# Tag Info

Accepted

### Finding the optimal stopping time to place a bet in an urn problem

Betting on the last ball is an optimal strategy, regardless of what the prior is. Here's how I know: Imagine that after seeing 8 balls, you decide to bet that the 9th ball is red. This is equivalent ...

### Finding the optimal stopping time to place a bet in an urn problem

Below is a recipe to compute the expectation value for winning the prize 1] As a function of the number of drawn red and blue balls (let's call them $x_r$ and $x_b$) we can compute a posterior ...
Accepted

### How to use Truncated Normal for observation distribution in GLM model?

General remarks The truncated normal model (just like the censored normal model) does not belong to the GLM (generalized linear model) family in the classical sense (a la McCullagh & Nelder, 1989, ...
1 vote

### Understanding a parameter in a bayesian Poisson model ($\beta$)

This is a hyperparameter arising in a mixture representation of the prior For hierarchical Bayesian models of this kind, the parameter $\beta$ is what we usually call a hyperparameter. A ...

1 vote
Accepted

### Intuition for chain rule in Bayesian approach for prediction?

Do you have a link to somewhere that claims this is Bayes rule? As far as I can see line (1) Is marginalization, and line (2) is chain rule. These are all very general probabilistic statements that ...

### Bayesian mixture model with Random Effects in Linear Predictor

Here is a potential viewpoint of the sort of model that you can have: $$y_i|z_i,x_i \sim \mathcal{N}(\mu_{z_i,x_i},\sigma_\epsilon)$$ where $x_i$ is an index for the individual. With priors \begin{...

### Fitting a nonlinear model for a CDF

If you have a model with behavior like an increasing function then often you do not get random behavior in the form of some additive noise term $\epsilon_i(t)$, and instead it is more like the errors ...
1 vote
Accepted

### question on the computation of the predictive uncertainty in bayesian neural networks

I did not know how bayesian neural networks perform this operation prior to this answer, however I think the equation you mention is not specific to Bayesian neural networks but is indeed a generic ...
1 vote
Accepted

### Parameter distribution of $\theta$ from a rectangular matrix multiplication $C\theta$

In a Bayesian linear regression we can indeed encode the wanted form of relation by considering a prior covariance which is "infinite". This is sometimes called a diffuse prior or a ...
1 vote

### How to properly put lower/upper limits on a Bayesian posterior

The uniform distribution is often applied to situations where $w \in [l,u]$ represents a segment on the real line, with no preferred value for $w$ within this segment. However, on the one hand, this ...
1 vote

### Why are Bayesian mixed-effects models (e.g., brms) more able to estimate complex models than Frequentist mixed models (e.g., lme4)?

Random effects are used to capture correlations in the data, namely, within the same level of the corresponding grouping factors. The parameters that quantify the strength of these correlations are ...

### Why are Bayesian mixed-effects models (e.g., brms) more able to estimate complex models than Frequentist mixed models (e.g., lme4)?

When you “estimate” a Bayesian model most often what you do is you sample from the posterior distribution. Posterior is, by Bayes theorem, basically a product of the priors and the likelihood. If you ...

### Estimating sigma in Bayesian inference

A completely flat inverse-Gamma, i.e. letting the shape and scale tend to zero, will often lead to the same problems in practice. Gelman's 2006 paper on prior distributions for variance parameters is ...

### Proving that a function is always increasing

It doesn't make sense to me that you say that they are independent, but then say that the conditional probability is increasing. If they are independent, then the conditional probability must be ...
By the law of iterative expectations and conditional independence, for any $n \in \mathbb{N}$ and $u_i \in \{0, 1\}$, $i = 1, \ldots, n$, we have \begin{align} & P(X_1 = u_1, \ldots X_n = u_n) = ...