## Approximate marginal posterior for chosen model

### Description

lapadj provides the Laplace approximation to the marginal posterior (over coefficients and dispersion parameter) for a given genetical model for a quantitative trait. A by-product is the parameter value corresponding to the maximum posterior or likelihood.

### Usage

 lapadj(reg.formula, ana.obj,
rparm = NULL,  tol = 1e-10,
return.hess = FALSE, mode.names = NULL, mode.mat = NULL,
maxit = 100, nem = 1,setup.only=FALSE,subset=NULL,casewt=NULL,
start.parm=NULL, ...)


### Arguments

 reg.formula A formula, like y~add.X.3+dom.X.3+add.x.45*add.x.72 ana.obj Seemake.analysis.obj, which returns objects like this rparm One of the following: A scalar that will be used as the ridge parameter for all design terms except for the intercept ridge parameter which is set to zero A vector who named elements can be matched by the design term names returned in $reg.vec. If no term named "intercept" is provided, rparm["intercept"] will be set to zero. A vector with (q-1)*k elements (this works when there are no interactions specified). If names are provided, these will be used for matching. Positive entries are 'ridge' parameters or variance ratios in a Bayesian prior for the regression coefficients. Larger values imply more shrinkage or a more concentrated prior for the regresion coefficients. tol Iteration control parameter return.hess Logical, include the Hessian in the output? mode.names names to use as dimnames(mode.mat)[[2]] mode.mat Not usually set by the user. A matrix which indicates the values of regressor variables corresponding to the allele states. If mode.mat is not given by the user, ana.obj$mode.mat is used. maxit Maximum Number of iterations to perform nem Number of EM iterations to use in reinitializing the pseudo-Hessian setup.only If TRUE, do not run. Return an object that can be use for a direct call to .C subset expression to evaluate using ana.obj\$data as the environment  casewt  a vector of non-negative weights start.parm Vector of starting values for the maximization ... other objects needed in fitting

### Details

The core of this function is a quasi-Newton optimizer due to Minami (1993) that has a computational burden that is only a bit more than the EM algorithm, but features fast convergence. This is used to find the mode of the posterior. Once this is in hand, one can find the Laplace approximation to the marginal likelihood. In addition, some useful quantities are provided that help in estimating the marginal posterior over groups of models.

### Value

A list with components to be used in constructing approximations to the marginal posterior or a list that can be used to call the underlying C code directly. In the former case, these are:

 adj The ratio of the laplace approximation to the posterior for the correct likelihood to the laplace approximation to the posterior for the linearized likelihood logpost The logarithm of the posterior or likelihood at the mode parm the location of the mode posterior The laplace approximation of the marginal posterior for the exact likelihood hk.approx Laplace approximation to the linearized likelihood hk.exact Exact marginal posterior for the linearized likelihood reg.vec A vector of the variables used rparm Values of ridge parameters used in this problem.

### Author(s)

Charles C. Berry cberry@ucsd.edu

### References

Berry C.C.(1998) Computationally Efficient Bayesian QTL Mapping in Experimental Crosses. ASA Proceedings of the Biometrics Section. 164–169.

Minami M. (1993) Variance estimation for simultaneous response growth curve models. Thesis (Ph. D.)–University of California, San Diego, Department of Mathematics.

[Package bqtl version 1.0-33 Index]