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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10 views

Conditional Probability in Multivariate Normal

Given a tri-variate Normal, the conditional probability of an element given others truncated information is Now if I know that the mean vector u is (-0.91,-1.31,-1.39) and R is ...
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0answers
7 views

conditional probability in correlated variables

I tried to generate random samples to provide some scenarios for a stochastic programming model. I have three correlated stochastic variables. It is needed to calculate probability of each sample ...
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1answer
18 views

Does martingale model work for betting football matches?

Imagine I have 1 million USD and will be betting 1.000 USD on the win of FC Barcelona each time they play a match in La Liga (Spanish Tier 1 football league). If FC Barcelona loses or ties their last ...
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11 views

Describing a distribution of probabilities/percentages

Is there a better way to describe this probability? \begin{equation} Pr(Y_{sij}|R_n) = \frac{Y_{sij|R_n} \sum_{ij}Y_{sij}}{\sum_{ij|R_n} Y_{ij}\sum_{sij}Y_{sij}} \end{equation} The $R_n$ describes ...
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1answer
44 views

Graphical dependence in the DAG X->Z<-Y

In Barber's book pp. 40-41 he says that the belief network X->Z<-Y: is "graphically dependent" since: $$p(x,y|z) \propto p(z|x,y)p(x)p(y)$$ I don't understand why graphical dependence follows ...
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1answer
25 views

Can I rewrite conditional probability of three variables like this?

I know that the conditional probability $p(x\mid y)$ is defined as $\frac{p(x,y)}{p(y)}$. But what if I have $p(x,y \mid z)$, is that the same as $\frac{p(x,y,z)}{p(z)}$?
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1answer
46 views

Conditional probability of an event given two independent events

I am dealing with an interesting probability problem. I had $16$ subjects randomly divided into $4$ different rooms, each room having $4$ seats. The subjects were given a question to solve. We knew ...
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2answers
25 views

Conditions under which “explaining away” does vs. does not occur

My understanding of "explaining away" is as follows. If there is an effect, C, that can result from two independent causes, A and B, then observing only C makes A more likely than observing both C and ...
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24 views

How to calculate the conditional probability $p([x,y]|x=y)$?

How do you find conditional probability in a Multivariate Normal subject to the conditions of relationships in the individual variables? To write it mathematically, Given the fact that, How can we ...
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18 views

What are the state-of-the-art algorithms for training Conditional Random Fields?

What are some of the algorithms for learning the parameters of a Higher Order Conditional Random Field (such that the label Y_i depends on the labels Y_(i-1), Y_(i-2),...,Y_(i-o))? I am looking for a ...
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23 views

Volume-weighted probability of lead consumption by sales agent, generating HHI?

Weird question here, hopefully somebody with a heavier quant background than myself can answer. Context: I'm trying to get to a probability of a sales agent consuming a lead in a given state, ...
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8 views

How to find the probability of selecting a member from intersection of two subsets? [duplicate]

Consider two intersecting subsets of animals : mammals and hairy animals. There can be hairy mammals as well. Each of these subset can be further divided into two subsets: male or female. Consider ...
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1answer
31 views

Examples of marginal independence, conditional dependence

I am interested in finding "real-world" examples of when variables might exhibit marginal independence but are conditionally dependent given some other variable. It seems to me that the converse ...
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1answer
29 views

What does posterior “over” parameters $\alpha$ exactly mean? [closed]

From my understanding the posterior "over" parameters $\alpha$ is $$p(D|\alpha)$$ and not $$p(\alpha|D),$$ is it correct?
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68 views

Resources for the “ah ha” moment when learning Bayes' theorem

I've been studying statistics for a little while and I keep coming back to Bayes' theorem trying to relearn it and have that "ah ha" moment with it. I keep coming back to it because I understand just ...
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1answer
47 views

Deriving the Bayes Filter Correction Equation

The correction rule for Bayes filters is: $$p\left(x_{k}|D_{k}\right)=\dfrac{p\left(y_{k}|x_{k}\right)\cdot p\left(x_{k}|D_{k-1}\right)}{p\left(y_{k}|D_{k-1}\right)} $$ For: State at time $k$ is ...
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1answer
77 views

How can logistic regression have a factorial predictor and no intercept?

I tried a regression in the form ${\rm logit}(Y) = {\rm coefficient}\times X + 0 + e$, where $Y$ is a binomial variable and $X$ is a factor variable with $n$ levels. I noticed that removing the ...
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0answers
59 views

Computation of the entropy of marginals?

