# 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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### Can these asymptotic conditional expectations be bounded from above?

Problem Setup Let $\{X^d_1, X^d_2, \cdots, X^d_n\}$ be a $d-$dimensional zero-mean, i.i.d. random variables. Let $S_n^d$ be $$S^d_n = \frac{\sum_{i=1}^n X_i^d}{\sqrt{n}}$$ Let $Y^d$ be a zero-...
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### Cox's Theorem: ignorance, objective priors, and the Mind Projection Fallacy

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
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### Generating random matrices with specific equality constraints

Suppose I want to generate a nonnegative $n \times n$ matrix $\mathbf A$ for an odd $n$ (say, $n=5$ for a good enough example), such that the individual elements are drawn from a uniform distribution ...
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### Spinograms vs. conditional densityplots

I have a binary response variable (hail) and multiple continuous predictor variables. My aim is to understand the linear/non-linear relationship of the predictors to the response to be able to justify ...
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### Cox's Theorem: the necessity of (un)countably additivity

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
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### Testing for conditional independence: What's the correct way?

My goal is to check if two variables $X$ and $Y$ are conditionally independent given $Z$. For simplicity, let's assume the joint distribution is multivariate normal. In this case, we can compute ...
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### Combining posterior probabilities from multiple classifiers

I am new to machine learning and can't get my head around this problem. I have two patient datasets, the first ($D_1$) contains $Y,Z,X$ that convey blood-sample information and the second ($D_2$) ...
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### Probability with an unbalanced coin where consecutive flips are not independent

Thanks in advance for the help. Suppose someone has an unbalanced coin that they flip 100,000 or so times in a row. This person then gives you the results. You do not know the probability of ...
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### Trading signals example from Marginal Revolution blog

From http://marginalrevolution.com/marginalrevolution/2016/09/someone-give-doug-blog.html: Many trading signals reliably predict prices, but not strongly enough to overcome transaction costs (i.e....
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### Is stagewised feature engineering/ selection an invalid approach? What to do when all the features are not ready at one time?

Suppose we want to build a regression or classification model. However, the features (independent variables used) are not all ready at one time. This is very realistic in business, because the data ...
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### Is there any way to merge two conditional probability distributions?

Is there any way to construct an expected conditional probability distribution of the form p(x|(y,z)) if I am starting with p(x|y) and p(x|z)? All variables are categorical. My specific problem deals ...
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### Chances of hitting a deer depending on the vehicle's speed

My friend and I are arguing about the following hypothetical scenario. Context There is a stretch of road of let's say 100km. This road is prone to having deers crossing it. You drive a motorbike ...
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### What's the conditional distribution of X given X = Y

I'm in a setting in which X and Y are both $Beta(0.5, 0.5)$ and indipendent, that is $$f(x, y) = \frac{1}{\pi^2\sqrt{x(1-x)y(1-y)}}$$ What is the conditional distribution of X given Y = X? Normally i ...
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### Conditional Distribution of Multivariate Gaussian given Linear Inequalities

Consider a multivariate Gaussian $Y\sim\mathcal{N}(\mu,\Sigma)$ of dimension $n$. For fixed $c\in\mathbb{R}^n, A\in\mathbb{R}^{m\times n}$ and $c\in\mathbb{R^m}$, what is the conditional distribution ...
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### What is the correct definition of the Bayes rule?

I am familiar with $$P(\theta|D)=\frac{P(D|\theta) \, P(\theta)}{P(D)}=\frac{P(D|\theta) \, P(\theta)}{\int_{-\infty}^{\infty}P(D|\theta) \, P(\theta) d\theta},\quad\theta\in \Theta$$ where the ...
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### conditional and joint conditional probability manipulation

I have P(A | B, C). I know P(B | C), P(B) and P(C). I need to figure out P (B | C, A). I am trying to use the chain rule and still unable to get to where I need to. Any clues would be useful. P(B|C,A) ...
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### 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 ...
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### Derive Conditional Variance from Covariance Matrix

Given the mean, variance, and covariance of two random variables $X$ and $Y$, how would I find $\operatorname{Var}(Y\mid X)$? I know that I can find $E(Y\mid X)$ using the definition of covariance ...
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When sent a questionnaire, the probability is $.5$ that any particular individual to whom it is sent will respond immediately to that questionnaire. For an individual who did not respond immediately, ...