Description Usage Arguments Details Value Author(s) References See Also Examples

Hyper parameter tau selection for nonlocal priors using random sampling from the null distribution (Nikooienejad et al, 2016).

1 |

`type` |
a type of nonlocal priors; 'pimom' or 'pemom'. |

`X` |
a covariate matrix (a standardization is recommneded for nonlocal priors). |

`y` |
a response variable. |

`thre` |
a threshold; for details, see below. The default is p^-0.5. |

Nikooienejad et al. (2016) proposed a novel approach to choose the hyperparameter tau for nonlocal priors. They first derive the null distribution of the regression coefficient by randomly sampling the covariates, and shuffle the index of the samples in the covariates. Then, they calculate the MLE from the sampled covariates that are shuffled. This process is repeated large enough times to approximate the null distribution of the MLE under the situation where all true regression coefficients are zero. They compare the nonlocal density with different values of the parameter to the null distribution so that the overlap of these densities falls below the threshold; see Nikooienejad et al. (2016) for further details.

`tau` |
: the choosen hyper parameter tau |

Shin Minsuk and Ruoxuan Tian

Shin, M., Bhattacharya, A., Johnson V. E. (2018) A Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-dimensional Settings, Statistica Sinica.

Nikooienejad,A., Wang, W., and Johnson V.E. (2016). Bayesian variable selection for binary outcomes in high dimensional genomic studies using non-local priors. Bioinformatics, 32(9), 1338-45.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
p=50
n = 200
indx.beta = 1:5
xd0 = rep(0,p);xd0[indx.beta]=1
bt0 = rep(0,p);
bt0[1:5]=c(1,1.25,1.5,1.75,2)*sample(c(1,-1),5,replace=TRUE)
xd=xd0
bt=bt0
X = matrix(rnorm(n*p),n,p)
y = crossprod(t(X),bt0) + rnorm(n)*sqrt(1.5)
X = scale(X)
y = y-mean(y)
y = as.vector(y)
# piMoM
C0 = 1 # the number of repetitions of S5 algorithms to explore the model space
tuning = 10 # tuning parameter
#tuning = hyper_par(type="pimom",X,y,thre = p^-0.5)
print(tuning)
``` |

```
[1] 10
```

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