# Tagged Questions

Bayesian inference is a method of statistical inference which uses Bayes' theorem to find probability estimates of parameters or hypotheses.

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### State-dependent independence in graphical models

I have a graphical model with binary variables Y, X1, X2, and observed data D. D depends on Y X1 and X2 depend on Y When Y is false, X1 and X2 are independent: ...
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### how to solve this probability question

I have a question regarding how to solve this problem: There are two predictors A and B. If A is positive, there is 60% chance of raining. If B is positive, there is 60% chance of raining. A and B is ...
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### How do we pass from proportionality back to equality in a Bayesian derivation?

Here's an answer from one of the questions in the newsletter. I'm not trying to suggest that it's incorrect, I just don't understand why it's an acceptable practice. I know that simplifying ...
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### Weighted generalized regression in BUGS, JAGS

In R we can "prior weight" a glm regression via the weights parameter. For example: ...
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### Bayesian Belief Network - directions of arcs between nodes

I generated a BBN below based on environmental variables and a response of some organism. My aim here is to see how environmental variables (A-H in a graph above) interact with each other and ...
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### A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems)

As I know OVB, from a frequentist education, when you leave a variable $(z)$ out of your control set $(X)$ that is correlated with both your independent variable of interest (treatment $T$) and your ...
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### Credible interval for Bayesian posterior of variance and mean, and posterior predictive of normal

I am trying to do a "round trip" to verify that my code works with regards to recovering parameters of normal distributions. I'm using this document regarding the normal-gamma distribution: ...
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### Procedure to sample from an integrated marginal

I would like to sample from: $$p(\theta_2|x)=\int p(\theta_2|\theta_1,x) . p(\theta_1|x) . d\theta_1$$ Several persons suggest me to use the following procedure to draw $(\theta_2^i)_{i=1:N}$: ...
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### Question about foundations of the uniform shrinkage prior

I am collecting papers about the uniform shrinkage prior for hierarchical Bayesian model. In "A prior for the variance in hierarchical models" of Michael J. Daniels it is stated at the end of page two ...
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### WinBUGS: Multiple definitions of a node

So this question is about the BUGS modeling language. So you either know it or have no clue. I'm a newbie to this so it's been driving me mad. I want to define a simple two-state hidden Markov model ...
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### A question on Bayesian Search

I chanced on this article on wikipedia on Bayesian search. In the mathematics section, it states how the posteriors are estimated. While I understand how $p^{'}$ is calculated, I can't seem to figure ...
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### Flat, conjugate, and hyper- priors. What are they?

I am currently reading about Bayesian Methods in Computation Molecular Evolution by Yang. In section 5.2 it talks about priors, and specifically Non-informative/flat/vague/diffuse, conjugate, and ...
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### Can I have a bimodal likelihood function to represent a mix of two populations?

I came across the following toy example and am lacking a final answer/step to finish the analysis. Imagine a surgery or medical procedure where we don't know the success-probability. It can be ...
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### Empirical Bayes/MCMC references

I'm interested in references for running empirical Bayes (EB) in conjunction with MCMC. The closest thing I've found to what I'm looking at is a surprisingly recent and somewhat obscure paper ...
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### Probability of getting a specific Tetris piece given previous pieces

I'm doing a small reinforcement learning project involving Tetris, just for fun. Considering that each piece has a constant probability of being selected, how can I calculate the probability of ...
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### How to model probability of a web click using bayesian modelling with constraints?

I'm trying to model clicks in a Google AdWords campaigns. This is a function of impressions, the probability of a click (CTR) on that impression, the cost per click (CPC), and the budget of the ...
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### Is power analysis necessary in Bayesian Statistics?

I've been researching the Bayesian take on classical statistics lately. After reading about the Bayes factor I've been left wondering if power analysis is a necessity in this view of statistics. My ...
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### Bayesian regularized NNs over classical NNs

I have seen a few research articles which claim that the classical neural networks usually lacks satisfactory generalization ability, which usually results in an imprecise predictions, and Bayesian ...
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### Understanding how to get data from a dirichlet-multinomial distribution

I'm relatively new to Bayesian statistics and try to learn the fundamentals, maybe you can help. I have a three-sided die which produced in 100 trials: 45 times 1 10 times 2 35 times 3 I choose a ...
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### Weighting data sources in a bayesian model (BUGS)

I use a state space model to fit observations to a population dynamic model (using the BUGS language). In the "state" part, the dynamic model create a new "state" of the population (i.e. size and ...
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### Example of maximum a posteriori estimation

I have been reading about maximum likelihood estimation and maximum a posteriori estimation and so far I have met concrete examples only with maximum likelihood estimation. I have found some abstract ...
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### Bayesian Regularized Regression or LASSO with non-homogeneous Variance

I am working on Bayesian Penalized Regression especially BLASSO... I am stuck at a point which is a special case for my problem where I am applying the BLASSO... The linear model which is considered ...