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
21 views

conditional probabilty and the sample space

BACKGROUND Allow that an experiment 1 and 2 are defined by a probability space triple $(\Omega_1, \mathcal{F}_1, P_1)$, and $(\Omega_2, \mathcal{F}_2, P_2)$, respectively [1]. Allow that an ...
1
vote
1answer
22 views

Conditional probability of tossing coins with uncertain head probability

Suppose there are two coins A and B. When tossing a coin $i$, "head" happens with probability $p_i$. The problem is that $p_i$ itself is a random variable. Say that the associated probability ...
0
votes
0answers
10 views

Compound random experiment and product probabilities

As I understand, a random experiment is modeled with a probability space. Then, you have compound experiments, which are those that can be decomposed in several experiments (I am unsure whether this ...
1
vote
1answer
54 views

Probability of a box containing a combination of color

Let's say, we have a box containing 3 balls in it, they can be either red or blue. Someone draw a ball 5 times with replacement and get 4 red and 1 blue (not necessarily in order). Do you know how to ...
1
vote
1answer
21 views

What is the probabilty that X > 2 conditioning on Y = 2? (Homework)

another homework question here. Let 𝑌 be a binomial random variable with 10 number of trials and 0.2 probability of success. Let X be a uniformly distributed random variable over the interval [0, 3]. ...
0
votes
0answers
18 views

Conditional Probability Given Multiple Priors

Reference: ilanman Oct 3, '16 at 13:27. Even though years old, this discussion is relevant to my current interests. The P(Ai|B) in the last formula above, reverses the position of the posterior and ...
0
votes
0answers
16 views

Conditional Probability given sample size

I am working with a dataset of fraudulent credit card purchases. I want to represent on of the features as the conditional probability $P($fraud$|$feature$)$. The feature is categorical feature with ...
0
votes
0answers
28 views

exponential family form of discrete conditional distribution

What is the exponential family form of a discrete random variable conditioned on another discrete random variable? For example, p(y|x) where both x and y are discrete. Is there a standard form for ...
0
votes
1answer
14 views

Equivalence of expressions involving conditional probabilities

Take the following random variables $Y,\epsilon_0,\epsilon_1,V_0,V_1$, with finite supports $\mathcal{Y}\equiv \{0,1\},\mathcal{E}_0, \mathcal{E}_1,\mathcal{V}_0,\mathcal{V}_1$, respectively. Suppose ...
0
votes
1answer
31 views

Need help understanding Toru Tsujishita' theorem on Triple Information

I struggling to understand point (ii) of Toru Tsujishita's theorem (here) on Triple- (Interaction- or Co-) Information What is meant with the maps $\varphi_j$ and $\varphi_k$? A biunivocal ...
0
votes
0answers
36 views

Deriving conditional probability of bivariate bernoulli by using Dirichlet

While I was working on my research project, I found it difficult to derive a conditional probability from Dirichlet dist. Consider two Bernoulli trials that are possibly correlated with each other. ...
0
votes
0answers
29 views

What is to be done when PDFs are not Gaussian/Normal in Naive Bayes Classifier

While analyzing the data for a given problem set, I came across a few distributions which are not Gaussian in nature. They are not even uniform or Gamma distributions(so that I can write a function, ...
0
votes
1answer
23 views

Notation for conditional probability when the conditioned event is observed

I am trying to understand proper notation for functions related to state transition models (e.g., a HMM). There are two indexing variables $t$ (time step) and $i$ (state). Such that it matters, in my ...
0
votes
1answer
21 views

Calculating Conditional Probability without knowing individual probabilities

I have a case where I know the probability that three annotators will agree with each other pairwise, and I'm trying to find the probability that all three will agree on a yes or no question given ...
3
votes
0answers
30 views

What does “Normal distribution conditioned on $x \mod 1$” mean?

I understand what $Pr[X = x | Y = y]$ means, however, on this paper (Lemma 10 in Appendix A), we have the following: Let $D_r$ denote the continuous Gaussian distribution of parameter $r$,i.e., the ...
0
votes
0answers
42 views

Sampling with fixed probability from two different distributions. How is the sample distributed?

