The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

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Estimating latent probability variables from binary response data (logit GLMM)

Question: How can I calculate the standard error of an estimate derived from two coefficients of a logit GLMM? We're studying the effect of a categorical condition ('volume', 3 levels) on two latent ...
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16 views

What is the probability that the monthly meeting will be held today, after 3 times postponing?

Today (Sunday) the manager will hold a monthly meeting. But the meeting is postponed one day to Monday, after that the meeting is postponed to Tuesday again, and then it is postponed to Wednesday ...
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0answers
10 views

Conditional expectation in mixture distributions

I have a mixture distribution for observed lifetime data $(\delta_i,t_i,L_i)$, where $\delta_i$ is a censoring variable (1 indicating death, and 0 indicating censoring), $t_i$ is the observed lifetime ...
4
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1answer
28 views

Gibbs Sampler output: how many Markov chains?

When running a Gibbs sampler (for $n=200$ Iterations) with two full conditionals, I get the output $\mathbf{x} = (x_1^{(n)},x_2^{(n)})_{n =1,...,200}$. So $\mathbf{x}$ is the realizations of a Gibbs ...
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0answers
19 views

What are the odds of having the same Lawyer make a mistake in two wills involving the same person? [closed]

A lawyer made mistakes in my will and were caught while I was alive to have it fixed and then a loved one died and it turns out the very same lawyer made a mistake in his will that the deceased can't ...
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23 views

What are the odds of having 2 windows shot- one facing the west one year and another structure window the following? [closed]

It is a small rural community with fields between our house and a hedgerow between us and the neighbors to the north, and different neighbors across the street with a field. It was always assumed ...
6
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76 views

Bayesian inference with sampling and mixture models

I'm having some trouble doing Bayesian inference on an experience I have in hands. I apologize in advance if it is too complex, but I couldn't find a trivial way to split it in several parts. Let ...
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1answer
19 views

Proof of chapman kolmogorov equation

In the proof of Chapman Kolmogorov Equation $p_{ij}^{(m+n)}=\sum_{k=0}^{\infty}p_{ik}^{(n)}p_{kj}^{(m)}$ Proof: $p_{ij}^{(m+n)}=P[X_{m+n}=j|X_0=i]$ By the total probability it says ...
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1answer
33 views

Expected number of collisions for balls and bins problem

$n$ number of balls are thrown randomly to $m$ number of bins, standing in a row. The balls are labeled as $1,2,3,....n$ and bins are also labeled as $1,2,3,...,m$. The probability of $i_{th}$ ball ...
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1answer
18 views

Methods to weight probabilities that are being multiplied together?

I am trying to classify data according to a taxonomy: That is, given a feature vector $x$, I would like to compute: $P(A,\alpha)$ $P(A,\beta)$ $P(B,\delta)$ $P(B,\gamma)$ (You can think of the ...
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1answer
13 views

Factoring a probability distribution containing a latent variable

I distribution which involves 3 parameters, which I'll call (for now) $P(z | y, x)$. However, one of the parameters is a function of another. For instance, let the random variable $y$ be a ...
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2answers
118 views

What can we infer if P(A|B,C) = P(A|B)?

I want to understand what we can infer when the following equation holds: $$P(A|B,C) = P(A|B)$$ My understanding is that $C$ does not give us any extra information about $A$ that $B$ does not give us ...
3
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1answer
64 views

Conditional Poisson Distribution

The number of claims, $N$, in a year on a portfolio of policies follows a Poisson distribution with parameter $λ$. Large claims have a probability $p$ and small claims $(1-p)$, independently of ...
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0answers
46 views

3 Class Classification based on a Bernoulli feature and gaussian feature

Consider a 3-class classification problem with mixed features, where one feature is Gaussian and another is discrete Bernoulli: Prior class probabilities: P(C1) = .5, P(C2) = P(C3) = 0.25 ...
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0answers
10 views

Help interpreting this result based on conditioning on gender -Contigency Tables

The problem i'm having is how to interpret the results I got. For part a) I got that the abortion laws are independent of generation where I used a $\chi^2$ test. For part b) I got that the the age ...
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0answers
13 views

How to test a probabilistic fertility simulation?

