log-likelihood is: 𝑙(𝜆1,𝜆2) = 𝑦1 log(𝜆1𝐹1)−𝜆1𝐹1 −log((𝑦1)!)+𝑦2 log(𝜆2𝐹2) −𝜆2𝐹2 −log⁡ (...
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### Maximize profits by setting price

I am working on a model to set a price that maximizes profits. The equation for profits is: Profits=price x (# sold) - (fixed cost) x (# sold) I have models ...
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### Finding the slope at different points in a sigmoid curve

This is my data. x <- c(0.5,3.0,22.2,46.0,77.3,97.0,98.9,100.0) plot(x, pch = 19) I want to fit a curve through these points and then calculate the slope at ...
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### Can Regularization by achieved using Relative Sensitivity?

In a Mathematical Model we measure the sensitivity of the output with respect to the parameters and it is desirable that a small change in a parameter doesn't lead to wild fluctuations in the output ...
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### How do you obtain the standard error for a slope at a given data point, for curvilinear regression?

A distribution looks like this: modeled by an equation $y=1.0333x^2 - .5382x + 1.6905.$ Find the rate of change (i.e. the slope at that point of the regression equation) at point 6 (the x axis value)...
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My notes are rather light when it comes to this topic. I understand that the bayesian estimator, defined as (for sample space $\hat{x}$): $E[\Theta | \hat{x}] = \int_{ \forall \Theta}yf_{\theta|\hat{... 1answer 491 views ### gradient descent momentum vs step size In the gradient descent method, the learning rate (which is multiplied by the results of the gradient on each weight) identifies the size of the step (steep down) that the algorithm takes in each ... 1answer 357 views ### Calculating t-SNE gradient (a mistake in the original t-SNE paper) This is specific to the way the gradient of the KL divergence Loss function was derived in the original paper Visualizing Data using tSNE. In the Appendix A (Page 21), where they derive the gradient, ... 1answer 299 views ### Help with derivation of Mean Field Variational Inference I am studying Variational Inference using Bishop's book: Pattern Recognition and Machine Learning. At the moment, I am struggling to understand the Lower Bound derivation for the Mean-Field ... 0answers 2k views ### Deriving linear regression gradient with MSE So I've been tinkering around with the backpropagation algorithm and to try to get a better understanding of how it works and my calculus is quite rusty. I've derived the gradient for linear ... 2answers 255 views ### deriving z score for 95% confidence interval [duplicate] 95% of the area under the standard normal distribution lies within 1.96 standard deviations away from the mean (0). This 1.96 number is used to construct 95% confidence intervals. I was just ... 1answer 70 views ### Transformation of random variables in Generative Adversarial Nets Let$x$and$z$be real-valued random vectors, where$x = g(z)$, and$g$is an invertible, continuous and differentiable transformation of$z$. Then$p_z(z) = p_x(g(z)) \lvert det(\frac{\partial g(z)}{...
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how exactly is partial derivative different from gradient of a function? In both the case, we are computing the rate of change of a function with respect to some independent variable. While I was ...
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### What is the right method to estimate rate of change in daily values over a period of time?

I would like to ask you what is the best (or the right way) to calculate the rate of change in air temperature over a period of time and then see how this rate changes over time. Daily air temperature ...