Questions tagged [bayesian]

Question 1

SO the problem definition is: Have X clients talking to a single API and that API has some upper bound, N, on the number of requests it will handle before it shapes i.e. the traffic and takes ten ...

Question 2

I’ve been reading about objective Bayesian theories lately and came upon the concept of universal priors and specifically, the Solomonoff prior. This seemed to answer my initial query about whether a ...

Question 3

A prior distribution is given by distribution $f_\theta(\theta)$, with variance $\sigma^2$. A posterior distribution is $g_\theta(\theta)=h(x,\theta)\cdot f_\theta(\theta)$, where $x$ is our sample. ...

Question 4

Let $X$ be a $d$-dimensional random vector drawn from a Gaussian mixture $$ X \sim \sum_{k=1}^K \pi_k \, \mathcal{N}_d(\mu_k, \Sigma_k), $$ and let $$ Y = X + N, \quad N \sim \mathcal{N}_d(0, \Sigma_N)...

Question 5

In the DAG-GNN paper (Yu et al., NeurIPS 2019, paper link), the authors describe the linear Structural Equation Model (SEM) as follows: $$ X = A^TX + Z, $$ where A ${\in R^{m \times m}}$ is the ...

Question 6

Broadly: Given a parameter space $\Psi$ (say a Polish space) and a random variable $X$ whose distribution depends on $\psi \in \Psi$, how do we rigorously define sampling $X$, given the uncertainty in ...

Question 7

I have a time-series of events that go through a black box over a period of time. I need to determine if there is seasonality within the black box using these events, that are either True or False. ...

Question 8

I am currently studying bayesian theory and I was trying to tackle the following problem: Let $X_1, \ldots, X_n \mid \theta, \sigma^2$ be i.i.d. $N(\theta, \sigma^2)$, where both $\theta$ (real) and $\...

Question 9

Setup: Let $n\in\{2,3,...\}$. For each $t\in\{1,2,...\}$, suppose $X_t$ is distributed i.i.d., taking value $v\in \{1,...,n\}$ with probability $p_v\in(0,1)$. Let $S_{vt}:=\sum_{\tau=1}^t 𝟙\{X_t=v\}$...

Question 10

Say a test of 11 questions, and a person's score is from 0-11, and is categorized into level 1 (score 0-3), level 2 (score 4-7), and level 3 (score 8-11). The priors of the three levels are $p_1, p_2, ...

Question 11

I'm interested in carefully quantifying the number of local minima and stationary points of a Gaussian random field. While working through it, I came across a puzzling conclusion that doesn't seem ...

Question 12

How does one apply Bayes theorem on non-binary (i.e. not true/false or 1/0) Events? If we use the example given in the Veritasium video on Bayes, but instead of each disease-test result (i.e. the ...

Question 13

This is something I have been trying to understand. Consider the following local level linear state space model: Observation equation: $y_t = \mu_t + \epsilon_t$ where $\epsilon_t \sim N(0, \sigma_\...

Question 14

I am using an implementation of Metropolis-Hastings algorithm to figure out the distribution of neuron clusterings, given the precalculated probability of synchronizations between different neurons. ...

Question 15

Setup. Let $p\in[0,1]$ be a continuous random variable with density $f(\cdot)$. Assume that $f$ is bounded, continuously differentiable, and has full support $[0,1]$. Let $a_1$ and $a_2$ be distinct, ...

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Questions tagged [bayesian]

Optimal strategy for clients calling a rate limited API?

Can probability theory be made fully computable?

Is the variance of a posterior distribution always less than the variance of the prior?

Reference for the expected MSE of the optimal estimator in a Gaussian mixture channel

What is the meaning of $(I - A^T)^{-1}$ in the linear SEM formulation of the DAG-GNN paper?

Mathematically rigorous Bayesian sampling

Any methods to find if a binary time series has seasonality OR NOT?

Computing $BF_{01}$ using a Normal and a double exponential

Showing $\frac{\mathbb{P}\{\text{data}_t|\text{wrong pmf }\} }{\mathbb{P}\{\text{data}_t|\text{correct pmf }\}}\overset{\text{a.s}}{\to}0$.

Bayesian updating question

Hessians of Gaussian Random Fields at Minima and Stationary Points

Bayes theorem for non-binary events

Why is the Kalman filter so popular?

Metropolis-Hastings MCMC with a Chinese Restaurant Process proposal

Asymptotic conditional likelihood ratio with continuous random variables

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