# Questions tagged [bayes-rule]

The tag has no usage guidance.

18 questions
Filter by
Sorted by
Tagged with
60 views

### 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 ...
• 195
24 views

### 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 ...
12 views

### 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 ...
1 vote
45 views

### 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 ...
• 11
45 views

### 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 ...
• 155
31 views

### 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) - \...
• 328
95 views

The question and related table is given in the picture. I applied bayes rule as: $\cfrac{P(X_1=-1,X_2=1|C_1)}{P(X_1=-1,X_2=1)} = \cfrac{P(X_1=-1|C_1)P(X_2=1|C1)P(C_1)}{P(X_1=-1|C_1)P(X_2=1|C1)P(C_1) + ... • 13 1 vote 1 answer 160 views ### Marginal likelihood: Why is it difficult to compute in this case? I have been reading up a bit on generative models particularly trying to understand the math behind VAE. While looking at a talk online, the speaker mentions the following definition of marginal ... • 4,590 0 votes 0 answers 3k views ### Number of parameters to calculate in Naive Bayes with and without independence assumption I am just getting started with trying to understand the theory behind Naive Bayes a bit.$Y$= boolean-valued rv$X_i$= boolean-valued rv (part of random vector$\vec{X}$). From what I understand, we ... • 173 2 votes 1 answer 84 views ### Explanation of Equation 5.3 from Gaussian Processes for Machine Learning I am currently reading through C. E. Rasmussen & C. K. I. Williams' Gaussian Processes for Machine Learning and was going through chapter 5. I could not exactly understand the derivation of ... 0 votes 1 answer 40 views ### Question about some basics I have been wondering about an issue connected with prevalence. And came up to some conclusions which I would like to verify. It's not complicated. Let's assume we have two prevalences: (A) percentage ... • 1 1 vote 1 answer 332 views ### Posterior distribution from piecewise likelihood Consider a hierarchical Bayesian model for analysing data from an inhomogeneous Poisson process that we observe in discrete time. Let$Y_i, i = 1,...,n$, be the number of events occurring in the time ... • 11 0 votes 1 answer 1k views ### Computing posterior based on sum of multivariate normal distribution Currently I am exploring topics for my undergrad thesis. Although I took a course in Bayesian statistics, I am not yet sure how to proceed in finding the posterior in the following case. I have a d-... • 108 0 votes 1 answer 33 views ### Conditional Independence I have a joint probability, which factors as follows:$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)$.... • 317 0 votes 1 answer 61 views ### Conditional probabilities involving random variables and functions of these variables I have that$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)$... 1 vote 0 answers 48 views ### Conditional Probability Question$(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 \...
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 $p_{w|c} = .3$. ...