bayesian approach for animal breeding data analysis

7/21/2019 Bayesian Approach for Animal Breeding Data Analysis

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Application of Bayesian Model for

Animal Breeding Data Analysis

G. R. Gowane

ICAR-CSWRI Avikanagar


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Why do we need to estimate genetic

parameters?

They are necessary to plan an efficient breedingprogram for the trait of interest.

knowledge of the

genetic architecture of

the population


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Accurate estimation of VC:

Prediction error variances for

predicted random effects (BV)

increase as differences between

estimated and true values of VC

increase

Henders

on, 1975


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Choice of estimating VC

REML DFREML, MTDFREML, VCE, Wombat

Gibbs Sampling (GS) algorithm for Bayesian

analysis

MTGSAM (Van Tassell and Van Vleck, 1995)

RRGibbs (Meyer)


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Why Bayes?

Combine information from prior to obtain the

posterior distribution.

MORE ACCURACY!!

Memory space required for estimating

variance components.

Does it really matter these days?

Threshold traits analysis

Several algorithms are being searched

It is an alternate approach


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Bayesian statistics uses probabilityto express

uncertainty about the unknowns that are

being estimated.

The use of probability is more efficientthan

any other method of expressing uncertainty.

Unfortunately, to make it possible, inverse

probability needs the knowledge of some

priorinformation.


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Three problems of Bayesian approach

Difficulty of integrating priorinformation

how to represent ignorance

because there is no prior information,

because we do not like the way in which this prior isintegrated,

because we would like to assess the information provided

by the data without prior considerations

Use of probability to express uncertainty, this leads tomultiple integrals that cannot be solved even by using

approximate methods

1990s MCMCa numerical method came to resque


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In Bayesian theory we

know that all problems

are reduced to a single

pathway: we should

look for a posterior

distribution, given the

distribution of the dataand the prior

distribution.


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9

A brief history of Bayesian analysis

Bayes (1763) Links statistics to probability

Laplace (1800) Normal distribution

Many applications, including census

[sampling models] Gauss (1800)

Least squares

Applications to astronomy [measurement error models]

Keynes, von Neumann, Savage (1920s-1950s) Link Bayesian statistics to decision theory

Applied statisticians (1950s-1970s) Hierarchical linear models

Applications to animal breeding, education [data in groups]

Daniel Gianola (Wang et al., 1994) and Daniel Sorensen (Sorensen et al. 1994)brought these techniques into the field of animal breeding.


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Prior???

Litter Size of Landrace Pig ~ 10 Spanish Landrace?

Mean = 5

Prior mean = 10

What to do?

Prior information is the

information about the

parameters we want toestimate that

exists before we perform our

experiment.


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Bayesian Variance Components ModelPrior Distributions

"flat" prior distribution for the "fixed" effects, that is, thereis no prior knowledge about these effects.

Next, the random effects are assumed to be normallydistributed. For the genetic effects there will be an

additional assumption of a known covariance structureamong those random effects corresponding to therelationship matrix.

Finally, the residual effects are assumed to be distributednormally. These assumptions are the same as those usedwith most likelihood based methods.

Results in BLUE and BLUP solutions for fixed and randomeffects


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Gibbs Sampling Animal Model

Gibbs sampling (GS) is a method of numerical

integration that allows inferences to be made

about joint or marginal densities, even when

those densities cannot be evaluated directly.


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Posterior inference is affected by the specified

prior density unless the information in thedata analysed (likelihood) overwhelmsthe

prior.

With normality, the posteriordistribution issimply the (frequentist) likelihood function

scaled by priordistributions of the unknown

parameters in the model (Van Tassell and and

Van Vleck, 1996).


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Burn In:The number of rounds discarded

before the values are considered samples

from the posterior distribution is usually

called the burn-in period. Raftery and Lewis(1992)

Gibanal (Van Kaam, 1997) can be used to

define the burn in period and convergencecriteria for the problem


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Defining the Number of Iterations or length

of the Gibbs sampling

The number of Gibbs sampling for executing

the program should be large enough.

Although Gibanal also dictates the length of

the chain, however, one long chain suffices

the need for the program (Geyer 1992).


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MTGSAM

Van Tassell and Van Vleck (1995)

Model Assumptions y = X+ Zu + e

where is the vector of fixed effects associated with

records in ybyX, and uis the vector of random effects

associated with records in ybyZ, and eis the vector ofrandom residual effects.


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Prior Distribution: The MTGSAM

flat prior distributions for the fixed effects.

For the genetic effects there will be an additional

assumption of a known covariance structure

corresponding to the numerator relationship

matrix.

Inverted Wishart (IW) distributions are used asprior distributions for the (co)variance

components


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Variance Components:

The MTGSAM posterior mean estimate for

(co)variance components is based on the

expected value of the IW RV

The mean of a (co)variance component is

calculated as the average of expected values

over the length of the post burn-in chain.


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The MTGSAM for Genetic Analysis

Preparing a pedigree and data file


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This procedure completes the execution of theprogram. The results obtained are stored mainly in theMTGS60, MTGS61, MTGS62, MTGS63, MTGS81,MTGS82 and MTGS83 files.

The unit MTGS61 file contains the observed values ofthe variance components

The unit 62 file contains the parameters used togenerate the samples from the appropriatedistribution.

These values can be extracted by using the softwarePULLDAT.EXE (Annexure 2) for calculating the Mean, SEor SD for the estimates obtained.


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MTGS81 is the log file of information from the

execution of MTGSNRM. The information

includes number of animals in A-1, number of

non-zero elements, and inbreedinginformation


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Actual

results

are

given inthe

MTGS8

3


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MTGS72

Animal effect

Second

animal effect

P lld


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Pulldat.exeYou need to have pulldat.exe

in the same folder where

MTGS61, MTGS62 and

MTGS63 are present.Only after files are

subjected to pulldat they

can be further used for

Gibanal or other

analyses.

Open the CMD window andchange path directory to

pulldat

Give the name for output

fille.

Follow the options as given

except at the point Enterthe number of variables

in each record to be read

from MTGS61. Here in

our case, 5 variables

needs to be extracted,

however, the input will

change according to thedata in consideration and


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Gibanal.exe

the observed values of the fixed and random

effects are written to unit 61

We can use Gibanal to see

Serial correlation

Burn in

Chain length


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Bayesian analysis are carried out to estimate severalsampling for the same (co)variance component.These values for Va or Vm etc. do not depend of number of

animals, but of length chain you run.You can use 10,000 animal in your analysis, and infrequentist approach you'll estimate only one Va or Vmetc., but in bayesian approach you'll have sampling ofthese variances, it depend on the sampling length, for

example:1 - Iteration length = 11002 - Burn-in = 1003 - Thinning interval = 10

So, we have: iteration length - Burn-in = 1100 - 100 = 1000(Sampling after burn-in).Now, we made: Sampling after burn-in / thinning interval =1000 / 10 = 100(this is a number of sampled observationsfor Va or Vm etc.), not the number of animals


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Bloco Freqncia

2.18 1

2.46 3

2.73 5

3.01 10

3.29 13

3.57 22

3.85 23

4.13 9

4.41 2


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Thank You

bayesian approach for animal breeding data analysis

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