Questions tagged [bayes-rule]
The bayes-rule tag has no usage guidance.
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Formal Bayes rule for the bandit problem
We have two slot machines, $B_1$ and $B_2$. We've played the first machine $n_1$ times and gotten the rewards $R_1^1, \dots, R_1^{n_1}$ and played the second machine $n_2$ times and gotten the rewards ...
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how to calculate conditional probablity when one even'ts occurance is dependent on mutiple events
I have X, Y, and Z all as binary variables, values either 0 or 1. Y and Z are and got values of P(Y =
1), P(Z = 1), P(X = 1|Y = 1, Z = 1) , P(X = 1|Y = 1, Z = 0) and P(X = 1|Y = 0). here I need to ...
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How do I evaluate model performance using Bayes Theorem?
Assume that I have a model $f$ whose task is to do entity resolution. Given a name, say Samsung!!, it would (hopefully) return Samsung along with a confidence score in $[0, 1]$.
Now, assume that it ...
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Bayes' rule for mixed discrete and multiple continuous random variables
Consider the Bernoulli random variable $Z$ that takes $z=1$ with probability $1/2$ and $z=0$ otherwise. A different random variable, $X$, is defined on $x \in [0,1]$ has the following conditional ...
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Which Bayesian update is the right one to use in this case?
Suppose I have many widgets, and a widget can be good or bad. I can test widgets in batches. The batch is good if all widgets in the batch are good, and it is bad if any widget in the batch is bad. A ...
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Bayes rule when data $D$ is split into two independent parts: $D_a, D_b$
In this machine learning paper Overcoming catastrophic forgetting in neural
networks, they present to you equation 1, the log of bayes rule:
$$ \log p(\theta|D) = \log p(D|\theta) + \log p(\theta) - \...
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Interpreting a Table for Bayes Rule
The question and related table is given in the picture. I applied bayes rule as:
$\cfrac{P(X_1=-1,X_2=1|C_1)}{P(X_1=-1,X_2=1)} = \cfrac{P(X_1=-1|C_1)P(X_2=1|C1)P(C_1)}{P(X_1=-1|C_1)P(X_2=1|C1)P(C_1) + ...
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Marginal likelihood: Why is it difficult to compute in this case?
I have been reading up a bit on generative models particularly trying to understand the math behind VAE. While looking at a talk online, the speaker mentions the following definition of marginal ...
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Number of parameters to calculate in Naive Bayes with and without independence assumption
I am just getting started with trying to understand the theory behind Naive Bayes a bit.
$Y$ = boolean-valued rv
$X_i$ = boolean-valued rv (part of random vector $\vec{X}$).
From what I understand, we ...
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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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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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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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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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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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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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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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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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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 ...
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