# 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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### Bayesian approach to trend detection in non-parametric data

I have a series of data points, and I want to see how much evidence there is that the points are getting bigger over time. The data themselves are counts, but for various reasons I don't want to build ...
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### Queries on the Bayesian method

Currently I am working on a bayesian model framework and have questions related to the philosophy of using such techniques of modeling. How do I know that the prior which I have captured from the ...
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### CODA gleman.diag, Error in chol.default(W): [closed]

I'd like to use gelman.diag for an MCMC chain I ran in JAGS. It is very large, so I can't provide it. The chain contains several MVN distributions, and I use a wishart prior on the precision matrix. ...
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### Multilevel bayesian with AR1 correlation structure

How do I fit a bayesian multilevel model with with AR(1) correlation structure? I am trying to teach myself bayesian modelling and I am wondering how you could specify a multilevel model with an ...
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### Bayesian Predictive Function (Sum over all the parameters ?)

I have the following problem but I am not sure If the way of thinking is correct, so this is the purpose of the question! I have a Uniform prior over some data points. I know that I have observed the ...
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### Coin flipping, decision processes and value of information

Imagine the following setup: You have 2 coins, coin A which is guaranteed to be fair, and coin B which may or may not be fair. You are asked to do 100 coin flips, and your objective is to maximize the ...
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### How to model a network analysis problem

I have a weighted graph in which the nodes represent users and weighted undirected edges represent the tie between a pairs of users. For a piece of content $c$, and a node $A$ in the graph, given that ...
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### Group differences from a Bayesian Hierarchical Multinomial Model in Jags

I'm unsure about how to go about looking at group differences in frequency data using a Hierarchical Bayesian approach. Normally I would do a Chi-square Test of Independence between groups, but this ...
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### Coda output, joint quantile

I am running a hierarchical model in JAGS. It is a piecewise constant survival regression model. So I have 4 sets of regression coefficients and baseline hazard rates. I would like to plot a mean ...
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### How would we get the conditional distribution?

Having the marginal distributions, say $f(x)$ and $f(y)$, how would we get the conditional distribution $f(x|y)$? The relation is given by: $$f(x)=\int f(x|y)f(y)dy$$ Do we need to find the ...
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### Bayesian inference with Gaussian distributions

This is Problem 4(c), Chapter 2 from Thrun's Probabilistic Robotics . Note that this is self-study and not homework. Suppose I know my position $x$ to be a normal distribution with density ...
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### Using priors to detect an effect? logistic Bayesian regression

I have designed an idea and am looking for similar approaches in other literature/areas or if I have applied the Bayesian concepts wrongly. Here is a statement of my problem: I am modeling the ...
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### what should be the parametric form of the l2 regularization in a Bayesian setting?

In a Bayesian setting for parameter estimation, what should be the parametric form of the prior distribution in order to perform l2 regularization?
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### Plotting predictor effects with credible intervals for Bayesian regression

this is probably a pretty basic problem but got stuck with it. When doing GLMM in R I’ve been using the nice package “effects” from John Fox when I had to display fixed effects of continuous ...
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### On FDA guidance about Bayesian practice

US FDA authorizes the use of Bayesian statistics with informative priors (in certain contexts): ...
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### Probability model for repeated survey data

I'd like to find a suitable probability model but I'm not sure if the one I've thought of makes sense. The intention is to apply a Bayesian analysis to survey data which has been sampled twice. The ...
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### Normalizing constant irrelevant in Bayes theorem?

I've been reviewing Bayesian literature in an attempt to utilize Bayesian inference for hypothesis testing when I have very well established priors, but there's one thing I cannot get my head around: ...
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### Bayesian variable selection — does it really work?

I thought I might toy with some Bayesian variable selection, following a nice blog post and the linked papers therein. I wrote a program in rjags (where I am quite a rookie) and fetched price data ...
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### Statistical inference about degree of a node in a genetic network

I am working on Gene-Gene interaction networks. I build a graph by adding edges between genes (nodes) representing statistical interaction in prediction of a quantitative parameter value (say, brain ...
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### Bayesian Stats--Normal Distribution: known variance, unknown mean

I am given a situation where I have an unknown mean, mu, and a known variance. I have prior information about the mean that it follows a normal distribution and has a particular mean and variance that ...
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### Bayesian parameter estimation of a Poisson process with change/no-change observations at irregular intervals

Consider a Poisson process with unknown parameter $\lambda$. We perform a sequence of $n$ observations at intervals $\overline{t}=t_1,\,t_2,\,\dots,\,t_n$. Each observation is a binary variable $x_i$ ...
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### Bernoulli variable on pymc

Im not fully sure that this is the right place to ask, but I have a problem with pymc that I'm not able to grasp. I'm trying to simulate a simple counting under two different scenario: Under the ...
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### Can someone point me to a good example of using bayesian models for making marketing decisions?

I am tasked to build a bayesian model to support decision making for paid search marketing. I've researched online and found several scholarly articles on using Hierarchical Bayesian model or MCMC in ...
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### Multiplying a matrix by a scalar which has a prior distribution in OpenBUGS

So I am having a problem specifying my model in OpenBUGS. A set of vectors in a linear regression model is given a multivariate normal prior with a constant mean vector and a constant precision matrix ...
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### Is there any reason to prefer a bayesian model with few variables?

I have two alternative hierachical bayesian models that were designed to the describe the same process (from a high-level point-of-view). Both model provides comparable (but not identical) inferences ...
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### Calculating conditional probabilities given a bivariate gaussian

This is a continuation of my previous question. I have two classes, $C_1$ and $C_2$. $C_1$ is a bivariate Gaussian with mean $\mu = (0,0)$ and covariance $\Sigma = I$ $C_2$ is a bivariate ...
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### Bayesian estimation of Dirichlet distribution parameters

I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that: Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What ...
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### How to derive the conditional posterior density in hierarchical bayesian models?

I was reading on Gelman's Bayesian Data Analysis - Chapter 5 - Hierarchical model Suppose: data : $y_j$ s parameter: $\theta$ hyperparameter: $\phi$ On page 126, he mentions the analytical ...
Suppose we are given data $y_j \sim \text{Poi}(\lambda)$ and assume $y_j$ are iid. We can assume the prior distribution for $\theta$ follows $\text{Gamma}(\alpha, \beta)$, The posterior ...