Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [conditional]

This tag is ambiguous. Consider replacing it with a more specific tag such as [conditional-probability], [conditional-expectation], [conditional-random-field] or [conditional-independence].

This tag is ambiguous. Consider replacing it with a more specific tag such as , , or .

54 questions
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Is it possible that marginally independent random variables are conditionally dependent?

Suppose that $X,Y$ and $Z$ are random variables. If $X$ is independent of $Z$ and $Y$ is independent of $Z$, is it possible that $X$ is dependent on $Z$ given $Y$ and $Y$ is dependent on $Z$ given $X$? If so, what are some examples?
mhdadk
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What is the posterior mean of $\mu$ given a randomly stopped i.i.d. observations from a Normal

Let's imagine I have a machine giving me an independent random number from a normal distribution $N(\mu,1)$ whenever I push a button. I have a stopping rule to decide how many samples to collect - I will collect samples until the sum of observations…
JaeHyeok Shin
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Marginalization over the nuisance variable

I was reading a paper in which they state $$ \text{P}(\mathbf{y}, \mathbf{f}, \mathbf{u}) = \text{P}(\mathbf{y}| \mathbf{f})\text{P}(\mathbf{f}| \mathbf{u})\text{P}(\mathbf{u})$$ With $\mathbf{f}$ being conditionally independent to $\mathbf{y}$…
lefe
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Deriving Bayes Rule from conditional probability

Bayes Rule and Conditional Probability look so similar to me. I'm having a hard time figuring out how to derive Bayes from the conditional probability equation. If I start with $$P(A,B) = P(A|B)P(B)$$, how do I get to $$ P(A|B) =…
TryHarder
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Prove P(A|B) = P(C|B)*P(A|C) + [1-P(C|B)]*P(A|C')

My textbook claims the following probability derivation, but I am still having trouble understanding where the formula came from. The derivation is as follows: P(A|B) = P(C|B)*P(A|C) + [1-P(C|B)] * P(A|C') Can anyone explain how this formula was…
Meghan
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Poisson Process Conditional Probability computation

Given $N(t)$ a Poisson Process with generation rate $\lambda$ with $t_1N_1$ I'm looking for a way to express the following probability: $$ P[N(t_2)>N_2|N(t_1)
Knyq
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$k$-th order statistics when the value of $j$-th one is known

Suppose there are $n$ random variables $X_i,~i\in\{1,\cdots,n\}$ which are independently drawn according to a CDF $F$ and pdf $f$. Suppose also that we know one of the realization, say $X_{(j)}=x_{(j)}$, and we also know that it is the $j$-th…
Andeanlll
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Conditionalizing events on more than one event

I am currently working on a question which seems to have an obvious answer, but it it seems just impossible for me to find a stringent proof of this relation (if it is true). Imagine the following scenario: You are asked to bet on the chance of your…
Zito
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combinatorics questions from coursera

Question 1 Imagine that now host have the following instructions. Put a prize behind a random door. Let the guest guess a door. If the guest chooses an incorrect door (with no prize), roll a dice (in such a way that the guest does not see this and…
revathi
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"Automatically" detect biased subsets in probability distribution

Background: Suppose we have a model generating probabilities conditional on a state vector - for simplicity we can just assume the outcome is 0 or 1 (imagine for example simple logistic regression): $P(X = 1|S = s) = f(s)$. An obvious sanity check…
Christian
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How to compute conditional mean in GLM?

I have understood the basic knowledge of GLM. I know why a GLM consist of a predictor, a link function and a distribution. But I don't know how does the conditional mean connect to the distribution. Using Poisson regression as example, we have…
Stanley Chan
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Conditional distribution of Yt, non-Gaussian linear growth model (time series)

Given the following modelling specifications: $Y_t = µ_t + σ_ee_t, \quad e_t ∼ t_1$ $µ_t = µ_{t−1} + β_{t−1} + w_t, \quad w_t ∼ N(0, σ^2_w)$ $β_t = β_{t−1} + v_t, \quad v_t ∼ N(0, σ^2_v)$ What is the conditional distribution for $Y_t|\mu_t$? I…
username97
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Coherence of conditional probabilities

Dennis Lindley's paper The Philosophy of Statistics in 2001 includes the following 'simple' example of statistical coherence: "A set of uncertainty statements is said to be coherent if they satisfy the rules of the probability calculus. Thus, the…
Micks
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What is calibration of a probability model? A take using Bayes’ rule

As a discussion from last year about spam/ham email classification shows, just because a model gets perfect classification accuracy does not mean that it really knows what it's doing. In that example, the emails with $P(\text{spam}) < 0.49$ are…
Dave
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Defective Subpopulation Distribution and Conditional Probability

A colleague and I have tried two different approaches to this problem, both of which seem to make sense but are resulting in very different answers. Suppose we have some units undergoing B hours of testing and are interested in the probability of…
user2613562
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