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BayesC and BayesR Comparison (Single-Trait)

This page compares the current single-trait JWAS implementations of:

  • BayesC
  • BayesR
  • Annotated_BayesC
  • Annotated_BayesR

The comparison is organized around:

  1. starting values
  2. prior structure
  3. sampler order

Starting Values

MethodMixture state at iteration 1Marker prior at iteration 1Annotation state at iteration 1
BayesCMarker effects start at 0. Indicators are binary, δ_j ∈ {0,1}.One shared exclusion probability π. In typical JWAS BayesC runs this starts from the supplied scalar Pi.None.
BayesRMarker effects start at 0. Indicators are four-class, δ_j ∈ {1,2,3,4}. The shared BayesR variance factor sigmaSq starts either from the supplied marker-effect variance input, or from a genetic-variance-to-sigmaSq conversion if the user supplied genetic variance instead.One shared four-class probability vector π = (π_1, π_2, π_3, π_4). If Pi=0.0, JWAS uses the default BayesR start (0.95, 0.03, 0.015, 0.005).None.
Annotated_BayesCSame binary marker state as BayesC. Marker effects start at 0.JWAS expands the supplied BayesC starting Pi to a marker-level exclusion vector π_j, so all markers start from the same BayesC prior.Annotation coefficients start at 0. Annotation linear predictor μ starts at 0. JWAS does not fit the annotation model before the first phenotype-informed marker sweep.
Annotated_BayesRSame four-class marker state as BayesR. Marker effects start at 0.JWAS expands the supplied BayesR starting vector π to a constant marker-level class-probability matrix snp_pi, so all markers start from the same four-class BayesR prior.Step-specific annotation coefficients start at 0. Annotation linear predictors μ start at 0. JWAS does not fit the annotation model before the first phenotype-informed marker sweep.

Starting Value Sources

This section states whether a starting value is actually used, and if so whether it is:

  • supplied by the user
  • filled from a JWAS default
  • computed from other supplied quantities
  • not used at all
StateBayesCBayesRAnnotated_BayesCAnnotated_BayesR
Marker effects αIf starting_value is provided to get_genotypes, JWAS uses it. Otherwise marker effects start at 0.If starting_value is provided to get_genotypes, JWAS uses it. Otherwise marker effects start at 0.Same rule as BayesC: user-supplied starting_value if provided, otherwise 0.Same rule as BayesR: user-supplied starting_value if provided, otherwise 0.
Marker indicators δNo separate user starting value is used. The first sampled δ values come from the first BayesC marker sweep.No separate user starting value is used. The first sampled class labels come from the first BayesR marker sweep.No separate user starting value is used. The first sampled δ values come from the first phenotype-informed annotated BayesC marker sweep.No separate user starting value is used. The first sampled class labels come from the first phenotype-informed annotated BayesR marker sweep.
Mixture prior πJWAS uses the supplied scalar Pi. If no Pi is supplied, the default argument is Pi=0.0.JWAS uses the supplied 4-class Pi. If Pi=0.0, JWAS replaces it with the BayesR default (0.95, 0.03, 0.015, 0.005).JWAS uses the supplied BayesC Pi, then expands it to a marker-level vector π_j. If no Pi is supplied, the default argument is Pi=0.0.JWAS uses the supplied BayesR Pi, then expands it to a constant marker-level matrix snp_pi. If Pi=0.0, JWAS first replaces it with the BayesR default (0.95, 0.03, 0.015, 0.005).
Annotation coefficientsNot used.Not used.Used. If no user start is provided, they start at 0.Used. If no user start is provided, they start at 0.
Annotation linear predictor μNot used.Not used.Used. If no user start is provided, it starts at 0.Used. If no user start is provided, it starts at 0.
Marker-effect variance startA positive starting value is used. It comes from the supplied genomic variance input G, or from a value computed from phenotypes if G is omitted.A positive starting value is used. Two cases exist. If G_is_marker_variance=true, JWAS uses the supplied value directly as the BayesR shared marker-effect scale sigmaSq. If G_is_marker_variance=false, JWAS treats G as genetic variance and converts it to sigmaSq.Same as BayesC.Same as BayesR.
Marker-effect variance prior scaleUsed. Once the starting marker-effect variance mean is available, JWAS computes G.scale from it.Used. Once the starting sigmaSq mean is available, JWAS computes G.scale from it.Same as BayesC.Same as BayesR.
Residual variance startA positive starting value is used. It comes from the R argument in build_model, or from a value computed from phenotypes if R is omitted.Same as BayesC.Same as BayesC.Same as BayesC.
Residual variance prior scaleUsed. Once the starting residual variance mean is available, JWAS computes R.scale from it.Same as BayesC.Same as BayesC.Same as BayesC.

