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Bayesian linear regression model with diffuse conjugate prior for data likelihood

The Bayesian linear regression
model object `diffuseblm`

specifies that the joint prior
distribution of (*β*,*σ*^{2})
is proportional to 1/*σ*^{2} (the
*diffuse prior model*).

The data likelihood is $$\prod _{t=1}^{T}\varphi \left({y}_{t};{x}_{t}\beta ,{\sigma}^{2}\right)},$$ where
*ϕ*(*y _{t}*;

In general, when you create a Bayesian linear regression model object, it specifies the joint prior distribution and characteristics of the linear regression model only. That is, the model object is a template intended for further use. Specifically, to incorporate data into the model for posterior distribution analysis, pass the model object and data to the appropriate object function.

`PriorMdl = diffuseblm(NumPredictors)`

`PriorMdl = diffuseblm(NumPredictors,Name,Value)`

creates a Bayesian linear
regression model object (`PriorMdl`

= diffuseblm(`NumPredictors`

)`PriorMdl`

) composed of
`NumPredictors`

predictors and an intercept. The joint
prior distribution of (*β*,
*σ*^{2}) is the diffuse model.
`PriorMdl`

is a template defining the prior
distributions and dimensionality of *β*.

uses additional options specified by one or more
`PriorMdl`

= diffuseblm(`NumPredictors`

,`Name,Value`

)`Name,Value`

pair arguments. `Name`

is
a property name, except `NumPredictors`

, and
`Value`

is the corresponding value.
`Name`

must appear inside single quotes
(`''`

). You can specify several
`Name,Value`

pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

`estimate` | Fit parameters of Bayesian linear regression model to data |

`simulate` | Simulate regression coefficients and disturbance variance of Bayesian linear regression model |

`forecast` | Forecast responses of Bayesian linear regression model |

`plot` | Visualize prior and posterior densities of Bayesian linear regression model parameters |

`summarize` | Distribution summary statistics of Bayesian linear regression model |

You can also create a Bayesian linear regression model with a diffuse prior using
`bayeslm`

.

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