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).

learn more… | top users | synonyms

0
votes
0answers
5 views

marginal posterior distribution in linear regression

Let's assume our posterior distribution looks like the bayesian linear regression posterior, \begin{equation} p(\mathbf{w}|D) = \mathcal{N}(\mu, \sigma) \end{equation} where \begin{aligned} \mu ...
0
votes
0answers
21 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 ...
1
vote
0answers
18 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 $0<a2<a1<1$. ...
0
votes
1answer
17 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 ...
1
vote
0answers
50 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? ...
5
votes
1answer
105 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 ...
0
votes
0answers
11 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: ...
0
votes
0answers
10 views

Probability of reordering based on sample distributions

I am evaluating a computer system for which I obtained certain sample data, and I am trying to get some meaningful information from it, but I have only a basic knowledge of the statistics and ...
5
votes
1answer
97 views
+50

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 ...
0
votes
3answers
42 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
votes
1answer
60 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 ...
0
votes
0answers
8 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 = ...
2
votes
1answer
42 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) ...
3
votes
2answers
95 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 ...
1
vote
2answers
40 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?
2
votes
1answer
74 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, ...
0
votes
0answers
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. ...
1
vote
1answer
66 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: ...
1
vote
0answers
39 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 ...
0
votes
0answers
29 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
votes
1answer
110 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 $g$ ...
2
votes
3answers
64 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 ...
0
votes
0answers
24 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
votes
1answer
74 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 ...
0
votes
0answers
17 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 ...
0
votes
0answers
15 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 ...
0
votes
0answers
47 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 ...
-1
votes
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?
0
votes
0answers
17 views

Conditional Probability Or Condition

What is the general way to look at a conditional probability of the form : $P(A=true|B=true\;OR\; C=true)$
2
votes
0answers
48 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 ...
0
votes
0answers
16 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 ...
0
votes
0answers
19 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 ...
0
votes
0answers
24 views

Interesting question about full rank of random matrix

I have a question about rank of a random binary matrix. Assume that I have to make a random binary matrix with its size are k rows and n colmuns (k<=n). Each columns only has 1 or 0 values. Now I ...
0
votes
0answers
11 views

Conditional probabilty - case study

I am investigating the time on book (t) before write off.The sample data consists of times taken until write off, however these times have been calculated from accounts that have been written off ...
1
vote
1answer
35 views

Help setting up a Bayes rule problem

I am relatively new to using Bayes rules for continuous variables and am having trouble setting up part of the formula and am looking for help. The example I am trying to work through is the ...
2
votes
2answers
62 views

What is the mean of this exponential random variable?

I have read a paper that says that the following is exponentially distributed $$ Y= \bigl| \sum_{i=1}^n \gamma_i^{-\frac{1}{2}} h_i \bigl|^2$$ where $\gamma_i$ are non-negative constants and ...
0
votes
0answers
18 views

Probability generating function of poisson point process

Assume you have a 1D non homogenous PPP $\Xi$ with intensity $$\lambda(x)=\lambda x^{\frac{2}{\alpha}-1} \ x \in \mathbb{R}^+$$ where $\alpha$ is positive integer. Now define $$\gamma_k = ||x_k||$$ ...
0
votes
0answers
7 views

a joint probability distribution that passes through all markov network graph without being filtered

from filter view of the Markov Network where only those distributions can pass that satisfy all conditional independence statements given by the graph. • Can we think of distribution that can pass ...
1
vote
1answer
47 views

How to draw a Markov network graph for two or pair of variables

For $i \in \{1, 2, 3\}$, let $X_i$ be a random variable for the event that a coin toss comes up heads (which occurs with probability $q$). Supposing that the $X_i$ are independent, define $X_4 = X_1 ⊕ ...
0
votes
0answers
5 views

Multiplying distributions with different conditioning

I saw this expression in a UBC machine learning class lecture, and I'd like to understand how the math works. Suppose we're trying to predict a class label $y$ given some data $x$. There are prior ...
2
votes
1answer
55 views

Sum of RV : probability for the value of operands when the result is known

A random variable $Z$ is the sum of two independent random variables $X$ and $Y$, with known probability densities $f_X$ and $f_Y$, respectively. Now suppose you sample $Z_1=X_1+Y_1$ but you don't ...
2
votes
3answers
529 views

conditional probability trick questions - drawing cards from a deck and the meaning of 'at least'

Suppose that a box contains one blue card and four red cards, which are labeled A, B, C, and D. Suppose also that two of these five cards are selected at random, without replacement. a. If ...
0
votes
0answers
22 views

How to calculate distribution of Y|X from distributions of X|Y and Y [duplicate]

I'm trying to solve the following homework problem: Let $X$ given $Y=y$ have a normal distribution with mean $y$ and variance one, and let the marginal distribution of $Y$ be normal with mean ...
1
vote
1answer
28 views

PDF of sum of independent Gaussian variables

I am looking for deriving the pdf of $Z$ where $Z= (\sum\limits_{i=1}^N a_i X_i +Y_1)^2 + (\sum\limits_{i=1}^N b_i X_i +Y_2)^2$, where $X_i$ and $Y_i$ are independent, zero mean Gaussian random ...
0
votes
0answers
23 views

Regarding Naive Bayes and conditional independence

We all have been talking about how Naive Bayes may, in some cases, not perform well due to the fact that this assumes conditional independence of features and MOSTLY, this is not true for real world ...
0
votes
1answer
47 views

Covariance of a compound distribution

I am trying to find the covariance of a compound distribution. Given $X=x$, where $X \sim \mathrm{Uniform}(0,1)$, $Y$ is (conditionally) normally distributed with mean $x$ and variance $x^2$. I ...
0
votes
1answer
38 views

Bayesian Network

I am preparing for midterm exam and need to know what is the step by step solution to this question? Answer is shown in red. Also any external related link is very much appreciated.
1
vote
1answer
43 views

Probability distribution of Y in regression?

I'm trying to predict the probability distribution of $Y$ given $X_0, X_1, ...$ with a nonlinear regression. The probability distribution of $Y$ is likely not normal. So far, I've set up and trained ...
2
votes
1answer
67 views

Convolution of random vectors

Suppose, I have two random vectors $A=[A_1, A_2, \dots A_k]$ and $B=[B_1, B_2, \dots B_m]$. What could be the joint PDF $f_{\mathbf{y}}(y_1,y_2,\dots y_N)$ where $\mathbf{y}=A \ast B$, here $\ast$ ...
0
votes
2answers
75 views

basic probability problem

Problem 2 (page 33 of text) Assume that every patient with a particular type of disease has the probability 0.1 of being cured within a week, if the patient is given no treatment for the disease. Ten ...