Imagine I want to build a simulation of a certain society. One part of it is a fertility model, which describes under which circumstances people are born. Let's assume that the model is very simple: ...
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18 views

Variance of multinomial distribution that is product of 4 Beta random variables

I have a system of 4 binary random variables, $A$, $B$, $C$ and $D$. $A$, $B$ and $C$ are conditionally independent given $D$, and I'll call one set of samples $ABCD$ an event (e.g. $ABCD$ meaning all ...
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12 views

scikit learn gaussian mixture conditional distribution

I am using scikit-learn to fit a Gaussian Mixture Model to a dataset. However, I now need to find the distribution conditional on one or more variables and I have not found a way to do that. Can ...
2
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1answer
73 views

An 'easy' exercise on conditional expectations and filtrations

I am struggling with the following exercise in the context of modeling information structure via filtration to evaluate contingent claims. I hope that someone can explain me how to derive the ...
2
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1answer
60 views

Marginal, joint, and conditional distributions of a multivariate normal

Let $Y$ ~ $MVN_3(\mu, \Sigma)$ where $\mu = (5,6,7)$ and $\Sigma = \begin{bmatrix}2 & 0 & 1\\0 & 3 & 2\\1&2&4\end{bmatrix}$ Find (a) The marginal distribution of $Y_1$ (b) The ...
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18 views

On conditional/joint probability [duplicate]

Problem 1 The table on the left shows the joint probability distribution between two random variables - X and Y; and the table on the right shows the joint probability distribution between two random ...
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6 views

Dependence of PDF of LLR of symbols

I have a system model with $y=hs+\sum_i^n gx+n$ where h is rayleigh fading desired channel, g is interfering channel x is interfering symbols. $\hat{s}=w*y$ where w is MMSE filter. On what factor pdf ...
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32 views

conditional distribution question

I have a joint distribution which factorizes as follows: $$ P(y, w, \beta) = P(y|\beta, w) P(w) P(\beta) $$ Now, I want to write the conditional distribution for $P(w|y, \beta)$, so this should be ...
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24 views

t-student distribution [duplicate]

I've got this problem: Here, if $Z,W$ are independent random variables, and $Z$ has normal standart distribution and $W$ has $\chi^2$ with $n$ degrees of freedom, $T=\frac{Z}{\sqrt{\frac{W}{n}}}$. I ...
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1answer
29 views

conditional probability, change of variable and Jacobean

I have a question, and I am guessing that the question arises due to my lack of good understanding in the change of variable technique. I would like to evaluate $f_X(x)$. When $f_Y(y)$ exists, I can ...
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10 views

Estimating conditional probability of bernoulli data

Assume I have $i=1,\dots,N$ fathers, each with $j=1,\dots,n_i>0$ sons. Now there is a binary event $A_{i,j}$ with outcomes 1 and 0 and the respective probabilities $p$ and $1-p$. Now I want to ...
2
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1answer
43 views

On an implication of the memoryless property of the exponential random variable

I know that if we take $X \sim Exp(k)$ then we have this property: $$P(X \ge s + t | X \ge s) = P(X \ge t)$$ But why does this imply that $X | X > x$ has the same distribution of $X$ only ...
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1answer
16 views

Posterior probability of an image when the posterior of local features are known

Lets assume the local features $x_1, x_2, \dots x_n$ of an image $I$ are independent. I know if $p(x_i|c)$ are given $p(I|c)$ can be defined by $\prod_{i=1}^N x_i$ But I dont know how to calculate ...
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30 views

A question about raising the power of the integrand

Given that we know $P(X<x)=F(x)=\int_{\theta}F(x|\theta)dG(\theta)=1-\alpha$, is there any way to express $\int_{\theta}[F(x|\theta)]^{n}dG(\theta)$ also in terms of $\alpha$?
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34 views

Is is possible to determine conditional conjugacy in this case?

I'm working on a problem where I have to extract sufficient statistics for parameter estimation in a state-space model. Usually these come from the quantities used for conjugate updates. I'm OK with a ...
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2answers
146 views

A Question on Elementary Statistical Inference

A box contains $5$ white and $2$ black balls. A coin with unknown $P(Head)=p$ is tossed once. If it lands HEADS then a white ball is added, else a black ball is added to the box. Then a ball is ...
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1answer
39 views

What does “if” mean in this question?

What is the probability that Sam is guilty if Tom and Devi gave conflicting testimonies? Is it conditional probability? Or intersection simply?
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1answer
65 views

Sufficient statistic for a Gamma distribution

I am confused about the steps I need in order to solve the equation below. I must use conditional distribution (and NOT the factorization theorem). Q: $X_1, . . . , X_n$ is a random sample from a ...
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39 views

Bayes Net: how to calculate joint distribution?

