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0
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0answers
12 views

Kullback-Liebler's divergence on a conditioned function

Let $q$ be a conditioned pdf over $\mathbf{X}=X_1,\dots,X_n$ binary r.v.s in the form $$q(\mathbf{X})=\begin{cases}q_{0}(\mathbf{X}_{\setminus i}) \text{ if } X_{i}=0\\q_{1}(\mathbf{X}_{\setminus i}) ...
0
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0answers
32 views

Conditional independence conjecture

Suppose there are four random variables (events), $A$, $B$, $C$ and $X$. If we have $X\perp A|B$, saying $X$ and $A$ are conditional independent given $B$, then I want to ask that whether we have ...
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0answers
12 views

Factor conditioning variables

Let $A,B,C$ be $3$ random variables. If $p(A,B\mid C) = p(A\mid C) \cdot p(B\mid C)$ holds, then $A$ and $B$ are conditionally independent given $C$. My question is: What are the underlying ...
9
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2answers
176 views

On Fisher's exact test: What test would have been appropriate if the lady hadn't known the number of milk-first cups?

In the famous lady tasting tea experiment by RA Fisher, the lady is informed of how many milk-first/tea-first cups there are (4 for each out of 8 cups). This respects the fixed marginal total ...
0
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0answers
49 views

Explanation that the prior predictive (marginal) distribution follows from prior and sampling distributions

While I have a vague intuition that this makes sense, I am interested in the formal demonstration that the prior predictive distribution in Bayesian inference is equal to the integral over $\theta$ of ...
2
votes
1answer
67 views

Law of iterated expectations with two random variables

Let $X$ and $Y$ be two random variables. I want to calculate $E[X|X<Y]$. I am wondering whether I can use the law of iterated expectations in order to calculate it, i.e. $E[E[X|X<Y,Y]]$. Do I ...
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0answers
23 views

conditional analysis and gene-wide analysis

I have a project where there is a list of genome-wide significant SNPs and we are interested in performing fine-mapping using only the summary stats data of GWAS. I was suggested to do a conditional ...
1
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2answers
100 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
35 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
vote
0answers
90 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
77 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
42 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
55 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
66 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
210 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
862 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
31 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
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0answers
97 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
486 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
77 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
240 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
3k 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
63 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
210 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 ...