# Questions tagged [bayesian-probability]

Questions in this tag should be about the Bayesian approach of probability theory and its relevance to AI-related issues.

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### Methods for sequential decision optimization problem with nonlinear bayesian reward function

I am attempting to grasp if there are any other methods out there that i am not aware of that can be beneficial given my problem context. Being inspired from optimal experimental design communities ...
• 35
79 views

### Given A and B, C are independent of each other. Given A, B and C, D and E are independent of each other. What is the minimal number of parameters?

Assuming all variables $A, B, C, D,$ and $E$ are random binary variables. I come up with Bayes net: $D \rightarrow B \rightarrow A \leftarrow C \leftarrow E$ which has the minimal number of parameters ...
• 1
50 views

### What makes Sequential Bayesian Filtering and Smoothing tractable?

I'm currently diving into the Bayesian world and I find it pretty fascinating. I've so far understood that applying the Bayes' Rule, i.e. \text{posterior} = \frac{\text{likelihood}\times \text{prior}...
1 vote
99 views

### Why is the E step in expectation maximisation algorithm called so?

The E step on the EM algorithm asks us to set the value of the variational lower bound to be equal to the posterior probability of the latent variable, given the data points and parameters. Clearly we ...
1 vote
100 views

### Understanding how to calculate $P(x|c_k)$ for the Bernoulli naïve Bayes classifier

I'm looking at the Bernoulli naïve Bayes classifier on Wikipedia and I understand Bayes theorem along with Gaussian naïve Bayes. However, when looking at how $P(x|c_k)$ is calculated, I don't ...
• 65
288 views

### How can I draw a Bayesian network for this problem with birds?

I am working on the following problem to gain an understanding of Bayesian networks and I need help drawing it: Birds frequently appear in the tree outside of your window in the morning and ...
• 41
1 vote
260 views

### How does maximum approximation of the posterior choose a distribution?

I was learning about the maximum a posteriori probability (MAP) estimation for machine learning and I found a nice short video that essentially explained it as finding a distribution and tweaking the ...
• 737
581 views

### What is the relationship between fuzzy logic and objective bayesian probability?

I understand fuzzy logic is a variant of formal logic where, instead of just 0 or 1, a given sentence may have a truth value in the [0..1] interval. Also, I understand that logical probability (...
• 755
2k views

### How does the Dempster-Shafer theory differ from Bayesian reasoning?

How does the Dempster-Shafer theory differ from Bayesian reasoning? How do these two methods handle uncertainty and compute posterior distributions?