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).

Filter by
Sorted by
Tagged with
0
votes
0answers
6 views

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 ...
0
votes
0answers
15 views

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 ...
0
votes
0answers
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?
1
vote
0answers
21 views

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 ...
0
votes
0answers
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 $k(x, x')$ ...
0
votes
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(...
0
votes
0answers
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} ...
0
votes
0answers
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 ...
0
votes
0answers
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&...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
0
votes
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 ...
1
vote
0answers
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: ...
0
votes
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 ...
0
votes
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 ...
0
votes
0answers
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, ...
0
votes
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 ...
0
votes
1answer
44 views

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,...
0
votes
0answers
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: \...
1
vote
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 ...
0
votes
0answers
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 ...
-1
votes
0answers
14 views

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, ...
0
votes
0answers
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 ...
0
votes
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 ...
2
votes
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 ...
0
votes
0answers
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 ...
1
vote
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
votes
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 ...
0
votes
0answers
11 views

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* ...
0
votes
0answers
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 ...
1
vote
0answers
32 views

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 $Y|X=x$?
2
votes
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 ...
1
vote
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 }...
1
vote
0answers
49 views

"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 ...
3
votes
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 $\max(Y,Z)$?
0
votes
0answers
16 views

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 ...
0
votes
0answers
11 views

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{\...
0
votes
0answers
29 views

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 ...
0
votes
0answers
13 views

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 ...
3
votes
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 ...
4
votes
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 ...
0
votes
0answers
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 ...
3
votes
1answer
74 views

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
votes
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 ...
0
votes
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 ...
0
votes
0answers
19 views

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
votes
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 ...
0
votes
0answers
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 ...
1
vote
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 $n$), $\...
0
votes
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 ...

1
2 3 4 5
43