I originally posted this question to Computer Science Stack Exchange, but then I was told that CrossValidated site existed. I've been reading many questions, but none of them seem to answer my doubts. ...
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28 views

conditional density wrt lebesgue measure

$X,Y$ are two r.v. $(\Omega,\mathcal{A},\mathbb{P}) \rightarrow (\mathbb{R},\mathcal{B}(\mathbb{R}))$ and have joint density wrt to $\lambda^2$, the two dimensional lebesgue measure. So $f_X(x) = ...
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39 views

Conditional distribution function of sum of correlated Bernoulli variables

Let $X_i$ be a Bernoulli variable with probability $p$ for $i=1,...,N$. Hence $\sum_i X_i$ is binomial and approximately normal$(p,(1-p)p/n)$ for large $N$ The conditional probability distribution of ...
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21 views

Conditional distribution of current state of HMM given past observations and state

I want to compute the following conditional probabilities for an HMM, where I shall refer to the state at time $t$ as $X_t$ and the observation at time $t$ is $O_t$: $$\text{Pr}\left(X_t | O_1, ...
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38 views

Conditional probability attributes

Let $(\Omega,\mathcal{A},\mathbb{P})$ a probability space and $\mathcal{F} \subset \mathcal{A}$. For $B \in \mathcal{A}$ is $\mathbb{P}(B|\mathcal{F}):= \mathbb{E}[I_B | \mathcal{F}]$ the conditional ...
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18 views

Dealing with independent events and a “given” statement

I'm given a question: Two buddies, plan a squirrel-hunting trip. B has a shot 2x better than A. A's chance of hitting the squirrel is 0.39, they see a squirrel and both shoot at the same time. ...
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50 views

Probability problem (Urn 1 contains 3 white and 4 black balls, and Urn 2 contains 2 white and 6 black balls …)

I'm studying probability. This is not homework. I have been studying for a graduate master's since September 2015. The textbook is Probability : An Introduction (Grimmett & Welsh). You are ...
4
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1answer
89 views

Gibbs Sampler transition kernel

Let $\pi$ be the target distribution on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R^d}))$ which is absolutely continuously wrt to the $d$-dimensional Lebesgue measure, i.e : $\pi$ admits a density ...
8
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3answers
192 views

Conditional probability of continuous variable

Suppose that random variable $U$ follows a continuous Uniform distribution with parameters 0 and 10 (i.e. $U \sim \rm{U}(0,10)$ ) Now let's denote A the event that $U$ = 5 and B the event that ...
5
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1answer
183 views

Gibbs Sampler contradiction proof

I want to prove that the systematic scan Gibbs sampler yields an aperiodic chain $X$ on a general state space. Let $\pi$ be the stationary distribution for the resulting chain. Suppose to get a ...
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1answer
47 views

Conditional distribution for Exponential family

We have a random variable $X$ that belongs to the exponential family with p.d.f. $$ P_X(x|\boldsymbol \theta) = h(x) \exp\left(\eta({\boldsymbol \theta}) . T(x) - A({\boldsymbol \theta}) \right) $$ ...
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63 views

Using inverse probability with conditional events

To reach Grenoble, France, from Turin, Italy, one can follow either of two routes. The first directly connects Turin and Grenoble, whereas the second passes through Chambery,France. During extreme ...
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22 views

joint distribution translated into union of intersection?

Consider the declaration of the intersection property for conditional independence. $$ \left.\begin{align} X \perp\!\!\!\perp A \mid B \\ X \perp\!\!\!\perp B \mid A \end{align}\right\}\text{ and ...
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1answer
98 views

Conditional Probability [duplicate]

A judge is 35% sure that X has committed a crime. A and B are two witnesses who know whether X is innocent or guilty. However, A is X’s friend and will lie with probability 0.25 if X is guilty. He ...
0
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1answer
30 views

Selecting the best subset of features in binary logistic regression [duplicate]

I am using a binary logistic regression (a type of probabilistic statistical classification model, is used to predict a likelihood of belonging to a class (True, False)). I have 4 features and I want ...
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1answer
42 views

Conditional probability density function

Let $\theta$ be the parameter of the probability density function $f(x)$. If it is mentioned that $f(x|\theta)$ be the conditional probability density function, then what does $f(x|\theta)$ mean? ...
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18 views

Finding conditional probability on movement of knight

A knight makes 10 random moves on a chessboard, starting from bottom left hand corner. Let $A_k$={no square is repeated within the first $k$ moves} Find $P(A_{10}|A_5)$