I have implemented this paper: Efficient graph-based semi-supervised learning of structured tagging models In the last sentence of the section 4.2, the authors have mentioned another possible way of ...
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13 views

The probability that a process signals (simple conditional probability)

I have this problem (from Montgomery's Applied Probability and Statistics, 5th Edition, problem 2-145, if anyone wants to see the original problem) but it's long, so for the sake of brevity I'll give ...
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3answers
194 views

Why Normalizing Factor is Required in Bayes Theorem?

Bayes theorem goes $$ P(\textrm{model}|\textrm{data}) = \frac{P(\textrm{model}) \times P(\textrm{data}|\textrm{model})}{P(\textrm{data})} $$ This is all fine. But, I've read somewhere: ...
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1answer
35 views

Independent events in sequence

If I flip a fair coin twice, the probability of at least one Head is 0.75 (HH, HT, TH and TT). I flip the coin once and it lands Tails. In order to get at least one Head, the probability of the ...
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31 views

Quadratic model as linear decrease in proportions

Assume $Y_i <= X_i$ for all $i$. The conditional expectation of our data was found to satisfy $E[Y|X=x] = a1*x-a2*x^2$ to very good accuracy for a large range, with $0<a2<a1<1$. ...
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1answer
19 views

How to compute $\mathbb{P}(A|B)$ of two independent RVs? [duplicate]

There are two independent RVs $X \sim \mathcal{U}(-1,5)$ and $Y \sim \mathcal U(-5,5)$. Let $A = \{ X \ge Y \land Y \ge -1 \land Y \le 1\}$ and $B = \{ X \le 1\}$. What is $\mathbb P (A | B)$? My ...
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61 views

Conditional Probability of a variables given five independent variables

I have six independent variables A, B, C, D, E and F and I would like to compute the conditional probability of A given B, C, D, E and F. To illustrate the problem, is this answer correct? ...
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1answer
125 views

Why the mixtures of conjugate priors is important?

I have a questions about the mixture of conjugate priors. I learnt and say the mixture of conjugate priors a couple of times when I am learning bayesian. I am wondering why this theorem is such ...
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13 views

Calculate probability distribution $p\left(\left.X_{1:T}\right|Z_{1:T},y_{1:T}\right)$ in linear- non-Gaussian state space model

I have a linear, non-Gaussian state space model. Observation equation: $y_{t}=a+bX_{t}+cZ_{t}+\epsilon_{t}$ $\,\,\,\,$ $\epsilon_{t}\sim\mathcal{N}\left(0,\omega^{2}\right)$ Transition equations: ...
4
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1answer
184 views

computing the posterior of two Gaussian probability distributions

I am a bit confused how to solve a Bayesian statistics problem. I have a parameter $\epsilon^s$ which is defined as following: $$\epsilon^s=\frac{\epsilon-g(\pi,z)}{1-g^*(\pi,z)\epsilon}$$ where ...
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3answers
54 views

The Probability of Life on Earth and the Question of Divine Intervention

Physicists today seem to believe that human life on Earth is the consequence of a series of highly unlikely events. For example, the universe needed to expand with a specific speed after the big ...
3
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1answer
64 views

Guessing the length of a fish

I would like to solve the following excercise. Any help is appreciated. 90% of the fish in our pond are males, the rest are females. The length of the males are: $X+5$ inches, where $X\sim ...
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9 views

Lumping of data

I have some time series $X = (X_t)_{t\leq T}$ that range over a finite set of values. For each $X_t$ let the next different value $X_{n(t)}$, that is $n(t)\geq t+1$ $X_{n(t)}\neq X_t$ and $X_s = ...
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1answer
44 views

What is the distribution of $X$ since $X|Y \sim \mathrm{Bi}(Y, p)$ and $Y \sim \mathrm{NB}(r, q)$?

