Questions tagged [probability]
A probability provides a quantitative description of the likely occurrence of a particular event.
11,956
questions
2
votes
1
answer
13
views
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 ...
- 289
0
votes
0
answers
9
views
Choosing element from list according to value that tells how good I am at choosing
I have a list $L$ that contains $n$ options, sorted from the worst to the best option.
My objective is to choose an option from $L$.
I have a value $P \in [0,1]$, that can be understood like this: if $...
- 205
2
votes
1
answer
53
views
Use of $p_1/(p_1+p_2)$ to compare two probabilities $p_1$, $p_2$?
Let's say we want to compare two probabilities $p_1$ and $p_2$, not necessarily referred to the same population. For example, $p_1$ may be the probability of getting a certain disease conditioned on ...
- 875
0
votes
1
answer
19
views
Calculate ROC probability for highy correlated variables
The usual assumption of i.i.d. is made with such frequency that it risks being applied to things like difference of correlations for highly dependent (correlated) variables. To calculate dependent ...
- 12.2k
0
votes
0
answers
23
views
Distribution of Poisson Sample Variances
Understanding that the variance of a sample of normally distributed random variables is chi-squared distributed with mean = population variance, what distribution describes the variance of a sample of ...
- 121
0
votes
0
answers
17
views
Explain the intuition of Y = X/2 [duplicate]
I have some issues with understanding the intuition behind the following assignment.
Problem 2. When they say Y = X/2 what does this mean?
Does this mean whenever x takes any random value X, then y ...
- 163
3
votes
1
answer
97
views
Derivation of the Pitman estimator
I am having trouble with a step of a proof in the book Statistical Estimation Asymptotic Theory by Ibragimov and Has'minskii.
Lemma 2.1: Let $T=T(X_1, ..., X_n)$ be an arbitrary statistic with $\...
1
vote
0
answers
22
views
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?
- 11
1
vote
1
answer
23
views
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 ...
0
votes
1
answer
57
views
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 ...
- 3
3
votes
2
answers
116
views
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 ...
- 279
0
votes
0
answers
16
views
What is the non-asymptotic counterpart of the mutual information?
The mutual information of a joint probability distribution $p(x,y)$ tells us, if we send $n$-letter messages with each letter drawn from the marginal distribution $p_X(x)$, that we can use roughly $2^{...
- 249
0
votes
0
answers
22
views
Aggregating probabilities of events occurring along a linear feature
I am stuck in one problem and don't know how to approach it. So, let's say I know that a spatial event A has occurred, and the conditional probabilities of the same events Bi occurring along a linear ...
- 1
1
vote
1
answer
43
views
Importance of the standardization of a normal distribution
For a normally distributed random variable $X$, we can "standardize" $X$ by defining a new random variable $\frac{X-\mu}{\sigma}$ where $\mu$ is a mean of $X$, and $\sigma$ is a standard ...
- 217
0
votes
0
answers
24
views
Selecting without replacement a subset of items from a set knowing the final probabilities that items will be chosen
I don’t know if my title makes sense so I will try to explain using basketball as an analogy.
Say you have a set of players and you know the probabilities of them being on court at a given moment. ...
0
votes
0
answers
33
views
Is cross-entropy a reliable measure of similarity between probability distributions? [closed]
I'm working on a project that involves measuring the similarity between distributions using cross-entropy. However, I'm a bit confused about the reliability of this measure.
For example, let's say I ...
- 1
0
votes
0
answers
19
views
Multilevel (Hierarchical) Bayesian Model in R
I have my dataset with different mutations as unit of analysis. These mutations belong to 5 different classes. Also, I have collected, 9 features about these mutations. In other words I have 12 ...
- 1
1
vote
0
answers
16
views
Taking derivative of a function containing random variable wrt the variance of that variable [closed]
Say, I have a function containing a random variable such as $ f(X)$, where $X $ is the random variable. how can I take derivative with respect to the variance of $X$?
- 11
0
votes
0
answers
18
views
The probability integral transform when the CDF is non-decreasing
I'd like to ask about middle of the discussion in this answer. Writing things out in reverse, $\mathrm{Prob}(F_X(X) \leq y) = \mathrm{Prob}(X \leq \mathrm{inf}\{x: F_X(x) \geq y\})$. Why is $\mathrm{...
- 289
1
vote
0
answers
28
views
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 ...
- 11
0
votes
0
answers
17
views
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/...
0
votes
0
answers
18
views
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 ...
- 123
1
vote
0
answers
34
views
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 ...
- 111
-1
votes
0
answers
34
views
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-...
- 1
0
votes
0
answers
15
views
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 ...
