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In essence, one where inference is based on using Bayes theorem to obtain a posterior distribution for a quantity or quantities of interest form some model (such as parameter values) based on some prior distribution for the relevant unknown parameters and the likelihood from the model.

i.e. from a distributional model of some form, $f(X_i|\mathbf{\theta})$, and a prior $p(\mathbf{\theta})$, someone might seek to obtain the posterior $p(\mathbf{\theta}|\mathbf{X})$.

A simple example of a Bayesian model is discussed in this question, and in the comments of this one - Bayesian linear regression, discussed in more detail in Wikipedia here. Searches turn up discussions of a number of Bayesian models here.

But there are other things one might try to do with a Bayesian analysis besides merely fit a model - see, for example, Bayesian decision theory.

In essence, one where inference is based on using Bayes theorem to obtain a posterior distribution for a quantity or quantities of interest form some model (such as parameter values) based on some prior distribution for the relevant unknown parameters and the likelihood from the model.

i.e. from a distributional model of some form, $f(X_i|\mathbf{\theta})$, and a prior $p(\mathbf{\theta})$, someone might seek to obtain the posterior $p(\mathbf{\theta}|\mathbf{X})$.

A simple example of a Bayesian model is discussed in this question, and in the comments of this one - Bayesian linear regression, discussed in more detail in Wikipedia here. Searches turn up discussions of a number of Bayesian models here.

But there are other things one might try to do with a Bayesian analysis besides merely fit a model - see, for example, Bayesian decision theory.

In essence, one where inference is based on using Bayes theorem to obtain a posterior distribution for a quantity or quantities of interest form some model (such as parameter values) based on some prior distribution for the relevant unknown parameters and the likelihood from the model.

i.e. from a distributional model of some form, $f(X_i|\mathbf{\theta})$, and a prior $p(\mathbf{\theta})$, someone might seek to obtain the posterior $p(\mathbf{\theta}|\mathbf{X})$.

A simple example of a Bayesian model is discussed in this question, and in the comments of this one - Bayesian linear regression, discussed in more detail in Wikipedia here. Searches turn up discussions of a number of Bayesian models here.

But there are other things one might try to do with a Bayesian analysis - see, for example, Bayesian decision theory.

In essence, one where inference is based on using Bayes theorem to obtain a posterior distribution for a quantity or quantities of interest form some model (such as parameter values) based on some prior distribution for the relevant unknown parameters and the likelihood from the model.

i.e. from a distributional model of some form, $f(X_i|\mathbf{\theta})$, and a prior $p(\mathbf{\theta})$, someone might seek to obtain the posterior $p(\mathbf{\theta}|\mathbf{X})$.

A simple example of a Bayesian model is discussed in this question, and in the comments of this one - Bayesian linear regression, discussed in more detail in Wikipedia here. Searches turn up discussions of a number of Bayesian models here.

But there are other things one might try to do with a Bayesian analysis besides merely fit a model - see, for example, Bayesian decision theory.

In essence, one where inference is based on using Bayes theorem to obtain a posterior distribution for a quantity or quantities of interest form some model (such as parameter values) based on some prior distribution for the relevant unknown parameters and the likelihood from the model.

i.e. from a distributional model of some form, $f(X_i|\mathbf{\theta})$, and a prior $p(\mathbf{\theta})$, someone might seek to obtain the posterior $p(\mathbf{\theta}|\mathbf{X})$.

A simple example is discussed in this question - Bayesian linear regression.

But there are other things one might try to do with a Bayesian analysis - see, for example, Bayesian decision theory.

In essence, one where inference is based on using Bayes theorem to obtain a posterior distribution for a quantity or quantities of interest form some model (such as parameter values) based on some prior distribution for the relevant unknown parameters and the likelihood from the model.

i.e. from a distributional model of some form, $f(X_i|\mathbf{\theta})$, and a prior $p(\mathbf{\theta})$, someone might seek to obtain the posterior $p(\mathbf{\theta}|\mathbf{X})$.

A simple example of a Bayesian model is discussed in this question, and in the comments of this one - Bayesian linear regression, discussed in more detail in Wikipedia here. Searches turn up discussions of a number of Bayesian models here.

But there are other things one might try to do with a Bayesian analysis - see, for example, Bayesian decision theory.