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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Finding conditional probability of getting a number on a die and Jacks in Hand

Suppose we roll a fair six-sided die and then pick a number of cards from a well-shuffled deck equal to the number showing on the die. (For example, if the die shows 4, then we pick 4 cards.) (a) ...
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20 views

How to draw a conditional distribution graph for B given A

Below is a frequency table which has data for testing a theory that students who speak a foreign language are also strong mathematics students. The question says to draw a graph showing conditional ...
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147 views

conditional probability results in value greater than 1

I am not an expert in probability theory so please bare with me. Suppose I have a one sentence corpus as follows: How to go about it It's quite obvious to see that the corpus has 5 words. Here is how ...
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18 views

Conditional independent Poisson variables modelling count data

A study question I have been looking at for sometime has confused me somewhat. I have conditionally independent Poisson count observations with a hierarchical structure to the data. The format of ...
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10 views

Confusion regarding conditional distirbution of the product of gaussian process with a normal

I am getting confusedregarding a simplae problem. say $Y = WX$ where $X$ is a q X n matrix with each row a Gaussian process denoted as $\mathcal{GP}(M(\mathbf{X_i}),C(\mathbf{X_i},\mathbf{X_i}))$, in ...
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19 views

Conditioning within definition explanation

I have a doubt on the meaning of a conditioning within a definition. In a book I've found the following definition of upper tolerance limit: $P(P(X<\bar X+kS|\bar X, S)>p)=1-\alpha$ where $X$ ...
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61 views

What is the probability of the first positive event in an sequence of binary events where sequences have finite but random lengths?

I have a time series of observations from a longitudinal study of individual objects. These observations are seen as discrete sequences of features, one sequence per object. The sequences have ...
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16 views

Gibbs Sampling for LDA example

Can someone provide an example of 1 (or more) iteration(s) of Gibbs sampling for LDA using real values? I have been searching for a while and I can't seem to find any good examples. Thank you.
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44 views

number of parameters for a Bayesian network over binary random variables

I am working through the exercises of a book (Bayesian Reasoning and Machine Learning) for machine learning but I got stuck (I do not understand the question). The following three variable ...
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36 views

Conditional expectation of a univariate Gaussian

Suppose I have a univariate Gaussian distribution with mean $\mu_X$ and standard deviation $\sigma_X$, and I know the random variable $X$ is least some positive value $y$: $X \geq y$. What is the ...
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2answers
46 views

I need help with this stat problem [duplicate]

A friend claims that because there is a 50% chance for a coin to land on heads, the fact that the last three coin flips landed on tails means that there is a higher chance for the coin to land on ...
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57 views

Gibbs sampling and conditional distribution

I need to simulate the posterior distribution of intraclass correlation coefficient $\pi(\rho|y)$ where $y$ is the data set and $\rho=\frac{\sigma_a^2}{\sigma_a^2+\sigma_e^2}$ with $\sigma^2_a\sim IG(\...
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78 views

Question involving Bayes' Theorem and Law of Total Probability

Usually I know how to do these problems, but this one stumped me. This is what the problem says: "Let $D$ denote the event that a person selected randomly from a population has a disease, and suppose ...
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37 views

What are the differences between stochastic v.s. fixed regressors in linear regression model?

If we have stochastic regressors, we are drawing random pairs $(y_i,\vec{x}_i)$ for a bunch of $i$, the so-called random sample, from a fixed but unknown probabilistic distribution $(y,\vec{x})$. ...
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6 views

Is it possible to derive a relation between parameters in Poisson process representation of extremes and parameters in GPD model?

