Questions tagged [conditional-probability]
The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).
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questions
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How to interpret a statement about probabilities of arbitrary sets conditioned on random variables?
The following passage was extracted from section 6 of Chapter 2 in Kumar and Varaiya (2015). While the book is about stochastic optimal control, my question stems from a lack of understanding about ...
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how to convert deterministic function to probability function [closed]
given the follow structural equation:
y: = f(x) + n
how does one (in general) convert the above equation to the conditional probabilility distribution i.e. p(y|x)? Are there any books, video lectures ...
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10 views
Conditioning on random vector
If I have a conditional probability distribution $\mathbb{P}(X|Y)$, with $X, Y$ being random vectors, do $X$ and $Y$ need to have the same size, i.e., dimensionality?
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Derive $P(A|C)$ from $P(A|B)$ and $P(B|C)$
I'm working myself through renormalization theory (doesn't matter) and made up a problem to solve for myself, where in the solution seem to be missing one step, which can be summarized as follows:
For ...
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21 views
Prove that the variance of a Gaussian Process is minimum on its train data points
I want to prove that the variance of a Gaussian Process (GP) is the lowest on any one of its $p$ training data points.
The prior distribution for a zero-mean GP prior, with kernel function $k(x, x')$ ...
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1answer
36 views
If P(A) + P(B) = 1, does P(A|C) + P(B|C) = 1?
Just to explain where this is coming from. I was working on question 5(b) from stat 110 on conditional probabilities. I'll put a picture of the question and its solution below
I worked on question 5(...
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11 views
Log-likelihood Cox process
I have a question regarding the slide below. How did they obtain the log-likelihood function?
I would say it equals:
$$ \displaystyle \sum_{x,t} \log\left( \int_{-\infty}^{+\infty} f(D_{x,t} = d_{x,t} ...
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21 views
Conditional probability of a uniform distribution given a coin flip
Let $X \sim U(0,1)$ and $Y \sim U(0,1)$. Let $X$ and $Y$ be independent of each other. Assume that we observe the realization of $Y = y$.
Now, suppose that we throw a coin. The probability that it ...
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31 views
Probability X>Y given X>Z
Suppose $X$, $Y$ and $Z$ are independent but non-identically distributed random variables. How do we find $\mathbb{P}(X > Y| X > Z)?$
EDIT: My attempt at a solution.
We have $\mathbb{P}(X>Y|X&...
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26 views
How to caluclate conditional probability over 2 confidence intervals after a softmax on a classifier prediction?
Given 2 confidence intervals from 2 different models with 3 classes each:
ci1 = [0.2, 0.4, 0.4]
ci2 = [0.1, 0.5, 0.3]
Where each score corresponds to a class.
How to find the conditional probablity of ...
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20 views
Inference on a selectively revealed sample
I think this question may be related to cryptography, so I may have the wrong stack exchange, but I am not really sure.
Suppose there are two people Sam and Pam. Suppose we have a distribution, a set ...
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1answer
34 views
distribution of r.v. when it's broken down in binomials
there is a result I remember being right but I couldn't find it by googling.
Assume A and B indendepent random variable.
I know that when B is fixed (knowing B), A behaves like a binomial law of ...
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27 views
How to model risk with Neural Networks (is there a better approach)?
What should be our target if we have our features and our return is variable. Suppose we have:
...
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0answers
19 views
Can we combine CIs from dependent events?
Suppose we have calculated the following two confidence intervals:
We are 95% confident that the increase in the proportion of event x is between 0.50% and 1.50% of all events.
We are 95% confident ...
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1answer
29 views
Replication Probabilities
Imagine observing a random variable over time, let's say N = 20 years.
I compute the mean of the random variable within each year and obtain N estimates of the within year mean.
For each N estimates I ...
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19 views
Justification for writing Bayes' rule in the form of (H)ypothesis and (E)vidence?
I can see a straightforward derivation of Bayes' rule for events A and B using the definition of conditional probability. But, ...
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1answer
23 views
Using Bayes to Find Basketball Player's True Shooting % Talent Level
"Suppose you know that a basketball player’s true talent level is either a 20% shooting percentage or a 30% shooting percentage. At the beginning of the season, there is a 50% chance he is in ...
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1answer
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Is it possible to calculate conditional PD / unconditional PD from Hazard Rate?