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $\mu$ be a probability measure on $(\mathbb R,\mathcal B(\mathbb R))$ $X$ be real-valued random variable on $(\Omega,\mathcal A,\...
2
votes
1answer
63 views

Probability of A given B and C

I'm trying to write an algorithm and I'm rusty on my statistics. Basically my question comes down to how do you get the probability of A given B and C. I'm trying to walk myself through a made up ...
-1
votes
1answer
35 views

Conditional Probability Question in a Diagram

I know Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / Pr(X3 = F) but I don't know how to figure out each probability individually. Anyone have any idea how to do it?
0
votes
0answers
20 views

Why this could not be represented by a Bayesian network

A, B, C, D are four variables. Why $A \perp C | \{ B , D \}$ and $B \perp D | \{ A , C \}$ could not be represented by a Bayesian network?
1
vote
1answer
31 views

Conditional Probability Question from Diagram [closed]

Anyone have any idea how to approach this problem?
23
votes
4answers
6k views

Monty Hall Problem with a Fallible Monty

Monty had perfect knowledge of whether the Door had a goat behind it (or was empty). This fact allows Player to Double his success rate over time by switching “guesses” to the other Door. What if ...
0
votes
0answers
16 views

Rewrite joint probability as product of marginals when all the probabilities are $1$ or $0$

I have a question about the possibility of rewriting a joint probability as the product of the marginals when all the probabilities can only take value $1$ or $0$. I start with introducing some ...
1
vote
2answers
29 views

Marginalize probability with three variables

I am reading a book and saw the following equation: $$ P(X|\theta) = \sum_{z}P(X|z,\theta)P(z|\theta)$$ I know that that it is: $$ P(X) = \sum_{z}P(X|z)P(z)$$ But I don't know how the above equation ...
1
vote
2answers
57 views

Writing the Conditional probability correctly

I was reading the book statistical rethinking chapter 3. There is the following example: To repeat the structure of common examples, suppose there is a blood test that correctly detects ...
0
votes
0answers
18 views

Questions Regarding Conditional Entropy

I have a question related to a conditional entropy that I have to solve and I struggle a bit on the understanding of my implementation. So I formalized the questions here as follows. Any suggestions ...
1
vote
0answers
14 views

Which distribution should I use for Naive Bayes algorithm(Gaussian or Rayleigh)? What to do with categorical data?

I am predicting whether credit card application of an individual would be approved or not given his/her credentials. I have the following dataset: The variable descriptions are as follows: I need ...
0
votes
1answer
22 views

Conditional probability for binary events [closed]

I have 2 columns of data called level 1 event and level 2 event. Both are columns of 1s and zeros. I want to find the probability of a level 2 event given that the previous event was a level 1 event....
1
vote
2answers
131 views

Gibbs algorithm using negative binomial produces NAs

I have the following full conditionals distributions: $$ X_2|X_1=x_1\sim Bin(x_1,p)\\ X_1|X_2=x_2\sim NegBin(x_2,p) $$ So I'm using the following code to generate a sample from each one: ...
0
votes
0answers
23 views

Conditional distribution of a function of a random vector given conditional distribution of random vector

Let $\mathbf{X}=(X_1,...,X_n)^T$ be a multivariate normal distribution. Now we have $\mathbf{Y}=(Y_1,...,Y_n)^T$ defined by $Y_i = e^{X_i}$. Let $\mathbf{Y^1}, \mathbf{Y^2}$ be partitions of $\mathbf{...
4
votes
1answer
74 views

How do I calculate $s$ from $\mathbb P(X+Y>u\mid X<s)=q$

Suppose $X,Y$ are (not necessarily independently) normally distributed, how can one calculate the maximal limit $s$ that $X$ may reach such that the probability of the sum $X+Y$ overshooting a given ...
1
vote
1answer
36 views

How to infer a missing observation in a state space model?

I read here that "structural time series models handle missing values naturally, following the rules of conditional probability. Posterior inference can be used to impute missing values, with ...
0
votes
1answer
59 views

Conditional survival probability up to time $T$ given $t > s$

This is a really basic question I know but for some reason I'm failing to convince myself of the right answer here. Given a survival model that has CDF $F(t) = \mathbb{P}(\text{failure before}\ t)$ ...
1
vote
1answer
22 views

Calculate a Conditional Expectation via Samples

Consider a binary random variable $Y \sim p(Y)$, a random variable $X \sim p(X)$ (can be discrete or continuous) and a conditional distribution $p(X|Y)$. Suppose that I generate $N$ samples from $p(Y)$...
0
votes
0answers
26 views

Expected value with respect to a conditional distribution

I am reading the thesis Variational Inference and Deep Learning. On page 16, while deriving the ELBO, the expectation is w.r.t. a conditional distribution $q_{\phi}(\mathbf{z} | \mathbf{x})$: $$ \...
3
votes
0answers
18 views

