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].

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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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Conditional probability problem (Bayes Theorem ?) [closed]

Hello, basically, I can't find 1/2 for the very last question. I tried to use the Baye's Theorem, but it wasn't successful Could someone help me ?
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Problem understanding and computing the Conditional likelihood: example [closed]

I am asked by the exercise to find the conditional likelihood for $\psi$. I know that is not difficult but I am having a hard time in understanding how to start. This is the exercise: Let $Y_{1}, \...
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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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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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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 , ...
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2 votes
1 answer
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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 ...
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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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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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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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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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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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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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Conditional Poisson Regression Derivation

In this article (Relative Incidence Estimation from Case Series for Vaccine Safety Evaluation): https://www.jstor.org/stable/2533328, Farrington derives the likelihood kernel as follows: $$ h(v_i,\...
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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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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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MLE from conditional distribution

Suppose that \begin{eqnarray*} \left[ \begin{array}{c} \mathbf{y}_{i} \\ \mathbf{x}_{i}% \end{array}% \right] &\sim &iidN\left( \left[ \begin{array}{c} \mathbf{0 } \\ \mathbf{0 }% \end{...
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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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Conditional Probability for Threshold Based Binary Classification Model

I was wondering, if I had a classification model where: f(x) = 1 if f(x) < t f(x) = -1 if f(x) >= t How would one compute the conditional probability of ...
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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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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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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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Is there a method for testing conditional independence between category and continuous variables?

I have some question about Conditional Independence Test. I realized there are conditional independence test methods for continuous and categorical variables. But, I am curious whether there is a ...
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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, ...
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Conditional probability with 4 variables

I know that $$p(x,y) = p(x|y)p(y)$$ How do I get this?: $$p(w,x,y,z) = p(w,x,y|z)p(z) = p(w,x|y,z)p(y|z)p(z)$$ I don't see how to go from the middle expression to the one on the right..
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How to add spline in conditional logistic regression model in R?

I want to add a continuous variable with spline into conditional logistic regression model in R. I tried this: ...
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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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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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Find the conditional distribution to calculate a probability

I have a question that has been posed to me with 4 multiple choice answers. I cannot see how any of these answers are correct. Can somebody please let me know how to solve this? I'm getting $e^{-1}$ ...
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Conditional kendalls vs partial kendalls

I read about conditional kendall's tau for independent test. I also found partial correlation kendalls tau test. My question is, are they different? If yes, how? I tried to calculate the conditional ...
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Goodness and prediction measures for conditional logistic regression models

As mentioned in this comment and answer How to get fitted values from clogit model, it is not clear that predicting from a conditional logistic regression model is meaningful. It seems to me that it's ...
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interpretation of conditional probability

São Paulo Futebol Clube probably wins 0.7 if it rains and 0.8 if it doesn't. In September the chance of rain is 0.3. São Paulo won a game in September, how likely was it to rain that day? (A) Answer ...
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How to create a distribution for a feature that is conditional on more than one other variable

I have a variable, r. It has a distribution P(r). I have found two other variables, A and B that are correlated with r. I want to build a distribution P(r) that is conditional on these two variables. ...
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Can diagnostic accuracy measures be used in case-control studies?

I want to assess the predictive ability of biomarkers in a nested case-control study. The primary analysis with use conditional regression. I’d some questions: 1)Can I determine the AUC, sensitivity ...
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Conditional expectation, conditional on sum of weighted average of two iid RVs

I have an arbitrary distribution $F$, and two variables $z, x \sim F$. I only observe the weighted average $y = \alpha z + (1 - \alpha) x$. Conditional on $y$, what is the expected value of $z$? I ...
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1 vote
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Possibility n independent random events ocuuring per year? An event is any piece of equipment failing per year

So I am an engineer. We have a method at our organization of defining the probability of an equipment failure based on frequency of occurrence. So for example we may categorize a piece of equipment ...
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Conditional expectation versus correlation

Consider two random variables $X$ and $Z$. Suppose $E(X)=3$ and $E(X|Z=z)=0$ for some realisation $z$ of $Z$. Does this imply that $X$ and $Z$ are correlated? Does this imply that $X$ and $Z$ cannot ...
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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 $X$?...
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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: ...
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conditional covariance of $b$ and $\hat{\sigma}^{2}$

By definition of the normal linear model (i.e. standard linear regression under the assumption of gaussian noise with constant variance), we know that the regression coefficient vector $b$ is ...
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Reject the claim that a sports league's regular season performance can occur by chance

For a tournament where each of $K$ teams plays each other team exactly once, what is the probability that the most number of games any team wins is $N$? The answer to this question is to create ...
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maximum likelihood with conditional distribution

Let $(y_i,x_i),(i=1,...,n)$ be observations with $y_i|x_i \sim iidN(0,\sigma^2(\theta,x_i))$. I want to estimate $\theta$ by maximum likelihood. But I cannot derive the likelihood function. If $x_i$ ...
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Poisson Process Conditional Probability computation

Given $N(t)$ a Poisson Process with generation rate $\lambda$ with $t_1<t_2$ and $N_2>N_1$ I'm looking for a way to express the following probability: $$ P[N(t_2)>N_2|N(t_1)<N_1]$$ In ...
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Interpretation of conditional Granger results

I have a question about the Granger package. How are the numbers obtained in the frequency and causal output of the conditional Grangers interpreted? Thank you.
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Under which conditions does $X_1 \perp X_2, X_3$ imply $X_1 \perp X_2 | X_3$?

E.g. let us imagine we have $X_3 := X_1 \text{XOR} X_2$ with both $X_1, X_2$ being sampled from $\{0, 1\}$ with $p=0.5$. Then $X_1 \perp X_2, X_3$ but $X_1 \not \perp X_2 | X_3$. Are there conditions ...
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Conditional expectation and variance of a poisson distribution, where $𝑋_𝑛$ is conditioned on $𝑋_{𝑛−1}$ [closed]

Suppose that $𝑋_0 \sim \text{Poi}(𝜇)$ (where $𝜇 > 0$ is fixed) and that for $𝑛 = 1, 2,…$ the distribution of $𝑋_𝑛$ conditional on $𝑋_{𝑛−1} = 𝑥$ is Poisson with parameter $𝑥$. Determine ...
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is a pair of two conditional gaussian distribution imply a joint gaussian distribution

suppose x,y are two random variables, if p(x|y) is normal distribution, and p(y|x) is also normal distribution, can we say that p(x,y) is also joint normal distribution? i know that two normal ...
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How to produce a nomogram for a conditional survival model?

Conditional survival is the survival probability after already surviving a predefined time period. The formula used for conditional survival (CS) was: CS(x|y) = S(x + y)/S(x), where S(x) represents ...
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is there a R function to do multiple comparison for all levels of a categorical variable by capscale (vegan) with a covariate? [closed]

First, I did DB-RDA for a community dataset with two factors and one covariate. The results showed the interaction effect was significant. Then, I need to do the pairwise comparison for all the levels....
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