I'm just wondering that can I convert hazard rate to probability of default? Suppose I have the lifetime table data as per below:
Time
Total
Default
Non-Default
At Risk
0
-
-
-
356,335
1
5,587
1,...
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29 views
Conditional probit to unconditional model?
I have a study in R in which I use public disclosures from companies and stock market data to estimate the probability that a new public disclosure (dividend announcement, etc...) will be published:
\...
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1answer
39 views
How to Interpret Conditional Distribution
Considering the following contingency table:
We calculate the conditional distribution for the city Manchester:
Why do we need the conditional distribution and how we interpret the result?
Is ...
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14 views
"Completely" Marginalizing Out a Variable from a Probability Distribution
Suppose you have a multivariate probability distribution function for 4 variables X1, X2, X3, X4 : P(X1, X2, X3, X4)
Normally, you can write P(X1|X2 = x2, X3 = x3, X4 = x4) : Then, you can find also ...
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Simulating Conditional Responses
I am trying to simulate data from a medical study. In this simulated data, each row should represent a patient, and each column should represent measurements from that patient (e.g. height, age, ...
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21 views
Bayes' Rule for second order Markov Chain
I want build two second order Markov Chains and compute the conditional probability naturally through Bayes' rule. Assuming for a sequence of transactions, say $T_i=(t_1,\dotsc,t_i)$, I want to find ...
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1answer
28 views
Probability of 2 simultaneous conditional probabilities for the same event
Suppose I have lamp L and two independent switches A and B. Both switches have a bit of a loose contact. From experience, I know that the probability of switch A turning on the lamp is 60% and switch ...
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1answer
49 views
How are copulas used in the real world?
I have been reading about copula models. Essentially, copula models seem to be a creative method for creating a joint probability distribution from several variables, in which each individual variable ...
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19 views
Variance of a normal random variable when conditioning on a correlated normal random variable being above a threshold
Suppose $X$ and $Y$ are correlated with correlation coefficient $\rho$. They are jointly normal with means $\mu_X$ and $\mu_Y$ respectively. Then what is $Var[X | Y \geq T]$? Feel free to add ...
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2answers
29 views
Connecting Survival Analysis to Overall Predicted Survival Probabilities
I've got a question on combining survival analysis with predicted survival probabilities that I'm sure someone must have thought about, but I just can't find anything out there.
Imagine I have a good ...
2
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2answers
45 views
Expectation of a normal random variable when conditioning on a correlated normal random variable being above a threshold
Suppose $X$ and $Y$ are correlated with correlation coefficient $\rho$. They are jointly normal with means $\mu_X$ and $\mu_Y$ respectively. Then what is $E[X | Y \geq T]$? Feel free to add additional ...
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Python: Generating conditionally dependent probabilities for Apriori data generation
Goal:
I want to generate fake transaction data to use as input to the Apriori association rule mining algorithm using python (3.9). The data should be generated such that for some reasonable* ...
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9 views
How to calculate expected normalization probability in following problem?
I have created a hypothetical example analog to my actual problem.
Suppose there are 500 houses randomly located in the city. People live 100 of these houses belongs to country A,
50 of these houses ...
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What's the difference between Y|X and Y|X=x
Suppose that Y and X are two random variables.
What is the difference between $Y|X$ and $Y|X=x$?
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1answer
52 views
Survival analysis using Linear Probability Models and Panel data
This question might have been answered somewhere else but I could not find it.
Hi all.
My research is about investigating whether a certain policy increases the speed of construction of housing units ...
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2answers
96 views
What is the hazard-rate of a truncated probability distribution?
Suppose $X$ is a random variable with pdf and cdf in forms of $f(X)$ and $F(X)$, with hazard-rate $h(X)$. Now, we define a new variable $Y$ which is a truncated random variable, $Y=X, \quad
\text{if }...
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"Linearity" of the Normal Distribution
I am trying to understand the following statement:
Can someone please explain what is meant by "the conditional expectation function m(x) is linear in x"?
In the case of regression, I ...
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1answer
65 views
For normally distributed random variables, if X is independent of Y and X is independent of Z, is X independent of max(Y,Z)?
Suppose $X,Y,Z\sim N(0,\sigma^2)$. $X$ is independent of $Y,$ $X$ is independent of $Z$ (but $Y$ and $Z$ are not independent), is $X$ independent of $\max(Y,Z)$?
