4 Bayesian analysis

In this section, we discuss how to run INTERQTL in WINDOWS for Bayesian analysis. You must have all input data files ready before you start Bayesian analysis. You can prepare input data files in the edit window. The formats of these files are discussed in Section 2. You may also prepare these files using other editors such as Notepad. Note that these files are automatically generated in simulation approaches, except that the pedigree file must be prepared manually in all cases.

Once all the input data files are ready, following the following steps to run Bayesian analysis and visualize the results.

è Step 1: Click “QTL analysis” on the main window and a pull-down menu will show up

è Step 2: Choose “Setting parameters” and set up parameters to meet the need of your analysis. Click “OK” to accept all the parameters

è Step 3: Repeat step 1

è Step 4: Choose “MCMC analysis” to start your Bayesian analysis. A window will be activated that shows the progress of MCMC iterations

è Step 5: Once the “MCMC analysis” is done, close the window.

è Step 6: Repeat step 1 to activate the pull-down menu

è Step 7: Choose “Posterior graphs” to view graphic presentation of location-wise posterior of QTL intensity. This window provides a quick and brief visualization of QTL location and number. Users need to analysis saved Markov chains in the mix_xxMy.txt file for more accurate results.

4.1 Setting parameters

Going through steps 1 and 2 leads to a “Setting parameter” dialogue, which is discussed in details below.

~[OK] Accept all parameters and quit the “Set parameters for MCMC analysis” dialogue

~[Cancel] Discard all parameters and quit the “Set parameters for MCMC analysis” dialogue

Default:

~[Use] Use default parameters for MCMC analysis

~[Set] Set your own default parameters for MCMC analysis that can be used repeatedly.

Distributed with the package, mult_Al.def provides a set of default parameters for MCMC analysis.

Sampling methods:

~[Metropolis-Hastings] Use Metropolis-Hastings algorithm to generate posteriors for all model parameters.

~[Gibbs sampling] Use Gibbs samplers to generate posteriors for all model parameters except that posteriors of QTL position, QTL number or allele number and allele configuration are still given via M-H algorithm. This option is currently not available in the beta 1.00 version.

QTL number:

~[Variable] Turn on the subroutine that gives posterior QTL number via reversible jump. Thus, the number of QTL in the model varies. When this subroutine is on, the one for changing allele number is off.

~[Fixed] Turn off the subroutine that gives posterior QTL number. The number of QTL in the model equals to a pre-defined number.

Effect of QTL:

~[Random] Turn on the subroutine to update QTL variance in each cycle of MCMC iteration

~[Fixed] Turn off the subroutine to update QTL variance.

Number of alleles:

~[Variable] Turn on the subroutine to give posterior number of alleles. Thus, the number of alleles varies in the model. When this subroutine is one, the one for changing QTL number is off.

~[Fixed] Turn off the subroutine to give posterior number of alleles. By default, the number of alleles in the model equals to the number of founder parents when this switch is off. But you may a fixed number of alleles that is different from the number of founder parents.

Input files and Progeny type:

~[Genome info] Input here the file that contains genome information. By the default, the file name is given as “genome.txt”. If you have the file in a folder elsewhere, use browse button at the right side to search for it.

~[f1 markers] Input here the file that contains F1 marker genotypes. By the default, the file name is given as “f1.txt”. If you have the file in a folder elsewhere, use browse button at the right side to search for it.

~[Progeny mrks] Input here the file that contains marker genotypes of all progeny. By the default, the file name is given as “markers.txt”. If you have the file in a folder elsewhere, use browse button at the right side to search for it.

~[Trait value] Input here the file that contains trait values of all progeny. By the default, the file name is given as “pheno.txt”. If you have the file in a folder elsewhere, use browse button at the right side to search for it.

~[Pedigree file] Input the name of the pedigree file. By the default, the file name is given as “pedigree.txt”. If you have the file in a folder elsewhere, use browse button at the right side to search for it.

~[Progeny type] Choose the type of inbred crosses. Currently, INTERQTL is able to deal with BC1 (backcross to paternal parent), BC2 (backcross to maternal parent), F2 (intercross of F1), DHL (double haploid lines), and RIL (recombinant inbred lines).

Prior information of QTL:

èThe number of QTL must be given before you work on setting for each QTL.

Entries for each QTL include:

è [Current QTL] Give no of current putative QTL

è [on chromosome] Give initial prior of chromosome where the QTL is located

è [position, cM ] Give initial prior of location for the current putative QTL.

è [allele number] Give initial prior of allele number for the current putative QTL

è [additive variance] Give initial prior of additive variance for the current putative QTL

Use the following buttons to navigate these QTL:

~[|<<] Go to first QTL

~[<<] Go to previous QTL

~[>>] Go to next QTL

~[>>|] Go to last QTL

Caution: you need to press “confirm” button to accept entries for each QTL. Once you change the number of QTL, settings for each QTL become invalid. You’ll have to re-enter and re-confirm settings for each QTL.

