Questions tagged [bayes-rule]

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Explanation of Equation 5.3 from Gaussian Processes for Machine Learning

I am currently reading through C. E. Rasmussen & C. K. I. Williams' Gaussian Processes for Machine Learning and was going through chapter 5. I could not exactly understand the derivation of ...
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1answer
33 views

Question about some basics

I have been wondering about an issue connected with prevalence. And came up to some conclusions which I would like to verify. It's not complicated. Let's assume we have two prevalences: (A) percentage ...
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1answer
44 views

Posterior distribution from piecewise likelihood

Consider a hierarchical Bayesian model for analysing data from an inhomogeneous Poisson process that we observe in discrete time. Let $Y_i, i = 1,...,n$, be the number of events occurring in the time ...
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1answer
50 views

Computing posterior based on sum of multivariate normal distribution

Currently I am exploring topics for my undergrad thesis. Although I took a course in Bayesian statistics, I am not yet sure how to proceed in finding the posterior in the following case. I have a d-...
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1answer
25 views

Conditional Independence

I have a joint probability, which factors as follows: $P(A,B,C,D) = P(A,B) \cdot P(C|A) \cdot P(D|B)$ So I know that $C$ and $D$ are independent given $P(A, B)$ right? I want to infer $P(A,B|C,D)$....
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19 views

Is there an error in those tables?

I recently came across this popular answer on Stack Overflow (1st result for profiling code linux on Google). I have some knowledge of Bayesian Statistics and I ...
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1answer
38 views

Conditional probabilities involving random variables and functions of these variables

I have that $Z = X + 2Y$. $X, Y$ are independent. I know $f_X(x), f_Y(y), f_{X,Y}(x,y)$ and $f_Z(z). $ How can I find $f(x,y|z)$? I know that $f(x,y|z) = f(x, y, z)/f(z) = f(z| x, y)*f(x, y)/f(z)$ ...
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0answers
41 views

Conditional Probability Question $(X \cup Y)$

I cannot seem to solve this conditional probability question. Suppose $X$ and $Y$ are two events from a sample space with $\Pr(X) = 0.25$, $\Pr(Y) = 0.5$ and $\Pr(X|X \cup Y) = 0.5.$ Find $\Pr(X \...
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1answer
33 views

Bayesian Updating from Two Perspectives

Suppose there is a game of luck with chance of winning $p_w = .01$. You can attempt to cheat with success probability $p_c = .005$. If you successfully cheat, your win probability is $p_{w|c} = .3$. ...
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1answer
1k views

Why ignore the denominator of bayes rule? [duplicate]

I am a new beginner in stats. I have specifically diverted my attention towards this because, I wish to understand the concept of Deep Bayesian Learning, so I am starting with the basics. The question ...