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0
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1answer
19 views

Conditional expectation with conditioning on two independent variables

Let $Y_1$ and $Y_2$ be independent r.v.s, and $X$ be another random variable. What is $E[X|Y_1, Y_2]$? Is $E[X|Y_1, Y_2]$ equivalent to $E[X|Y_1] \cdot E[X|Y_2]$? More specifically, is there a ...
0
votes
1answer
19 views

updating posterior parameters when involving conditioning

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
3
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0answers
36 views

Conditioning on a variable

I am looking at some software code that performs conditioning on random variables. For example, one can have a set of random variables which have a multivariate normal distribution associated with ...
2
votes
1answer
41 views

Joint probability of two correlated RVs

I am trying to get the joint PDF of two RVs $X$ and $Y$ where $aX<Y<bX$, so I am stuck in calculating the probability of $\mathbb{P}(X<x,Y<y|aX<Y<bX)$ any idea?
0
votes
0answers
38 views

Estimating the conditional probability that continuous $Y \leq c$

Consider a continuous response $Y(i) \sim N(0,\sigma^2)$ and design matrix vector $i$; $\mathbf{X}(i)$. Suppose that I am interested in estimating the probability that $Y(i+1) \leq 0.1$ given ...
1
vote
1answer
111 views

Using quantile regression to predict probability of surpassing threshold

Consider a continuous response $Y$ and design matrix vector $\mathbf{X}$. These are related through some function $f(X) = Y$. Suppose that I am interested in estimating the probability that $Y \leq ...
10
votes
4answers
447 views

Expected number I will be on after drawing cards until I get an ace, 2, 3, and so forth

I am having some trouble solving the following. You draw cards from a standard 52-card deck without replacement until you get an ace. You draw from what is remaining until you get a 2. You continue ...
0
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0answers
23 views

How to improve location and scatter estimation conditioning on higher order statistics?

Using sample moments, how can the mean and variance estimators be improved if e.g. skewness and kurtosis are known exactly? And what about using estimates for these instead, which should imho be of no ...
1
vote
0answers
82 views

Determining confidence intervals: using partial information on possible outcomes

Let's say we have a mathematical model that provides the probability of finding oil at a location in terms of a system of 10 bins with probabilities going from very low, say 2%, to 20% for the best ...
0
votes
1answer
219 views

Sampling from the conditional distribution assuming sampling from the joint

I am struggling with this question, which I thought it should be easy: suppose we have a method of sampling from the joint distribution of a collection of (discrete ordinal) random variables. We do ...
2
votes
0answers
64 views

conditional on the total, what is the distribution of negative binomials

If $x_1, x_2, \ldots, x_n$ are i.i.d. negative binomial, then what is the distribution of $(x_1, x_2, \ldots, x_n)$ given $x_1 + x_2 + \ldots + x_n = N\quad$? $N$ is fixed. If $x_1, x_2, \ldots, ...
-1
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2answers
223 views

Compute $\mathrm{Cov}(\sum_{i=1}^NX_i,\sum_{i=1}^NY_i)$

Let $X_1,X_2,\dots$ be i.i.d. Bernoulli random variables with parameter $\frac{1}{4}$. Let $Y_1,Y_2, \dots $ be another sequence of i.i.d. Bernoulli random variables with parameter $\frac{3}{4}$. And ...
2
votes
0answers
2k views

Collinearity diagnostics disagree - VIF, condition index, and correlation matrix

I'm working with a large dataset consisting of just over 1 million cases. The data are longitudinal covering 14 years and hierarchical with about 500 of the level 2 units. Each case is a criminal ...
0
votes
1answer
59 views

How can conditional be substituted with a function of same variable?

I was studying on a PAMI article and I have seen an equation like this: $$ \begin{align*} P(B|X) &= \prod_c{P(B^c|X)} \\ &= \prod_c{P(B^c|A^c)} \end{align*} $$ where $A^c$ is a ...
4
votes
1answer
169 views

What is conditioning in spatial statistics?

Could someone explain to me: the concept of "conditioning" in spatial statistics in a fairly advanced context? Here is an example to clarify the question: Step 1) generate a 2D point process, here 6 ...