I want to derive the theoretical relation between the parameters in a point process model for extremes and the parameters in the GPD model for extremes. I'm following Coles - An introduction to ...
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193 views

Looking for proof of conditional dependence, when the conditioning variables are linearly related

Suppose we have three random variables, $X$, $Y_1$, and $e$ (for error). Variable $e$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture ...
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10 views

Merge a set of probabilistic statements

I have a machine learning problem for which I would like to split the mostly binary variables in groups of independent variables (independent across groups, dependent within). Then, I can learn the ...
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30 views

Monte Carlo conditional pdf

I have a question which as been bothering me. It's best explained by way of a dumb example: Suppose one wants to compute the value of pi by sampling within the unit square (i.e. https://en.wikipedia....
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42 views

The Second Hearts Problem

Intro: According to the last part of these lecture notes, if we have a standard deck of playing cards and turn cards until the first heart appears, the probability that the next card is a heart is $\...
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33 views

intuitive difference between joint probability and conditional probability in this example

I was reading a tutorial on marginal densities when I came across this example (rephrased). A person is crossing the street and we want to compute the probability when he gets hit by a passing car ...
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270 views

Monty hall problem, getting different probabilities using different formulas?

In my Monty hall problem, I am computing what is the probability that P(H=1|D=3) i.e. price is behind door 1 and the 3rd door is opened. $P(H=1|D=3) = p(H=1) * \frac{p(D=3|H=1)} {p(D=3)} = 1/3 * 1/...
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26 views

Solve for iteration of conditional expections

I have been reading The Perils of Peer Effects paper by Josh Angrist http://www.nber.org/papers/w19774 On page 4, he transforms a condition expectation function: $E(y|x,z)=\beta\mu_{(y|z)}+\gamma x ...
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32 views

Understanding statistical independence of events using a relative frequency interpretation

This is what I've read in my textbook: "If $n_A$ and $n_B$ are the number of times the independent events $A$ and $B$ have occurred, then we expect that the ratio $\frac{n_{AB}}{n_A}$ (num. of times ...
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45 views

Sampling from marginal distribution using conditional distribution?

I want to sample from a univariate density $f_X$ but I only know the relationship: $$f_X(x) = \int f_{X\vert Y}(x\vert y)f_Y(y) dy.$$ I want to avoid the use of MCMC (directly on the integral ...
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25 views

Probability of receiving each preference in an internship drawing

I have to write a 23 itens preference list of places where to perform my internship. There will be a lottery which I don't know how exactly they will weight the preferences to distribute us. The ...
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20 views

In a markov chain, how to deal with final states that are not in the initial states - Probability of Default

I'm analyzing a bank portfolio in order to determine the consequent probability of default using markov chains. For this I select the group of credits at the end of month 'n' and measure their credit ...
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6 views

Forming distribution conditioned on many variables from single conditional marginals using copulas

I'm brainstorming about a data analysis project, part of which can be thought of as estimating a joint distribution from marginals, so I'd like to know whether I can use some copula techniques. ...
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15 views

What are the differences in linearity in Non-stochastic and Stochastic Regression?

I have been confused with the difference/distinction between stochastic and non-stochastic explanatory variables for while. I was able to write down my current understanding some time ago and am ...
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16 views

Specifying conditional probability tables for nodes with large number of Parents in a Bayesian Belief Network

What is the ideal way to specify the conditional probability tables for belief propagation in a Bayesian Network, for nodes with large number of parents? I am currently using gRain package in R. But ...
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9 views

Naive Bayes and smoothing

For simplicity, let's say that we want to perform binary classification using Naive Bayes on a Boolean function. That is, the target function is $c: \{0, 1\}^n \rightarrow \{0, 1\}$. Hence, the two ...
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46 views

I need someone to check my conditional probability calculation function

I am following the book "Think Stats. Probability and Statistics for Programmers" and doing the exercises using numpy + pandas. Currently I am on exercise 2.7 on conditional probability: Exercise ...
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29 views

Asymptotic conditional expectation

Problem Setup Let $\{X^d_1, X^d_2, \cdots, X^d_n\}$ be a $d-$dimensional zero-mean, i.i.d. random variables. Let $S_n^d$ be $$ S^d_n = \frac{\sum_{i=1}^n X_i^d}{\sqrt{n}} $$ Let $Y^d$ be a zero-...
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78 views

Computing conditioned probability of $X$ by $U=\min(X,Y)$

Let $X$ and $Y$ be independent random variables with $P(X\leq x)=F_x(x)$ and $P(Y\leq y)=F_y(y)$. Let $U=\min(X,Y)$. I know that $F_u(u)=1-(1-F_x(u)(1-F_y(u))).$ By definition: $P(X \leq x |U=u)= \...
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1answer
39 views

