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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.
6
votes
Accepted
Bayes estimator of Bernoulli random variables
You drop the marginal density $p(x)$ (the normalizing constant ) because it is a function of the data which are fixed (in the Bayesian context ) but that leads the posterior density $p(\theta|x)$ to …
6
votes
Basic references on MCMC for Bayesian Statistics
When I started to learn statistics I found Gelman's book on Bayesian data analysis very difficult to understand , it may be a bit overwhelming for someone new to statistics !. … I recommend you to start with Peter Hoff's book A First Course in Bayesian Statistical Methods . …
2
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Bayesian inference, finding unknown function of parameter
You just need to solve the integral
$$ \int_{0}^{\infty}\pi(x|\theta)dx=\int_{0}^{\infty}C(\theta)x^2e^{-\theta x^3} dx=1 , \forall \theta > 0 $$
$$=C(\theta) \int_{0}^{\infty}x^2e^{-\theta x^3} dx …
5
votes
Accepted
confusing notion in Bayesian inference
Exchangeability is often interpreted as the Bayesian version of i.i.d assumption . … So that the assumption of exchangeability in Bayesian inference means we believe that the data are exchangeable then it is as if there is a parameter (say $\theta$) that derives a stochastic model generating …
1
vote
How does mice::mice work?
mice assumes at least MAR missing mechanism, under MAR (and MCAR) which is an ignorable missing-data mechanism a model for missingness is not necessary when the statistical inference aims at $\theta$ …
8
votes
1
answer
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Generate Posterior predictive distribution at every step in the MCMC chain for a hierarchica...
I'm trying to fit a Bayesian Hierarchical regression model with a random correlated coefficients using R ,I'm using data having 160 groups (schools) to fit a model of math score as a function of one … My second question is , If we ignore the multilevel model and run a simple bayesian linear regression model and generate a posterior predictive distribution form this simple model , how can we compare …