- 1
1
vote
1
answer
66
views
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 ...
- 715
1
vote
0
answers
20
views
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{...
- 11
8
votes
2
answers
401
views
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 ...
- 46.6k
0
votes
0
answers
40
views
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 ...
- 1,140
2
votes
0
answers
33
views
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 ...
- 21
8
votes
1
answer
220
views
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, ...
3
votes
2
answers
344
views
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 ...
- 715
1
vote
1
answer
16
views
Calculate marginal distribution using chain rule
I am trying to calculate the marginal distribution P(X) of the following joint distribution P(X, Y).
y=0
y=1
y=2
x=0
.2
.1
.2
x=1
0
.2
.1
x=2
.1
0
.1
Here is how I am calculating $P(X=0) = P(X = ...
- 242
1
vote
1
answer
78
views
Maximum of a distribution not invariant in different coordinate systems?
Let's say we have a probability distribution in x,y space:
$$
p(x, y)=\frac{1}{4 \pi} \sqrt{x^2+y^2} \exp \left(- \sqrt{x^2+y^2}\right)
$$
This can be converted into polar coordinates as:
$$
p(r, \...
- 11
2
votes
1
answer
19
views
Are there families of known parametric copulas for non-standard marginal normal distributions?
I know that a family of Gaussian copulas generates a standard bivariate normal distribution if and only if the marginal ones are standard normal. This characterizes the Gaussian copulas, where I have ...
- 21
1
vote
0
answers
10
views
Score for over/under representations of a variable in sub-group
I have a corpus of book publications split into different clusters. I have information about the nationality of the authors (variable A) and the nationality of the publishing company (variable B).
In ...
- 11
0
votes
1
answer
51
views
Normal Distribution/Probability problem
I have the following problem:
The weights of large eggs are normally distributed with mean 65 grams and
standard deviation 4 grams. The weights of standard eggs are normally distributed with
mean 50 ...
0
votes
0
answers
24
views
Uncertainty in slope
I've created a linear relationship between two different measurements. The equation is in the form of y=mx and I am trying to validate my slope within a certain range so that when I run my experiment, ...
- 1
0
votes
0
answers
25
views
What test should I use to compare self-ratings of two types?
I ran a goal setting program at my university. Students had four goals each. For each goal they could choose either basic or advanced level. They rated themselves between 1-5 each week. I want to ...
0
votes
1
answer
18
views
Confirmation of MGF of Shifted Exponential Distribution
Consider the probability distribution $D \sim X - a$ where $X \sim \text{Exp}(\lambda)$. My task is to find the MGF of probability distribution $D$. I think I have a solution but it contradicts what I ...
5
votes
3
answers
834
views
What is the "grid" in Bayesian grid approximations?
I tried looking for my specific question, but I only found partially related questions here, here, and here. I think my question is much simpler than what was asked and answered in these queries. I'm ...
- 3,885
1
vote
0
answers
21
views
Modelling a right-long-tailed distribution
The plot below models a sample of departure delays of flights, the x-axis is minutes delayed. The mean is about 10 (red line) and std is 36. The distribution has a very long tail (some flights are 800 ...
1
vote
0
answers
10
views
Scaling factor in forward-backward algorithm
I am studying forward-backward algorithm following the wikipedia page. I have little background in statistics and have managed to understand (hopefully) most part of the algorithm. However the scaling ...
- 11
2
votes
0
answers
24
views
How to calculate p-value for a survey question with three categorical answers options? [duplicate]
I conducted a survey of N=88 students.
I asked a question:
'What type of goal setting do you prefer?'
A: online
B: paper-based
C: no preference
Responses
A: 58
B: 9
C: 21
I will display this result in ...
0
votes
1
answer
44
views
What Is the Probability of Losing Money?
I was watching Veritasium's Would You Take This Bet? video. In a part of the video Derek asks people whether they would accept the bet in the case of each true guess for flipping the coin the person ...
- 11
0
votes
1
answer
48
views
Limiting value of the moment generating function
Suppose that the discrete random variable $X_{n}$has a geometric distribution given by
$$f_{X_n}(x_n)=P_n{(1-P_n)}^{x_n}$$ where $$x_n={0,1,2,3,}$$ and $$P_n\ =\ \frac{\lambda}{n}$$ for $0<\lambda&...
- 31
1
vote
1
answer
44
views
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 ...
- 13
1
vote
1
answer
24
views
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 ...
- 31
1
vote
1
answer
38
views
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 ...
- 11
2
votes
2
answers
240
views
Two Different Proofs of Continuous Mapping Theorem
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 ...
- 514