Sample Proportion for Estimating Conditional Probability

Suppose I have $n$ observations of binary data $(X, Y, Z, \ldots)$ and suppose I want to estimate $\theta = P(X = 1 | Y = 1)$. It seems clear to me that $$\frac{\sum_{i}\mathbb{1}_{X_i = 1, Y_i = 1}}...
0
votes
0answers
43 views

Conditional probability density function (PDF) of bivariate normal distribution

Let $X$ and $Y$ have bivariate normal PDF with correlation coefficient $\rho$, i.e.,: $f(x,y)=\frac{1}{2\pi\sigma_X\sigma_Y\sqrt{1-\rho^2}}\exp{(-\frac{1}{2(1-\rho^2)}[\frac{(x-\mu_X)^2}{\sigma_X^2}+\...
0
votes
1answer
16 views

Independent variables in conditional probability

So I am reading this paper about reasoning(Hall, Ali, Chater, & Oaksford, 2016). Consider this conditionals. ...
0
votes
1answer
53 views

Probability of an event at the outcome of a binary source

Let a binary (and independent) source $S$ generating a binary sequence with the following probabilities: $p$ for the symbol '0' and $1-p$ for the symbol '1'. What is the probability that $S$ gives $n$...
0
votes
1answer
32 views

Self study of basic probability: Can't solve exercise

I am currently working through 'Concepts of probability theory by Pfeiffer' and can't solve the following problem: A carnival man hides a pea under one of three nut shells. By a series of complicated ...
8
votes
2answers
183 views

Why not to use Bayes theorem in the form $p(\theta | x) = \frac{L(\theta | x) p(\theta)}{p(x)}$?

There are a lot of questions (like this) about some ambiguity with Bayesian formula in continuous case. $$p(\theta | x) = \frac{p(x | \theta) \cdot p(\theta)}{p(x)}$$ Oftentimes, confusion arises ...
0
votes
1answer
13 views

Rearranging Conditional Probability Equation to Show Dependencies

Given the random variables $X$, $Y$, and $Z$, with joint pdf given by $p(x,y,z)=kf(x,z)g(y,z)h(z)$ for some constant $k$, my task is to show that $p(x|y,z)$ is a function of $x$ and $z$. My work is as ...
0
votes
0answers
12 views

Conditional density under conditional indepencence?

Let $X,Y,Z$ three random variables such that the joint density can be factorized as $$f(x,y,z) = f(x \mid z) f(y\mid z) f(z).$$ This is, I am assuming conditional independence of $X$ and $Y$ given $Z$....
0
votes
0answers
8 views

Conditional probability formula for continuous random variables [duplicate]

Let $V,T$ be two random variables with supports $\mathcal{V},\mathcal{T}$, respectively. Let $P_{V|T}$ denote the probability distribution of $V$ coditional on $T$ $P_{V,T}$ denote the probability ...
3
votes
1answer
32 views

Application of law of total probability for continuous random variables

Consider 3 random variables $Y,V,T$, with supports $\mathcal{Y},\mathcal{V},\mathcal{T}$, respectively. Let $P_{Y,V}$ denote the probability distribution of $(Y,V)$ $P_{V}$ denote the probability ...
1
vote
1answer
27 views

Is the following definintion of Discrete Random Variable given in the book of Joe Blitzstein correct?

The following is the definition given in the book: A random variable $X$ is said to be discrete if there is a finite list of values $a_1, a_2,\ldots, a_n$ or an infinite list of values $ a_1, a_2,...
0
votes
1answer
49 views

Why $E$ and $F$ are conditionally independent given $C$ and $D$?

Below is a Directed Acyclic Graph (Fig.a). From this figure, it is said that: $E$ and $F$ are conditionally independent given $C$ and $D$. I am confused about it. Let's assume the causal ...
0
votes
0answers
22 views

How the conditional probability is being calculated in Rejection sampling

In a class lecture, the "Acceptance-rejection algorithm" was presented as follows: To generate $𝑋 \sim 𝑓(𝑥)$, Find density $g$ satisfying $\frac{f(t)}{g(t)}<=c$ for some constant $c$ for ...
0
votes
1answer
28 views

Computing a marginal distribution of a joint involving a delta function

Suppose that we have four continuous random variables $x,y,z,$ and $v$ and we want to compute the following integral: $$\int f(x\mid y)f(z\mid x,y)f(v\mid z,x,y)\,dx$$ There are a few conditions: $...
0
votes
0answers
9 views

Correct terminology to refer to a collection of conditional probability distributions

I would like your help to find the correct terminology to refer to a collection of conditional probability distributions. Consider two random variables $Y$ and $X$, with supports $\mathcal{Y}$ and $\...
0
votes
0answers
32 views

Changing a conditional probability to a deterministic function

Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...