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].
81
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Multivariate normal distribution conditioning inequalities variable [closed]
The bivariate normal distribution X is as follows.
$X = (X_1, X_2)^\top \sim \mathcal{N}(\mu, \Sigma), ~ X \in \mathbb{R}^2 $
I want to know the exact distribution(pdf) $P(X | X_1 > X_2)$ in which ...
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0
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20
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Bridging the gap from theory to implementation in "Conditional Distance Correlation" by Wang et al. 2015?
In an attempt to implement a form of conditional distance correlation for random variables represented as vectors of observations, I came upon this paper that nicely extends the notion of distance ...
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-1
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1
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73
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difference between two sets of pvalues
I am performing a biological experiment, where I am trying to capture potential mediation effects from some genes.
I have 150 significant results, containing 30 tissues with different sample size.
For ...
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1
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0
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26
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Given a DAG X<-Z->Y, how to test for conditional independence of X and Y given Z for non-normal random variables?
Consider data generated from a directed acyclic graph (DAG) of the form X<-Z->Y. Based on d-separation of DAGs, X is independent of Y given Z: X_||_Y|Z. If X, Y and Z are multivariate normal, ...
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Reformulating latent dirichlet allocation
can you guys help me solve this equation and go from :
to this one :
I have tried something but my result gives me this : p(θ, φ, z| α, β) = p(θ, φ, z, w|α, β)/p(w|α, β)
the equations are taken from ...
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23
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Difference between conditional survival and left truncation analysis for cancer patients?
I am looking at cancer patient survival and want to know how long-term survival is after already having survived some time.
I am more familiar with conventional conditional survival, but have recently ...
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22
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Imputation of a variable with missing data conditional on another variable in R
I have a medical data set with missing data in few variables. But on carefully observing, missingness of some variables are dependent on the response of another variable. For example, "age at ...
- 15
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42
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Binomial distribution conditional on the weigthed sum?
Suppose $\mathbf{X}$ is a vector of iid Bernoulli variables with the fixed success probability of $p$. The variance of X is $np(1-p)$.
Now, suppose, I am interested in the conditional probability of $...
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2
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1
answer
47
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are there any conditions on the data in ANN classification?
In regression models such as linear and multiple regression models, there are several conditions that must be met such as normality, non-autocorrelation, heteroscedasticity etc. does ANN also have ...
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2
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173
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Can we estimate ATE (average treatment effect at the population level) using both marginal or conditional models?
If I understood correctly, in principle when we estimate an unconditional/unadjusted treatment effect, it means marginal effect and vice-versa. If so, I wonder if the average treatment effect (ATE) at ...
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103
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Conditional probability - Finding a lost dog on the second, but not first day of a search
I am working on problem set 2, Q4d from the MIT 6.041
Oscar has lost his dog in either forest A (with a priori probability 0.4) or in forest B (with a priori probability 0.6).
On any given day, if ...
- 143
1
vote
1
answer
62
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Marginal predictions from a conditional survival model
I’m looking at making predictions of baseline and treated survival from a parametric survival curve that are unbiased. I have a matched sample to try to control for observed confounding and wanted to ...
- 531
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0
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71
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Efficient estimation of conditional probability density
The formulation of the conditional density is:
$$ f_{Y|X}(y|x) = \frac{f_{X,Y}(x,y)}{f_X(x)}. $$
I need to estimate this density from data and it's prohibitively time-consuming to calculate the joint ...
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3
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87
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A stick of length 1 is split at a random position $B\sim U(0, 1)$. Let $X$ be the length of the longer stick. What is the PDF of $X$?
A stick of length 1 is split at a random position $B$ where $B$ ~ $U(0, 1)$. Let $X$ be the length of the longer stick. What is the CDF of $X$?
This problem is challenging me. I know that the cdf of X ...
- 145
1
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2
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162
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Conditional Logistic Regression?
Firstly, I am new to all of this.
