# Compute posterior statistics, ignoring correlations.

### Description

Compute the mean and variance of the coefficients, and the posterior inclusion probabilities (PIPs), ignoring correlations between variables. This is useful for inspecting or visualizing groups of correlated variables (e.g., genetic markers in linkage disequilibrium).

### Usage

1 | ```
varbvsindep (fit, X, Z, y)
``` |

### Arguments

`fit` |
Output of function |

`X` |
n x p input matrix, where n is the number of samples, and p is the number of variables. X cannot be sparse, and cannot have any missing values (NA). |

`Z` |
n x m covariate data matrix, where m is the number of
covariates. Do not supply an intercept as a covariate
(i.e., a column of ones), because an intercept is
automatically included in the regression model. For no
covariates, set |

`y` |
Vector of length n containing observations of binary
( |

### Details

For the ith hyperparameter setting, `alpha[,i]`

is the
variational estimate of the posterior inclusion probability (PIP) for
each variable; `mu[,i]`

is the variational estimate of the
posterior mean coefficient given that it is included in the model; and
`s[,i]`

is the estimated posterior variance of the coefficient
given that it is included in the model.

### Value

`alpha` |
Variational estimates of posterior inclusion probabilities for each hyperparameter setting. |

`mu` |
Variational estimates of posterior mean coefficients for each hyperparameter setting. |

`s` |
Variational estimates of posterior variances for each hyperparameter setting. |

### Author(s)

Peter Carbonetto peter.carbonetto@gmail.com

### References

P. Carbonetto and M. Stephens (2012). Scalable variational
inference for Bayesian variable selection in regression, and its
accuracy in genetic association studies. *Bayesian Analysis* **7**,
73–108.

### See Also

`varbvs`