# Questions tagged [bayesian]

Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

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### Why do the non-informative a priori distributions give better results than the frequentist estimate?

For example, in the specific case of Markov-Switching GARCH models why is a non-informative prior distribution chosen for GARCH models with Bayesian estimation and why is this approach better than the ...
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### Metropolis Hastings proposal for one parameter restricted to less than the other

Suppose I have parameters $\theta_0$ and $\theta_1$ with prior $$p(\theta_0,\theta_1)=p(\theta_0|\theta_0<\theta_1)p(\theta_1),$$ that is, $\theta_0$ is less than $\theta_1$. The distributions ...
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My interests in statistics centre around statistical learning, including Bayesian inference, inference in combinatorial spaces, Monte Carlo methods, Markov decision processes, modeling stochastic ...
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### Combining multiple predictions with Bayes Theorem

I have multiple weather forecasters who each use their own unique, independent calculation for prediction of the weather for the next day. We are only concerned with rain predictions to know if we may ...
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### Probability of a box containing a combination of color

Let's say, we have a box containing 3 balls in it, they can be either red or blue. Someone draw a ball 5 times with replacement and get 4 red and 1 blue (not necessarily in order). Do you know how to ...
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### Two sample test for equality of 2 dimensional distributions

I have a large sample from a 2 dimensional continuous unknown distribution. From that sample I could compute any data structure I need to hold an approximation of the sample distribution. This will be ...
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### how to use depended / non-random observations when trying to inference exponential parameter

consider this case: There is a price rate for a certain product that changes throw time, The price rate is changed every x minutes (unknown, not constant). This price has depended / non-random ...
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### fit a model to data

I want to fit a model to a data set, however each point is actually a distribution (i.e. I have the samples for each distribution). In an ideal world, I would assume that the distributions are ...
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### Variance of evidence lower bound(ELBO) loss function

When using Bayesian optimisation in a neural network our loss function is equal to: Here the first term is the KL divergence between the approximate and true posteriors. The second term is the ...
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### Intercept in a Bayesian model with categorical predictors (with brms)

I have a Bayesian logistic model fitted in R with brms. The predicted variable is binomial, the predictors are categorical. The model uses bernoulli family and a ...
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### Interpreting mixture of Gaussians (Variational Inference)

I've recently stated reading about mixture models and variational inference in this excellent paper, but I'm having troubles dissecting the models described, and have a couple of questions. Please see ...
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### Adjustment for multiple comparison in bayesian multivariate regression model (using brms)

I am investigating age and timepoint effects on different (correlated) EEG parameters in a repeated measurements structure. I chose to use the brms R package to fit a bayesian multivariate model with ...
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### Exact posterior and marginal likelihood

I am working on an approximate method of Bayesian inference and I want to study its approximation properties by comparing my approximate posterior and marginal likelihood with its exact counterpart. I ...
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### Deriving conditional probability of bivariate bernoulli by using Dirichlet

While I was working on my research project, I found it difficult to derive a conditional probability from Dirichlet dist. Consider two Bernoulli trials that are possibly correlated with each other. ...
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### Multivariate bayesian inference: learnig about the mean of a variable by observing another variable

I want to derive a Bayesian learning procedure where I don't only learn from my own signal, but also from other signals which are correlated to mine. I thought it could simply work with Bayesian ...
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### Bayesian Hypothesis Tests with continuous priors

I am new to the Bayesian world, and I'm trying to understand how hypotheses tests are performed here (as opposed to the frequentist framework). I am aware that likelihoods, priors and posteriors can ...
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### Bayesian Inference: Feeding Posterior back in as Prior

I've just started reading about Bayesian Inference, and one thing I've wondered about is if it's possible to feed the posterior in as a new prior for a new model, using the same data. Or would that ...
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### If $f(x|\theta)$ is conjugate to $p(\theta)$ then is $f(x|r\theta)$ conjugate to $p(\theta)$?

If exponential family $f(x|\theta)$ is conjugate to $p(\theta)$ then is $f(x|r\theta)$ for $r>0$ conjugate to $p(\theta)$? If not, what can we do about it in terms of sampling to make use of ...
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### Bayesian estimation of mixed effects models covariance matrix

For a mixed model of the form: $$Y = X\beta + Z u + \epsilon$$ I know it is usually assumed in the parametric approach that: $u \sim N(0, D)$ and $\epsilon \sim N(0, \sigma^2I)$ Where $D$ is a ...
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### Incorporating Prior Information Into Time Series Prediction

Suppose I have data on my child C's height measured every week. Presumably there is a positive trend, due to growth, and some noise due to measurement errors, and maybe even seasonality (winter boots ...