Conditional expectation for non-gaussian variables

Let $A$, $B$ be two zero-mean random variables. Let the variance be $\sigma^2_A$, $\sigma^2_B$ and let the correlation be $\sigma_{AB}$. Consider the following expression :- $$ \mathbb{E}\big[A|B=b\...
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19 views

Conditional Distribution of Hidden Markov Model

I am trying to implement a Gibbs sampling algorithm for a toy Hidden Markov Model, but I am having trouble deriving the target conditional distribution. I am generating data through the following ...
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2answers
79 views

Is it correct? $ p(a,c|b) = p(a|c)p(c|b) $

I read two different papers on some similar problems. In one of the papers this statement is written: $ p(a|b) = \sum_{c \in C}p(a,c|b) $ While in the other it is written as: $ p(a|b) = \sum_{c \in ...
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42 views

How to do calculate both causal and diagnostic inferences simultaneosly in bayesian networks?

Consider a simple Bayesian network as given below. Question: How to find $P(S|C,W)$? It is fairly straight forward to compute the causal inference $ P(W|S) = P(W|S,R)\cdot P(R) + P(W|S,\bar{R}...
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48 views

If the # of people in a room is Poisson distributed, and you observe someone enter, what's the distribution of the # of people?

I hope this question is properly formulated. It's just something that occurred to me spontaneously. Consider a random variable $X$ representing some count data -- for instance, the number of people ...
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96 views

Probability distribution transformation of variables question

Problem: Hi there, I'm stuck trying to derive an equation stated in a research paper relating to Bayesian statistics in Cosmology (the paper is: http://mnras.oxfordjournals.org/content/398/4/2049....
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70 views

Estimating a function $f$ of a random vector $\mathbf{x}$ by a subset of the coordinates of $\mathbf{x}$ after a rotation of the input space

Suppose I have $$h=f(\mathbf{x})$$ with $f$ a deterministic function and $\mathbf{x}=(x_1,\ldots,x_n)$ a random vector of known distribution. I'm not using the capital letter notation for random ...
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9 views

Sample space in Linear regression

Say you want to model some trait of an individual using standard linear regression. Then you assume $Y|X\sim N(\boldsymbol{X}\beta,\sigma^2)$, where $\boldsymbol{X}=(X_1,...,X_n)$ is a row-vector of ...
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37 views

A question on conditional gaussian distribution

The book on Pattern Recognition (by Bishop) begins the section on conditional gaussian by saying: An important property of the multivariate Gaussian distribution is that if two sets of variables ...
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13 views

Conditional probability sub-model so solve setting with a factor that has many levels

I stumbled upon a post of the http://www.win-vector.com/ blog where they treat the problem when a factor with many levels occurs. In my understanding instead of using the factor itself, they use the ...
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31 views

how do i compute the probability [duplicate]

I have a continous dataset consisting of 4000 observation from each 400 features are extracted. Each observation has been labeled a class. Since the dataset is continous, have I created a distribution ...
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1answer
35 views

When is the probability of a variable equivalent to a function of the variable i.e. when does p(x)=f(x)?

What allows us to conclude that that p(z)= h(z) as shown in the yellow highlights in the below solution? If p(z) didn't equal h(z) then proportionality would still fail to show conditional ...
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55 views

P(X<Y|Z=t) where Z=min(X,Y)

Lets X and Y be uniform random variable where $x \in [0,a]$ and $y \in [0,b]$ where a < b. We design $Z=\min(X,Y)$. I know that the CDF of Z is $P(Z<z)=1-\frac{(a-z)(b-z)}{ab}$ And by ...
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36 views

Bayesian networks - prediction question

Let's consider a dumb spam filter BN (see figure below) for which I've already calculated the a posteriori parameter distributions (see normalized table values). I want to predict if next email ...
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1answer
68 views

Joint distribution of a discrete and a continous random variable

Consider this question and the working below: A coin-making machine produces pennies. Each penny is manufactured to have a probability $P$ of turning up heads. However, the machine draws P ...