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Check whether this conditional probability is correct
I have a conditional distribution $P(k_1, k_2 | a_1, e_1, a_2, e_2)$ and the distribution of $a_1, e_1, a_2, e_2$: $P(a_1, e_1, a_2, e_2)$, I want to obtain $P(k_1 | a_1, e_1)$, this is how I am ...
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Question about the conditional distribution of a sub-vector of a multivariate normal vector
For a multivariate normal vector $\mathbf{x} = (\mathbf{x}_1, \mathbf{x}_2, \mathbf{x}_3, \mathbf{x}_4)$ with mean 0 and variance $\mathbf{\Sigma} = \begin{bmatrix} \mathbf{\Sigma}_{11} & \mathbf{\...
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Joint densities do not exist, compute probability
I am taking a course in probability and in one of the PS I have got the following description:
$Y_i \sim \exp(\lambda_i)$ for $i=1,...,n+1$.
Define
$X_i = \min(Y_i,Y_{n+1})$.
In the first subsection ...
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The different between $P(O;\lambda)$ and $P(O|\lambda)$ [duplicate]
In hidden markov model (HMM), if I was given a particular observation $O$ and parameter of HMM $\lambda$, I want to compute the likelihood of a particular observation sequence $O$, $P(O|\lambda)$. Why ...
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3answers
177 views
Simulation in R to check graphically that marginal distributions are correct
The distribution on $R^2$ with joint density $h$ with respect to the Lebesgue measure is:
$$h(x,y)=\frac{3}{2}y 1_{A}(x,y), \ \ A=\{(x,y) \in R^2|0<y, x^2+y^2<1\}.$$
Then I have found the ...
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2answers
74 views
Find marginal distribution of Y while knowing distribution of X and $Y|X$
Assume that X is uniformly distributed on (0, 1) and that the conditional distribution of Y given $X = x$ is a binomial distribution with parameters $(n, x)$. Then we say that Y has a binomial ...
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36 views
Statistical Models that "Exploit" Distributional Knowledge of the Predictor Variables
I am trying to see if there any Statistical Models that (better) "Exploit" Distributional Knowledge of the Predictor Variables.
For example, I feel that is a common misconception (e.g Where ...
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1answer
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How is it possible to have $P(A|B \cup C)$ lower than both $P(A|B)$ and $P(A|C)$?
Let's say we investigate disease probability given two symptoms. Thus we have 3 variables:
A) has disease
B) has symptom 1
C) has symptom 2
We have following data:
Now we want to see which symptom ...
3
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1answer
34 views
Joint distribution where random variables always exist in the same orthant
I am sampling two vectors $x$ and $y$ ($\in \mathbb{R}^n$). First, I sample $x$ from an isotropic Gaussian distribution. Then I want to sample $y$ from the same distribution, but only in the orthant ...
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1answer
24 views
Law of total probability for random variables with Y < X
Could someone explain to me why the following equation holds? It is related to the law of total probability , but I don't get it. I'm confused because it's two random variables on the right side and ...
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interpreting p value in conditional testing
I have a question that may be related to multiple comparisons, but I'm not sure.
If I have a hypothesis to compare two groups (e.g., boys vs. girls) and I measure a continuous DV (e.g., the degree to ...
3
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1answer
81 views
How to generate data from this particular multivariate distribution?
Let $(X_0,X_1)$ be a random vector distributed according to the CDF $F_{(X_0,X_1)}(x,y)= \min (F_{X_0}(x),F_{X_1}(y))$ where $F_{X_0}(x),F_{X_1}(x)$ are the CDFs of $X_0,X_1$ respectively. We do not ...
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50 views
Bivariate Distribution for Milstein Scheme
I am seeking a density for $$Y_{t+1}\mid Y_{t},$$
where $$Y_{t}=\begin{pmatrix}Y_{t}^1\\
Y_{t}^2
\end{pmatrix},$$
and for $i=1,2$, the $i$th component of the 2-dimensional Milstein scheme is given ...
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1answer
52 views
Using Monte Carlo to sample from marginal distribution
I am defining a model on a vector, $T$, of size $n$, wherein each element $t_i \in T$ is independent and either $0$ or $1$. This model depends on 3 other parameters, $q$ (also a vector of size $n$), $\...
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1answer
78 views
Marginal Distribution in Beta-Binomial Model with Overdispersion Parameters
Problem Setting:
We assume there is a sequence of binomial trials of size $N_i$, $Y_i$ is the number of events of interest, $x_i$ is the predictor associated with trial $i$, and $\pi_i$ is the ...
