### INTRODUCTION

^{2}>0.24) in the simulation study, and they were also more accurate in mice data and other benchmark data sets.

_{g}and

### MATERIALS AND METHODS

### Statistical model

**g**~N (0,

**G**), where

### BayesCπ

**G**.

_{g}was set to 4.2, and

### Hyper-BayesCπ

_{g}using a Metropolis Hastings (MH) update and

_{g}and

_{g}~p(v

_{g}) ∝ (v

_{g}+1)

^{−2}, and

*α*

*=1.0 and rate parameter*

_{s}*β*

*=1.0. The full conditional density (FCD) of v*

_{s}_{g}did not have a recognizable form, and a random walk MH step other than a Gibbs step was used to sample v

_{g}from this FCD. The detailed procedure can be seen Yang et al [7]. The FCD of

### Ante-BayesCπ

**g**based on the relative physical location of SNPs along the chromosome was used:

_{j,j-1}was the marker interval-specific antedependence parameter of g

_{j}on g

_{j–1}in the specified order. δ

_{j}was the residual SNP effect following

### Ante-hyper-BayesCπ

_{g}and

**g**were combined.

*u*

_{t}_{0},

*v*

*, and*

_{t}_{j,j-1}was set 0 between the last SNP of one linkage group or chromosome and the first SNP in the subsequent group. The remaining priors were also specified, such as π~ U(0,1), v

_{δ}= v

_{g}and

_{δ}~p(v

_{δ})∝(v

_{δ}+1)

^{−2}in ante-hyper-BayesCπ. For all methods, the noninformative prior

### Simulation data

^{2}= 0.33, 0.22, and 0.14) of adjacent SNPs corresponding to the full set of SNPs and other two subsets with SNP intervals of 10 and 25, respectively. In our study, we selected trait 1 with both phenotype and genotype for first 20 of 30 replicates with the full dataset and other two subsets of SNPs as test data to investigate the influence of LD between adjacent SNPs on the prediction accuracy and bias. Generation 5001 was considered as the reference population, and generation 5002 as the candidate population.

### Analysis of the 15th QTL-MAS workshop data set

### Application to heterogeneous stock mice data set

^{2}among adjacent SNPs is 0.62 [13]. It is well known for the family structure and history of this population, and thus interpretation of results will be easy.

^{2}was 0.35 between adjacent markers. In the study of Gao et al [10], there were 1,940 animals and 9,266 SNPs on the 19 chromosomes after their quality control steps, which resulted in the average LD of r

^{2}about 0.60.

### RESULTS

### Results from the simulations

### Common data set of the 15th QTL-MAS workshop

### Real heterogeneous stock mice data set

### DISCUSSION

_{g}and a scale parameter

_{g}and

_{g}for the range (0,1) and a uniform distribution on

_{g}~p(v

_{g})∝(v

_{g}+1)

^{−2}for both BayesA and BayesB. In our study, we have applied

_{g}~p(v

_{g})∝(v

_{g}+1)

^{−2}for v

_{g}and a Gamma (1,1) prior distribution on

^{2}ranging from 0.136 to 0.333 and mice data with two different LD levels. This phenomenon is very different from the performance of ante-BayesA (ante-BayesB) over BayesA (BayesB) in the study of Yang and Tempelman [4]. They reported that ante-BayesA and ante-BayeB had significantly higher accuracies than their corresponding classical counterparts at higher LD levels in simulation data and real small data. However, subsequent studies did not show that the antedependence model performed significantly better. Wang et al [16] evaluated the antedependence model performance in Danish pigs and found that ante-BayesA showed lower accuracy compared to other models. Jiang et al [6] also introduced the first-order antedependence model to multi-trait BayesA, and the analysis from simulation and mice data showed that multi-trait ante-BayesA had less than 1% higher accuracies than multi-trait BayesA. The results from these studies were similar to the performance of ante-hyper-BayesCπ (ante-BayesCπ) over hyper-BayesCπ (BayesCπ) from our study.

### CONCLUSION

_{g}and