Other priors and parameters:

The following priors and parameters apply to all QTL.

~[Prior for QTL number::type] Choose either “Poisson” or “Uniform” prior for QTL number. By default, the prior of QTL number is “Poisson” with mean given in the right edit box. If you choose “Uniform”, the number of alleles has a uniform prior distribution with the probability being the inverse of a pre-defined maximum number of QTL (i.e. 50).

~[Prior for allele number::value] If you choose to use “Poisson” prior for QTL number, you must give the mean of “Poison” distribution of QTL number here, which by default is 2.

~[Prior for allele number::type] Choose either “Poisson” or “Uniform” prior for allele number. By default, the prior of allele number is “Poisson” with mean given in the right edit box. If you choose “Uniform”, the number of alleles has a uniform prior distribution with the probability of each allele number equal to 1/(number_of_parents).

~[Prior for allele number::value] If you choose to use “Poisson” prior for allele number, you must give the mean of “Poison” distribution of allele number here, which by default 4.

The following are required only when M_H algorithm is used.

~[Radius of change::QTL position] Restrict proposed QTL position within current_position±radius.

~[Radius of change::QTL variance] Restrict proposed QTL variance within current_variance±radius.

~[Radius of change::allele value] Restrict proposed allele value within current_value±radius.

~[Radius of change::family mean] Restrict proposed family mean within current_mean±radius.

~[Radius of change::family variance] Restrict proposed family variance within current_variance±radius.

~[Maximum value::family mean] Set a positive maximum value for proposed family means.

~[Maximum value::family variance] Set a positive maximum value for proposed family variance.

MCMC runs and iterations

~[Meta-runs] How many times of runs to go with a given set of priors and parameters?

~[Burn-in iterations] How many cycles of iteration to be discarded in the beginning of Markov chains?

~[Total iterations] How many cycles of iterations to go that follows burn-in iterations?

~[Iteration per save] How many cycles of iterations go between two consecutive saves. Dividing [Total iterations] by [Iteration per save] gives this number.

~[Random seed] This number is used as the seed for generating random numbers.

~[Bin length, cM] Each chromosome is divided into intervals of equal length defined by [Bin length,cM], and location-wise posteriors are averaged within each bin.

~[Update missing markers] Check this option when there are missing marker genotypes in your data. These missing marker genotypes will then be initialize and updated in the MCMC analysis.

~[Overdisperse starting chain] Check this option to overdisperse the starting values of the Markov chain.

~[Use single variance] Check this option if a single variance is to be estimated over all families. Otherwise, each family has its own variance.

~[Additional run without QTL] Check this option if an additional run is to be done without QTL effects in the model.

~[Save MC chain values] Check this option to save Markov chain values in files. By default, these files are named as “mix_xxMy.txt”, where xx standards for no of meta-runs and y represents the analysis type ( 0=runs without QTL effects in the model, 1 = runs assuming variable number alleles in the model, and 2=runs assuming fixed number of alleles in the model).

4.2 MCMC analysis

When “Setting parameters” is done, click “QTL analysis” on the main window and choose “MCMC analysis” in the pull-down menu to start the analysis. A new window will then show up indicating the progress of the analysis. Close the window when the analysis is finished.

4.3 Posterior graphs

INTERQTL provides a graphic window for visualization of location-wise posterior of QTL intensity or/and QTL variance, which serves to the need for quick view of the presence of QTL. However, for a better presentation of these results, we strongly recommend that the posterior data be analyzed and visualized using other professional software.

~[Posterior QTL intensity] Check this radio box to display graphic location-wise posterior QTL intensity.

~[Posterior QTL variance] Check this radio box to display graphic location-wise posterior QTL variance, if any random-QTL effect is defined.

~[Choose a chromosome] Specify which chromosome you are looking at. When 2 or more chromosomes are involved, use the following buttons to navigate them:

~[|<<] Go to first chromosome

~[<<] Go to previous chromosome

~[>>] Go to next chromosome

~[>>|] Go to last chromosome

~[Choose a replication] Specify which replication (meta-run) you are looking at. When 2 or more replications (meta-runs) are involved, use the following buttons to navigate them:

~[|<<] Go to first replication.

~[<<] Go to previous replication.

~[>>] Go to next replication.

~[>>|] Go to last replication.

~[Show all graphs] Graphs of location-wise posteriors are showed together for all replications, with different graph represented in different colors. Altogether, 16 colors are available. When the number of chromosomes or replications is greater than 16, some graphs may share the same color.

~[Show all graphs] Graphs of location-wise posteriors are showed as an average of all replications.

4.3 Markov chains

This graphic window is reserved for quick visualization of Markov chains of model parameters, and it is not activated in this trial version.