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-1
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0answers
13 views

Distribution with random parameter

I got a problem with Exercise 3.1(a). Since there's an example right before the exercise I assumed that X conditioned on M has the same distribution as in the example. I don't understand their ...
1
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2answers
63 views

conditional expectations

Hi i was wondering how to figure out the following Suppose $y=x+e$ where e is an i.i.d error. Say $x \sim N(\mu,\sigma_1^2)$ and $e \sim N (0, \sigma_e^2)$ which means $y \sim N (\mu, ...
1
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0answers
19 views

How to find conditional distribution for Rao-Blackwellizing an estimator?

Let's say I have an unbiased estimator $u(\underline x)$ for function $v(\theta)$ where $\theta$ is a parameter of the distribution of $x$, and $T(\underline x)$ which is a sufficient statistic for ...
1
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0answers
79 views

Given $N$ samples from $p(x|y=y_0)$ how can I infer $y_0$?

I have $N$ samples $x_i \sim p(x|y)$ for $y = y_0$. I don't know apriori what $y_0$ is but I know its a fixed value. I do not have the analytic form of $p(x|y)$, $p(y|x)$, $p(x,y)$. Instead I have ...
1
vote
1answer
34 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
28 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
votes
0answers
46 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
53 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?
1
vote
1answer
145 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
551 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
votes
0answers
26 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
87 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
295 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
67 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
votes
2answers
229 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
62 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
178 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 ...