I am currently trying to predict the chance of different students finishing top of their class. Students will be separated into different groups depending on the ...
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1
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1
answer
46
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Pre- and post-treatment binary outcome between treatment groups
I have two treatment groups (A and B), where I have a binary outcome of resistance against a particular antibiotic recorded at pre- and post-treatment. I am interesting in determining whether there is ...
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3
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Difference between E(Y) and E(Y|X) in regression
In linear regression, we postulate a model for estimating $E(Y|X)= \beta_0 + \beta_1 x$
We also propose $Y= \beta_0 + \beta_1 x + \mu$ where μ is an error team with expectation equal to zero. We also ...
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78
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Use indicator function in regression equation
I have 2 regression equations:
1st Regression:
$I_t = a_1 + \beta_1E_t+X'_t\delta_1+\epsilon_1$
2nd Regression:
$I_t = a_2 + \beta_2E_t+X'_t\delta_2+Y'_t\lambda_2+\epsilon_2$
The two regressions are ...
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39
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Is it still considered a generative adversarial network if the random vector z is not used?
I am using a model very similar to the pix2pix model (https://arxiv.org/pdf/1611.07004.pdf). I don't feed a random noise vector to the "generator", as it works just fine without. But I ...
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3
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239
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Can I say that $E[X | c] = E[c | X]$, when $c$ is a constant and $X$ is a random variable?
$X$ is a random variable defined in a sample space
$c$ is a constant $\in R$ (real numbers).
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45
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Conditional count based on second variable
I'm still somewhat new to R, so please bear with me. I'm trying to summarize the results of the variable riskT0. However, because I have some missing values in the variable riskT2 I would like to ...
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2
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71
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Multiple correlation formula
Given $v \sim N_{p+1}(\mu, \Sigma), v = (x, y)', \mu = (\mu_x, \mu_y)', \Sigma = \begin{pmatrix}
\Sigma_{xx} & \sigma_{xy} \\
\sigma_{yx} & \sigma_{yy}
\end{pmatrix}$, how do you prove the ...
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0
answers
34
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Given a Poisson distribution Poisson(n│λ) with expected value λ, which integer n is the most probable one? [duplicate]
Given a Poisson distribution Poisson(n│λ) with expected value λ, which integer n is the most probable one?
Prove that, if 𝜆 is integer, there are two most probable values for 𝑛.
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1
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97
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Implications of mean independence
Let $U$ be a random variable with mean $0$. Take other two random variables $X,Y$. Assume
$$
(1)\quad E(U|X,Y)=0.
$$
I believe (1) implies
$$
E(U\cdot X)=E(U \cdot Y)=0.
$$
Does (1) imply
$$
E(U \cdot ...
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1
answer
35
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A Condition a Conditional Probability Should Satisfy
Consider four random variables $V_1,V_2,V_3, V_4$.
Here, suppose that $V_2$ is a function of $V_3$ and $V_4$, say $V_2=V_3-V_4$.
In this case, I want to know whether the following conditional ...
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32
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Quick short question about understanding of conditional expectation
let me just ask one simple question, I am not sure if I understand this concept of conditioning w.r.t. sub-$\sigma$-algebras.
Let $(\Omega,\mathcal{A},\mathbb{P})$ be probability space and $X,Y:\Omega\...
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answer
214
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Condition on two random variables
I'm trying to set up the proper assumptions for a proof I'm working on:
Given that $P(A|e) = P(A)$ and $P(A|c,e) = P(A|e)$, can we prove that $P(A|c)=P(A)$?
I understand that A is independent of e and ...
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1
answer
689
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is P(notB|A) same as not(P(B|A)) [closed]
is P(notB|A) same as not(P(B|A)) if not then what is the difference between them? this is taken from bayes question.
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how do i empirically estimate variance of conditional normal distribution?
I've tried searching for this, but maybe I'm not using the correct search strings. suppose I have joint distribution $P(X_1,X_2)$ over 2 continuous random variables $X_1,X_2$ that I can sample from. ...
