Deborah.Esther.BootstrapDerivedCalculator

compute_bootstrap_derived!(
    bd::Dict,
    LatVol::Int,
    partition::DatasetPartitioner.DatasetPartitionInfo,
) -> Nothing

Compute bootstrap-averaged cumulants (condensate, susceptibility, skewness, kurtosis) for each subset directly from $Q$-moments ($Q_{n} \; (n=1,2,3,4)$), then construct post-cumulant bias-corrected combinations Y_P1, and Y_P2 from those cumulants.

This variant differs intentionally from the simpler overload that only maps $Q_n \; (n=1,2,3,4) \to \{ \Sigma , \chi , S , K \}$ for pre-defined labels. Here, bias correction is applied after cumulants are formed (i.e., on $\{ \Sigma , \chi , S , K \}$), not at the $Q$-moment level. This ordering is generally not recommended for production use, but is kept for completeness and for controlled comparisons.

Arguments

• bd::Dict: A dictionary that must contain a :mean table of bootstrap-averaged moments and will be mutated to include cumulants and their derived combinations. The following keys must exist for each subset label in ("Y_info", "Y_lb", "Y_bc", "Y_ul", "YP_bc", "YP_ul"):
  • "Q1:<label>", "Q2:<label>", "Q3:<label>", "Q4:<label>"
• LatVol::Int: Lattice volume used to normalize condensate and susceptibility.
• partition::DatasetPartitioner.DatasetPartitionInfo: Partition metadata used to compute weights and training coverage:
  • N_cnf: total configurations
  • N_lb: labeled configurations
  • N_ul: unlabeled configurations
  • N_tr: training configurations (subset of labeled)
  Internally we use:
  • $w_{\texttt{lb}} = \dfrac{N_{\texttt{lb}}}{N_{\texttt{cnf}}}$
  • $w_{\texttt{ul}} = \dfrac{N_{\texttt{ul}}}{N_{\texttt{cnf}}}$

Behavior

1. Per-subset cumulants. For each label $\in$ ("Y_info","Y_lb","Y_bc","Y_ul","YP_bc","YP_ul"), read $Q_n \; (n=1,2,3,4)$ from bd[:mean] and compute

   • "cond:<label>" = calc_quark_condensate(Q1, LatVol)
   • "susp:<label>" = calc_susceptibility(Q1, Q2, LatVol)
   • "skew:<label>" = calc_skewness(Q1, Q2, Q3)
   • "kurt:<label>" = calc_kurtosis(Q1, Q2, Q3, Q4)

2. Post-cumulant bias combinations. For each C $\in$ ("cond","susp","skew","kurt"), form:

   • YmYP = (C:Y_bc) - (C:YP_bc) (bias estimate on the cumulant)
   • Y_P1 = (N_tr == N_lb) ? (C:YP_ul) : (C:YP_ul + YmYP) (i.e., pass-through when TRP = 100%, ignoring YmYP)
   • Y_P2 = w_lb * (C:Y_lb) + w_ul * Y_P1

   Results are stored under keys "$C:YmYP", "$C:Y_P1", and "$C:Y_P2".

Returns

• Nothing. The function mutates bd[:mean] in place, adding cumulant and derived-combination arrays for all supported labels.

Notes

• Ordering caveat. Bias correction here is applied after mapping $Q_{n} \; (n=1,2,3,4)$ to $\{ \Sigma , \chi , S , K \}$. In most workflows, applying bias handling earlier (at the $Q$-moment stage) is preferable to preserve the algebra of derived observables. Keep this function for record-keeping, audits, or A/B comparisons.
• TRP=100% shortcut. When N_tr == N_lb, we set Y_P1 = YP_ul (pass-through) and effectively ignore YmYP for Y_P1. This matches the intent that no bias-correction set is available/needed in that limit.
• All vector operations are broadcasted element-wise; array shapes of inputs ($Q_{n} \; (n=1,2,3,4)$) must be consistent across labels.

Requirements

• bd[:mean] must contain the required "Qk:<label>" keys for all listed labels.
• The following functions must be defined and accept bootstrap-averaged inputs: Deborah.Esther.SingleCumulant.calc_quark_condensate, Deborah.Esther.SingleCumulant.calc_susceptibility, Deborah.Esther.SingleCumulant.calc_skewness, Deborah.Esther.SingleCumulant.calc_kurtosis.

Example

bd = Dict(:mean => Dict(
    "Q1:Y_lb"=>q1_lb, "Q2:Y_lb"=>q2_lb, "Q3:Y_lb"=>q3_lb, "Q4:Y_lb"=>q4_lb,
    "Q1:Y_bc"=>q1_bc, "Q2:Y_bc"=>q2_bc, "Q3:Y_bc"=>q3_bc, "Q4:Y_bc"=>q4_bc,
    "Q1:YP_bc"=>q1_ypbc, "Q2:YP_bc"=>q2_ypbc, "Q3:YP_bc"=>q3_ypbc, "Q4:YP_bc"=>q4_ypbc,
    "Q1:YP_ul"=>q1_ypul, "Q2:YP_ul"=>q2_ypul, "Q3:YP_ul"=>q3_ypul, "Q4:YP_ul"=>q4_ypul,
    "Q1:Y_ul"=>q1_ul, "Q2:Y_ul"=>q2_ul, "Q3:Y_ul"=>q3_ul, "Q4:Y_ul"=>q4_ul,
    "Q1:Y_info"=>q1_info, "Q2:Y_info"=>q2_info, "Q3:Y_info"=>q3_info, "Q4:Y_info"=>q4_info,
))

compute_bootstrap_derived!(bd, LatVol, partition)
# bd[:mean] now includes "cond:<label>", "susp:<label>", "skew:<label>", "kurt:<label>",
# as well as post-cumulant "YmYP", "Y_P1", and "Y_P2" for each cumulant.

compute_bootstrap_derived!(
    bd::Dict, 
    LatVol::Int
) -> Nothing

Compute and store derived observables (condensate, susceptibility, skewness, kurtosis) from bootstrap-averaged quark moment data ($Q_{n} \; (n=1,2,3,4)$).

Arguments

• bd::Dict: A dictionary containing :mean key, which maps to another dictionary that must include entries of the form "Qn:<label>" for n = 1 to 4 and various <label> strings.
• LatVol::Int: Lattice volume, used to normalize condensate and susceptibility values.

Behavior

• For each label in the predefined list of observables ("Y_info", "YmYP", etc.), the function computes:
  • "cond:<label>": chiral condensate using $Q_1$,
  • "susp:<label>": susceptibility using $Q_1$ and $Q_2$,
  • "skew:<label>": skewness using $Q_1$, $Q_2$, $Q_3$,
  • "kurt:<label>": kurtosis using $Q1$, $Q_2$, $Q_3$, $Q_4$.
• The results are stored in-place under bd[:mean].

Returns

• Nothing: This function mutates bd in-place.

Requirements

• The bd[:mean] dictionary must contain all required moment keys for each target label.
• The functions Deborah.Esther.SingleCumulant.calc_quark_condensate, Deborah.Esther.SingleCumulant.calc_susceptibility, Deborah.Esther.SingleCumulant.calc_skewness, and Deborah.Esther.SingleCumulant.calc_kurtosis must be defined.