For the BayesR genetic-variance conversion, JWAS uses the production rule in genetic2marker:

\[\sigma^2 = \frac{V_g}{\mathrm{sum2pq} \cdot \sum_k \gamma_k \pi_k}\]

where:

  • V_g is the genetic variance, not the marker-effect variance
  • sum2pq = \sum_j 2 p_j (1-p_j) for the current marker set
  • gamma_k are the BayesR class variance multipliers
  • pi_k are the current BayesR class probabilities

If the user instead supplies marker-effect variance directly by setting G_is_marker_variance=true, JWAS skips this conversion and uses that supplied value as sigmaSq.

Variance-Scale Starting Values

JWAS initializes the variance-component scale parameters from the corresponding starting variance means.

For single-trait residual variance, JWAS uses:

\[\mathrm{scale}_R = R \cdot \frac{df - 2}{df}\]

where R is the starting residual variance mean.

For single-trait marker-effect variance, JWAS uses:

\[\mathrm{scale}_G = G \cdot \frac{df - 2}{df}\]

where G is the starting marker-effect variance mean.

For BayesR, this same marker-scale formula is applied after the starting shared marker-effect variance sigmaSq has been determined. So if JWAS is given genetic variance first, the order is:

  1. convert genetic variance V_g to BayesR sigmaSq
  2. compute G.scale from that sigmaSq

In that step, sigmaSq is the shared marker-effect variance scale, while V_g is the genetic variance. They are not the same quantity.

Prior Structure

MethodMarker-effect priorPrior on mixture stateAnnotation role
BayesCTwo-component mixture: one zero-effect class and one nonzero normal class. The nonzero effect variance is the current marker-effect variance G.One shared exclusion probability π, updated from the total number of included markers.None.
BayesRFour-component mixture: class 1 is zero; classes 2 to 4 are normal with variances gamma[k] * sigmaSq.One shared four-class vector π, updated from class counts with a Dirichlet draw.None.
Annotated_BayesCSame BayesC effect prior as above.Marker-specific exclusion probabilities π_j. JWAS uses the probit rule `Pr(δ_j = 1aj, γ) = Φ(aj'γ), so the stored BayesC exclusion prior isπj = 1 - Φ(aj'γ)`.
Annotated_BayesRSame BayesR effect prior as above.Marker-specific four-class prior matrix π_j. JWAS builds it from three conditional probabilities: p1_j = Pr(δ_j > 1), `p2j = Pr(δj > 2δj > 1), andp3j = Pr(δ_j > 3

Sampler Order

MethodMarker updateMixture-prior updateVariance updates
BayesCSample binary inclusion δ_j and marker effect for each marker.Sample one shared exclusion probability π from the current number of included markers.Update marker-effect variance G, then update residual variance.
BayesRSample one four-way class assignment δ_j and then the corresponding marker effect for each marker.Sample one shared four-class vector π from the current class counts.Update shared BayesR sigmaSq, then update residual variance.
Annotated_BayesCRun the ordinary BayesC marker sweep using the current marker-level π_j.After the marker sweep, sample annotation liabilities and annotation coefficients, then rewrite the full marker-level exclusion vector π_j.Update BayesC marker-effect variance G, then update residual variance.
Annotated_BayesRRun the ordinary BayesR marker sweep using the current marker-level four-class prior matrix snp_pi.After the marker sweep, construct z1 = 1(δ > 1), z2 = 1(δ > 2), z3 = 1(δ > 3), fit the three annotation submodels, then rebuild the full marker-level four-class prior matrix snp_pi.Update shared BayesR sigmaSq, then update residual variance.

Key Distinctions

ComparisonMain difference
BayesC vs BayesRBayesC is a binary inclusion model with one shared exclusion probability. BayesR is a four-class mixture model with one shared class-probability vector.
Annotated_BayesC vs Annotated_BayesRAnnotated_BayesC uses one annotation-driven binary probit model to produce marker-specific π_j. Annotated_BayesR uses three nested annotation probit models to produce marker-specific four-class probabilities snp_pi.
Plain vs annotated methodsThe plain methods learn one shared mixture prior. The annotated methods learn marker-specific priors from the supplied annotations.