# 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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### Semi-conjugate inverse Wishart posterior, can we obtain the marginal?

In Hoff's text (A First Course in Bayesian Statistical Methods), he uses a semi-conjugate inverse-Wishart prior for the covariance matrix of a multivariate normal process. In equation 7.9, he has the ...
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### Calculating Bayes Factor from a correlation coefficient

I'm wondering whether anyone knows whether it is possible to directly calculate a Bayes Factor (comparing null model of zero correlation to non-zero correlation) given just a correlation coefficient ...
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### Neural Networks - Strategies for problems with high Bayes error rate

I am building a Neural Network for a binary classification problem where the Bayes error (lowest possible error rate) is probably close to 50%. What makes the task easier is that I don't need to make ...
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### Closed form for Finite Gaussian Mixture Model when weights are known and prior variance can be 0

Suppose I have a normal likelihood $x|\theta \sim N(\theta, \sigma^2_{known})$ where the variance is known and a mixture prior $\theta \sim p * N(\mu_1, \sigma^2_1) + (1-p) * N(\mu_2, \sigma^2_2)$, ...
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### How would I use Evan Miller's sort criterion to modify the ranks of Bayesian average ratings?

Evan Miller wrote these guidelines for constructing a Bayesian average ratings and then sorting them using a multi-linear loss function: http://www.evanmiller.org/bayesian-average-ratings.html I ...
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### Parameter estimation by averaging over all high-likelihood possibilities?

I am refereeing a chemistry paper. The authors are trying to interpret some experimental data by comparison with numerical simulations. They have run many simulations using different combinations of ...
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### Why do non-informative a priori distributions be chosen to compare the Bayesian and frequentist estimation method?

For example for GARCH models $$\sigma_t^2=\alpha_0 +\alpha_1 y_{t-1}^2 + \beta_1 \sigma^2_{t-1}$$ it is usual to use as distributions for the parameters of truncated normal distributions with very ...
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### Unbiasedness of Bayesian Posterior Mean Under Bayesian and Frequentist Models [duplicate]

This is an extension to this previous question, and is related to exercise 4.7 from Gelman et al.'s BDA3. When is the Bayesian posterior mean $m(y) \equiv E[\theta \mid y]$ unbiased for $\theta$, ...
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### Treating missing data in making Bayesian inference

Suppose we have two biased coins $X_1,X_2$ that are possibly correlated to each other. In each round, when both the coins are tossed, there can be four possible outcomes: $(HH,HT,TH,TT).$ Let's ...
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### Can I use a bayesian spatio-temporal model in cluster areas I chose from local Moran's I?

I have crime rates for municipalities in a state with hourly frequency. I want to make predictions about the spatio-temporal behavior of that variable. Is it possible to run a local Moran's I to ...
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### How to create a distribution and sample?

Suppose we are given some small set of data on bundles of electrical wires and increasing voltages run through them, and we note how many of the individual wires fail. So for example, a large data ...