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Results tagged with bayesian
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user 43625
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.
2
votes
Accepted
Bayesian analysis of Plausible Values in large-scale education surveys
It is fairly straight-forward to use this information in a Bayesian model. … Then formulate a Bayesian model for the data generating process
Below is the code from the file model.stan that I use further down. …
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10
votes
Why is the posterior distribution the same as likelihood function when uniform prior distrib...
The posterior is prior$\,\times\,$likelihood$\,\times\,$constant; the uniform density is simply a constant and gets absorbed in the other constant term.
Take as an explicit example the prior $\mathrm{ …
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2
votes
Accepted
Model that shrinks a set of coefficients towards their common mean
A Bayesian hierarchical model would be something like
$$
\beta_i \sim \mathrm{Normal}(\beta, \sigma_\beta),\\
\beta \sim \mathrm{Normal}(0, 1),\\
\sigma_\beta \sim \mathrm{exponential}(1),\\
\gamma_i \ … Depending on how comfortable you are with Bayesian data analysis this will seem more or less natural and straight-forward. …
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6
votes
Accepted
Matt's trick (reparametrization) makes my models slower, not faster
It is not unheard of for the centered parameterization to be better. This post on the Stan forums goes into the exact same issue. There it is suggested that
[...] centered actually works better when …
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22
votes
Accepted
How is empirical Bayes valid?
He goes on:
By their nature, empirical Bayes arguments combine frequentist and Bayesian elements in analyzing problems of repeated structure. …
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14
votes
Accepted
Why do we say Bayesian statistics is suited for probability of one-time events?
This is all philosophical (as it must be):
When a probability is a frequency you will have difficulty applying it to something that can't happen more than once, like Thursday's match between Liverpool …
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3
votes
Accepted
Pick a prior for my bayesian generalised linear model with binary outcomes
One trick is to simulate from your priors and see whether you think the models produced this way make a priori sense.
Let's assume we have data $x$ in the range -5 to 5. Below I try three sets of pri …
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