- 425
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83
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CAPM Estimation
Please that might sound basic for all of you but I am not an expert and I need to estimate the following model using OLS regression: R= a + β1 RM + β2(z)RM + ε (the model is called conditional CAPM, ...
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1
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0
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215
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The discriminator is classifying everything as fake. What does it mean?
I am using a conditional GAN with a relativistic loss function for both generator and discriminator (https://arxiv.org/abs/1807.00734). Before I added the relativistic part, the discriminator ...
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1
vote
1
answer
145
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conditional quantile and conditional expectation
I was reading some papers and I found some parts are tricky to understand.
Assume I have price data , what does it mean to calculate the conditional mean of the price data given yesterday price ? ...
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0
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22
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mean and covarince matrix of AR(1) [closed]
assume I have a price data called pt, I fitted AR(1) model
p_t= alpha + beta pt_1 + e_t , ...
- 61
3
votes
1
answer
528
views
Are exact logistic regression and conditional logistic regression the same?
I have seen these two terms in practice. Are they actually referring to the same method? If not, what is the main difference between the two methods?
Conditional logistic regression is commonly used ...
- 617
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2
answers
54
views
Conditional probability to be calculated but I'm not able to solve the first part of the question [closed]
Suppose that a box contains one blue card and four red cards. The red cards are labelled $X$, $Y$ , $Z$, and $W$. Suppose also that two of these five cards are selected at random, without replacement.
...
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1
answer
26
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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 ...
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votes
1
answer
45
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Conditional mutual information
I have three RVs X, Y, and T. Is the following equation true?
I(X ; Y|T) = I(Y ; X|T)
Can we express the conditional mutual information as: (X;Y|T) = I(X;Y) - I(X;Y;T) ?
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246
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Is there a way to think about conditional vs unconditional heteroskedasticity graphically?
I find I understand concepts much better with the aid of charts/visualizations. I'm struggling to intuitively understand how one would be able to see whether error terms are correlated or not to the ...
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1
answer
110
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marginal and conditional distributions
Can someone help me, please?
Let X and Y be two random variables having the following marginal and conditional distributions.
𝑌|𝜇 ~ 𝑃𝑜𝑖(𝜇) 𝜇 ~ 𝐺𝑎𝑚𝑚𝑎(𝛼, 𝛽)
I want to obtain the ...
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0
answers
101
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combinatorics questions from coursera [closed]
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 ...
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1
vote
1
answer
243
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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):
$...
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vote
1
answer
200
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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.
...
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1
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82
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How to solve the probability of N events occurring at the same time, N is a random variable [closed]
How to solve the probability of N events occurring at the same time, N is a random variable and its PDF is known. The probability of each event is also known and the probability of each event is not ...
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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 ...
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1
answer
68
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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 ...
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votes
1
answer
395
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Deriving Bayes Rule from conditional probability [duplicate]
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)$$,...
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20
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Conditional Probability involving a mathematical sequence
I have a sequence of elements:
$$
T_1 \hspace{1cm} P(T1 = A) = .5 \, , \\
T_2 \hspace{1cm} P(T2 = B) = .2\, , \\
T_3 \hspace{1cm} P(T3 = C) = .3\, .
$$
Given the sequence $TT = (T_1 = A, T_2 = B, ...
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1
vote
0
answers
107
views
What is calibration of a probability model? A take using Bayes’ rule
As a discussion from last year about spam/ham email classification shows, just because a model gets perfect classification accuracy does not mean that it really knows what it's doing. In that example, ...
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1
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1
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75
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Defective Subpopulation Distribution and Conditional Probability
A colleague and I have tried two different approaches to this problem, both of which seem to make sense but are resulting in very different answers.
Suppose we have some units undergoing B hours of ...
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4
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3
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375
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Marginalization over the nuisance variable
I was reading a paper in which they state
$$ \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 $\mathbf{f}$ ...
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