# Multi Resolution Scanning for one-way ANDOVA using the multi-scale Beta-Binomial model

### Description

This function executes the Multi Resolution Scanning algorithm to detect differences across the distributions of multiple groups having multiple replicates.

### Usage

1 2 3 4 |

### Arguments

`X` |
Matrix of the data. Each row represents an observation. |

`G` |
Numeric vector of the group label of each observation. Labels are integers starting from 1. |

`H` |
Numeric vector of the replicate label of each observation. Labels are integers starting from 1. |

`n_groups` |
Number of groups. |

`n_subgroups` |
Vector indicating the number of replicates for each grop. |

`Omega` |
Matrix defining the vertices of the sample space.
The |

`K` |
Depth of the tree. Default is |

`init_state` |
Initial state of the hidden Markov process.
The three states are |

`beta` |
Spatial clustering parameter of the transition probability matrix. Default is |

`gamma` |
Parameter of the transition probability matrix. Default is |

`delta` |
Parameter of the transition probability matrix. Default is |

`eta` |
Parameter of the transition probability matrix. Default is |

`alpha` |
Pseudo-counts of the Beta random probability assignments. |

`nu_vec` |
The support of the discrete uniform prior on nu. |

`return_global_null` |
Boolean indicating whether to return the marginal posterior probability of the global null. |

`return_tree` |
Boolean indicating whether to return the posterior representative tree. |

### Value

An `mrs`

object.

### References

Ma L. and Soriano J. (2016).
Analysis of distributional variation through multi-scale Beta-Binomial modeling.
*arXiv*.
http://arxiv.org/abs/1604.01443

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
set.seed(1)
n = 1000
M = 5
class_1 = sample(M, n, prob= 1:5, replace=TRUE )
class_2 = sample(M, n, prob = 5:1, replace=TRUE )
Y_1 = rnorm(n, mean=class_1, sd = .2)
Y_2 = rnorm(n, mean=class_2, sd = .2)
X = matrix( c(Y_1, Y_2), ncol = 1)
G = c(rep(1,n),rep(2,n))
H = sample(3,2*n, replace = TRUE )
ans = andova(X, G, H)
ans$PostGlobNull
plot1D(ans)
``` |