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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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43 views

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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202 views

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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43 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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20 views

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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25 views

How to add spline in conditional logistic regression model in R?

I want to add a continuous variable with spline into condiotional logistic regression model in R. I tried this: ...
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1answer
20 views

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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3answers
95 views

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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64 views

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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40 views

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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23 views

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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9 views

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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1answer
39 views

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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Why embedding layers can be regarded as a form of conditional computation?

Recently, I am reading the paper, "Outrageously Large Neural Network: The Sparsely-Gated Mixture-Of-Experts Layer". In the introduction section of the paper, authors mention about the ...
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Vine Copula: Understanding Conditional Pairs

The regular vine copula below $ f\left(x1,x2,x3\right) = f_{3}\left(x_{3}\right)f_{2}\left(x_{2}\right)f_{1}\left(x_{1}\right) \times c_{12}\left(F_{1}\left(x_{1}\right),F_{2}\left(x_{2}\right)\right)...
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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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1answer
61 views

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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1answer
37 views

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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1answer
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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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1answer
54 views

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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20 views

How do I model conditional logit when some of the alternatives are not available to some individuals?

I am using conditional logit with discrete choices and random coefficients for some of the variables. There are 9 alternatives in my model that are the same for everyone in the sample. However, some ...
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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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49 views

Goodness-of-fit for conditional logistic regression in a 1:1 matched case-control study

Dear Stackexchange community; I would appreciate if someone would guide me on this matter. On data analysis of a 1:1 matched case control study based on age and gender through using conditional ...
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30 views

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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25 views

Conditional expectation of two random variables

Suppose we have $X \sim Exp(4)$ and $Y \sim N(0,1)$ which are independent. What can we say about $\mathbb{E}[X|Y]$?
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21 views

Logistic regression analysis or something else?

I have a dependent binary outcome and 6 independent variables. These are measured in the same group of people at two moments in time in a descriptive longitudinal study. I am assessing whether these ...
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1answer
65 views

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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1answer
23 views

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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2answers
48 views

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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51 views

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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24 views

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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1answer
263 views

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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1answer
55 views

Fisher Information for Cox Model

Actually, I'm working on a Statistical Genetics Article (Schaid and al,2010) in a retrospective likelihood context. In the article, authors present some result about conditional likelihood but I can't ...
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0answers
28 views

Scenario Analysis with a GARCH model - conditional forecasts with hard restrictions on dependent variables?

Waggoner and Zha (1999), see reference below, developed an approach to produce conditional forecasts for VAR models with hard restrictions on the variables using Gibbs Sampling. As an example, they ...
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1answer
301 views

Conditional expectations and variance - OLS

Apologies for starting a new post for such basic problems but I have an exam tomorrow and struggle to sort out two answers from last year's exam (2. and 3.). I gave as much context as possible: The ...
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0answers
32 views

Conditional and density probability (normal distribution)

I am trying to solve the following problem: Suppose that $\mu\sim N(1,4)$ and $Y|\mu\sim N(\mu,1)$. Show that: $$\begin{bmatrix}Y \\ \mu \end{bmatrix} \sim N\bigg(\begin{bmatrix}1 \\ 1 \end{bmatrix},...
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1answer
29 views

Inference problem, having issues translating problem from words into probabilistic terms

This is the question: There are particular readers for swipe cards, Under normal operating conditions, there is a small probability of 0.02 that swiping a card fails to open the entrance - some of ...
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62 views

conditional distribution for normal distribution

Assume $X = (X_1, X_2 , ... ,X_n )$ is observed, where the $X_i$ are (independently) $N(\theta , 1)$. find the conditional distribution of $X_1,....X_{n-1}$ given $\bar{X}$. I am having a problem in ...
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1answer
80 views

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 ...
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0answers
71 views

Conditional Covariance Problem

Suppose we have independent (not necessarily identical) normally distributed random variables X, Y. If we're given that, upon sampling each variable, X is some multiple a of Y (i.e. x = ay), what is ...
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40 views

Conditional dependence between two ordinal variables

I really hope that this question was not answered in any way before, but I couldn't find an appropriate solution to my problem - most probably due to my lack of statistical knowledge. I am trying to ...
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1answer
48 views

$k$-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_{(...