# Questions tagged [probability]

A probability provides a quantitative description of the likely occurrence of a particular event.

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### Difference HPDI and PI intervals

In Bayesian statistics, we may want to determine at what interval for example 95% of the posterior probability exists. For this we may want to use the Highest Posterior Density Interval (HPDI) which ...
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### Posteriori - How to determine the normalization coefficient without integrating the marginal [closed]

How can I deduce the posterior probability, up to a multiplicative coefficient, and how can I determine, without integral calculus, the normalization coefficient?
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1 vote
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### Combined Shapley Values for Probability Models

Using Python I have created two separate XGBoost probability models. From these two models, I compute a final value by multiplying the outputs (probabilities) together to give a probability of both ...
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### The probability of having disease is 0.1%; the test for it has 99% accuracy. What is the probability of having the disease given positive test result? [closed]

I got this question from an interview and failed to give an answer. I have been thinking about this for a while and would love some help. I think we have the following: P(D (disease)) = 0.1%, P(TP or ...
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### How do you find the KL Divergence between two multi-variable datasets?

Background I'm working on a tabular data model that performs a binary classification. The model has recently started underperforming and I'd like to know if that's due to a drift in the feature ...
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### Probability mass function of time of first head

This is an exercise from the probability book by Ross. This is not homework. Using conditional probability and the distribution of sum of two geometric random variables, the probability comes out to ...
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### probability distributions pdf cdf [closed]

Machine 1 works on task with duration S ∼ Exp(λ), machine 2 on task T ∼ Exp(µ). Tasks S and T are independent. a. Under which conditions are S and T iid? b. Find the CDF of S/T . c. find the PDF of S/...
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### What does positive likelihood ratio mean outside of medicine?

I am a meteorologist and I regularly hear of POD (we call it probability of detection) $POD = \frac{TP}{TP+FN}$ as well as FAR (False Alarm Rate) $FAR = \frac{FP}{FP+TN}$. But I recently had a ...
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### 2-dimensional functions of random variables with piecewise densities

From Meyer's Introductory Probability and Statistical Applications, 2nd ed: Suppose that the dimensions, $X$ and $Y$, of a rectangular metal plate may be considered to be independent continuous random ...
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### Probability of a Probability, how do I derive the P-Curve? [closed]

I am reading the following paper (https://arxiv.org/pdf/1603.07532.pdf) and I would like to understand how to derive a p-curve. By a p-curve, I mean the distribution of statistically significant p-...
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### Expressing intuition about surprise factor between three boxes in a guessing game

Suppose you are playing a guessing game where there is a box with three marbles. There are three kinds of boxes. Box A contains red, green and blue marbles; Box B contains red, green, and yellow ...
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### Is the iid assumption in Linear Regression necessary?

In linear or logistic regression, we have the following (adapted from Foundations of machine learning.): As in all supervised learning problems, the learner $\mathcal{A}$ receives a labeled sample ...
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### Number of samples for Hoeffding's Bound with Gaussian R.V

I am trying to obtain the required number of sample $n$ for a given confidence interval $\alpha$ and $X_1 ... X_n$ which are Gaussian rv with $\mu$ mean and $\sigma^2$ variance. I know that \begin{...
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### What is the algebra showing the logistic and log loss to be equivalent?

This question discusses two equivalent ways to express the canonical loss function for a logistic regression, depending on if you code the categories as $\{0,1\}$ or $\{-1,+1\}$. In the following, let ...
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### Stochastic Calculus: probability

Suppose two people want to play a game in which person A has probability 2/3 of winning. However, the only thing that they have is a fair coin which they can flip as many times as they want. They wish ...
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### Package for Multidimensional Density Estimation

I may be missing something obvious, but is there a python package that can reliably do density estimation of a PDF in high dimensions (e.g. 512)? I know of scipy's ...
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### What is the roadmap to self-taught probability and statistics for artificial intelligence?

I am trying to self-teach probability and statistics for Machine Learning career. However I want to learn very well as doing research in AI is my goal. Which books should I use to learn probability, ...
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### Are we estimating the Bernoulli parameter in Logistic Regression?

In logistic regression, we often use maximum likelihood to estimate the parameter vector $\boldsymbol{\beta}$ that parametrizes the logistic equation. My confusion stems from the following: We know ...
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### generating integers from a list of real numbers that came out of distribution

My model generates numbers, say x= 0.2719094. In the output, this is supposed to be an integer (that follows Poisson distribution, which is accounted for in the generation) mostly 0s, some 1s and a ...
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### Same probability distribution for monthly/yearly data?

I don't know if this is the right forum to ask this, but anyway. I don't have enough yearly data to perform a study on. Suppose I put weights on my monthly data to transform the monthly data into ...
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### Game of guessing or is it! [closed]

I am trying to learn coding and want to create a simple game. The idea is that there are 20 different animals, and you have 5 rooms, each round 5 out of the 20 animals hide in the room, where behind ...
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The theorem to prove is that if $X_n$ converges weakly to $X$, and $P(X \in D_g) = 0$ where $D_g$ is the set of discontinuity of $g$, then $g(X_n)$ converges weakly to $g(X)$. In Durrett, this is ...