I have done the usual steps to calculate the marginal distribution of $X$, i.e. using the following formula: $$p(X) = \int p(X,Y) dY = \int p(X|Y) p(Y) dY$$ Therefore, it holds: \begin{align} P(X=k) ...
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2answers
97 views

What is the meaning of the conditional $y|b$

I think I'm confused about a very simple thing. When we say that some variable is distributed as a Poisson distribution and we write $y \sim \text{Pois}(\lambda)$, is this the same that saying ...
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2answers
44 views

Probability of getting 3 3s throwing 3 dice 3 times and saving the 3s

You can throw 3 dice 3 times. Every time a 3 comes, you save it and don't throw it any more. What are the odds you will end up with 3 3 3?
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1answer
76 views

Obtaining conditional distribution from mixed model

Suppose you have the following mixed model: $$y_{it} =X_{it} \beta + Z_{it}b_{i} + u_{it} \tag{1}$$ where $y_{it}$ is the response for a subject $i$ and time $t$, $X_{it}$ is a vector of features, ...
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18 views

Conditional correlation in Farlie–Gumbel–Morgenstern distribution

I am constructing a bi-variate Farlie–Gumbel–Morgenstern distribution with normal and exponential marginals. I was able to find conditional mean and conditional variance with the help of references. ...
2
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1answer
79 views

Problem expressing full conditionals

I have this problem, $Y_{i}$~Gamma($\alpha$,$\beta$) 1...N $\alpha$~Exp($\lambda$) $\beta$~Exp($\lambda$) $\lambda$=0.001,Find the full conditionals. I have done the following: ...
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40 views

Relationship between P(A|X,Y), P(X|Y) and P(A|X)?

My statistics training is only basic, so forgive any embarrassing misunderstandings. Here's my situation: I have a graph (a big one) with 20,770 nodes. This is Y. I have a subgraph, X (subset of ...
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31 views

The effect of independent variables in linear regression

I have N numbers of dependent(X) and independent(Y) variables. X variables are log-normally distributed data so that I used linear regression on log-log scale to obtain expected values as E [lnX|Y=y] ...
4
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1answer
120 views

Conditional independence iff joint factorizes

I have proven that: $X⊥Y|Z\ {\rm iff}\ p(x,y|z)=p(x|z)p(y|z)$ for all $x,y,z$ such that $p(z)>0$. The next question is to prove an alternative definition: $X⊥Y|Z$ iff there exist functions $g$ ...
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3answers
67 views

Regression function of “non-regressible” data

I have some background in probability, and now trying to understand statistics, which sometimes leads to the questions of the following kind. Let $X$ and $Y$ be two random variables that represent the ...
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39 views

Sampling from conditional copula under R

this is a follow-up thread dealing with sampling from conditional copulas: Original question (with nice answer by whuber): Sampling from conditional copula Trying to sample from a conditional copula ...
4
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1answer
99 views

Sampling from conditional copula

I am having trouble finding anything on sampling from conditional copulas. I am only interested in the bivariate case. So, if $C(u,v)$ is my copula, I want to sample from it given a specific ...
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19 views

Conditional and joint pmf of sequences of random variables

I have random variables $X_1...X_N$ which are Poisson($\theta$) distributed. I also have inclusion indicators $Y_1...Y_N$ which are Bernoulli($\pi$) distributed. These indicate whether $X_i$ is ...
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18 views

game scoring marginal probability estimation

I have a game scoring time series data, where X[i] shows the score of player 1 minus player 2 after the ith turn. The game is played in turns, meaning if player 1 plays at ith turn, player 2 plays at ...
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52 views

Is reverse of p-value also uniformly distributed?

If p-value, $p(F|H_0)$, is uniformly distributed $U[0,1]$, so is true to say, that $p(F|H_1)$ is also uniformly distributed $U[0,1]$ or even more: is it true $p(F|H_0) = 1-p(F|H_1)$? I'm not sure if ...
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1answer
28 views

Basic summation of conditional probabilities question

I read on Bishop Chap8 P 374 that: sum(P(b|c)P(c|a)) = P(b|a) where the sum is over c. Can you prove that?
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18 views

Conditional Probability Or Condition

What is the general way to look at a conditional probability of the form : $P(A=true|B=true\;OR\; C=true)$
3
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54 views

joint distribution, probability, calculating probabilities under false independent assumption, when the random variables are actually dependent

Suppose I have random variables $X,Y,Z$ and I would like to compute the probability that random variable $X$ is smaller than $Y$ and $Z$: $$ \pi_X \overset{def}{=} Pr(X < Y, X < Z) = \int Pr(x ...
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23 views

Can you use accelerometer data for classification with Conditional Random Fields?

I want to recognize activities, based on accelerometer data from the smartphone. I studied Conditional Random Fields and the CRFSuite. Now I am Confused. In my opinion CRF training uses static single ...
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20 views

The probability density function using the Laplace transform

I am reading a paper that is trying to derive the following probability $$ \mathbb{P} \biggl( F \geq T(I+W) \biggl)$$ Assumptions: 1- Assume that the $F$ has a finite first moment and admits a ...