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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 …
Bahgat Nassour's user avatar
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 votes

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 …
Bahgat Nassour's user avatar
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 …
Bahgat Nassour's user avatar
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 $\theta$ …
Bahgat Nassour's user avatar
8 votes
1 answer
1k views

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 …
Bahgat Nassour's user avatar