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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5 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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1answer
28 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). $E$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture variable $Y_2$ ...
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7 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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22 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. ...
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0answers
10 views

Not sure how to model some probabilities on web traffic

So, I have a dataset of web site visits (a tidy one, thankfully), of which the most important columns are user_id and page. I have a training set for the first 11 months of the year, and a test set ...
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36 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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2answers
29 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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24 views

How can we prove this equation using marginalization and conditioning? [on hold]

I want to prove $$P(A|C) = \sum_{B} P(AB|C) $$ How can we prove this using marginalization and conditioning?
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8 views

How to sample from Conditional Density Estimation estimated using hdrcde package in R? [on hold]

I wanted to use ARMS sampling technique (MCMC method) available in "HI" package in R. I'm not understanding how to give input for ARMS.
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18 views

Unconditional distribution of conditional binomial

I have been trying to model a situation in which some observed values, denoted $y_{i}^{r}$, are bounded from above by unobserved values $y_{i}$. In my work, in order to demonstrate some impossibility, ...
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3answers
254 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 * ...
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16 views

probability and lottery tickets [closed]

10 Tickets are drawn randomly from a barrel containing 200 tickets. There are 3 prizes to be won: first, second and third. Josephine has purchased 10 tickets. Assuming Josephine wins only one prize, ...
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1answer
25 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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1answer
29 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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1answer
40 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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0answers
19 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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18 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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13 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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0answers
13 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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0answers
7 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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1answer
40 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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28 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 ...
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2answers
77 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
38 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 :- $$ ...
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17 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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1answer
36 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) + ...
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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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1answer
94 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: ...
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1answer
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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1answer
11 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
34 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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2answers
52 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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1answer
35 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
65 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 ...
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38 views

Chi-squared goodness-of-fit test and conditional probability distribution

I have three discrete variables, let's say $A, B,$ and $C$. The number of possible values of $A$ is 3, and $B$ and $C$ take binary values. I also know the probability distributions, $Pr(A | B, C)$, ...
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19 views

Hidden Markov Model with sequence of 1

I'm not experienced with HMM. I read some research papers about HMM and they mention 3 basic problems. One of them is to find the probability of a sequence of $k$ emitted symbols $(S = x_1, x_2,..., ...
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2answers
54 views

Probability Question - Conditional Probability Quantity

A particular fault occurs in a certain type of mechanical devices with a frequency of 8 in 1,000. A screening test for this fault is developed such that (i) if the fault is present, it is detected ...
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245 views

How to derive this conditional distribution function for a Restricted Boltzmann Machine?

I am following along Ian Goodfellow's new Deep Learning book and, reading the last chapter, I am confused about equations 20.7-20.9. We have a joint distribution function, $P(v,h)$, and we are ...
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3answers
112 views

Bounds on a conditional probability

My friend asked me about this, and I couldn't give him a good answer. Say you have some favorable event $G$. You know that knowing either of events $A$ or $B$ will more likely than not result in $G$. ...
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15 views

Question about conditional probability for the multivariate normal distribution

How can I prove that the conditional probability of a multivariate normal distribution Pr(x1|x2=k) is the same for all k when the covariance is diagonal and the variables are independent ? Would the ...
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44 views

Expanding Joint probability distribution function having dependent random variables

Let $Z_1$ and $Z_2$ denotes two dependent random variables defined as \begin{align} Z_1&=\frac{XY}{aX+bY+c}\\ Z_2&=\frac{XY}{uX+vY+w} \end{align} where $X$ and $Y$ are independent ...
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22 views

Conditional cumulative probability

Given two jointly distributed random variables $X, Y$, I would like to compute the conditional cumulative (or cumulative conditional?) probability $P(X \leq x | y)$ that given a value $y$ of $Y$, $X$ ...
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6 views

Adding dependent random normal distributions and conditional expectations

My problem is as follows: Let $X, B_1, B_2, B_3$ be independent normal random variables with $\mu = 0$, $\sigma = 1$. Let: $Y_1 = X + B_1$ $Y_2 = 2X + B_2$ $Z = X + B_3$ Then, I had to find $Z' = ...
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1answer
34 views

Does Naive Bayes( library:klar) in R calculates denominator of conditional probability while giving output?

Generally, when using Naive Bayes for classification, denominator is ignored as probability is directly proportional to the numerator as denominator is same for all the classes. So, I want to know if ...
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1answer
34 views

Comparing the distribution fits of a bivariate and a univariate model

Suppose I've done an experiment and I have a distribution of observations $x$ that vary between $-\pi$ and $\pi$. Now suppose each $x$ is associated with a second observation $y$ that may or may not ...