denotes the N ( a, b $^{2}$) density function. The models considered were the following: 1. One-component models (7) and (8) with no warping and φ$_{1}$ ( t ) = ψ$_{1}$ ( t ) = ϕ ( t, . 3 , . 1) / 1 . 68 . The variances were γ$_{1}$ = . 2 2 and λ 1 = . 1 $^{2}$, so h$_{z}$ = . 80 . 2. One-component models (7) and (8) with no warping but with different components for α ( t ) and β ( t ) : φ$_{1}$ ( t ) as in Model 1, but ψ$_{1}$ ( t ) = ϕ ( t, . 6 , . 1) / 1 . 68 . The variances γ$_{1}$ and λ 1 were as in Model 1. 3. Same α ( t ) and β ( t ) as in Model 1, but with a Hermite-spline warping process w ( t ) with knot τ 0 = . 3 and variances Σ = . 2 2 and Ω = . 1 $^{2}$, so h$_{w}$ = . 80 . 4. Same α ( t ) and β ( t ) as in Model 2, with warping w ( t ) as in Model 3. 5. Same α ( t ) and β ( t ) as in Model 1, but with a warping process w ( t ) with knots τ$_{0}$ = ( . 3 , . 6) and covariance matrices Σ = . 2 $^{2}$I$_{2}$ and Ω = . 1 $^{2}$I$_{2}$ , so h$_{w}$ = . 80 as before. 6. Same α ( t ) and β ( t ) as in Model 2, with warping w ( t ) as in Model 5. 7. Same as Model 4, but the random factors U and V in (7) and (8) have Student’s t distributions with 4 degrees of freedom and scale parameters γ 1 / 2 1 = . 2 and λ 1 / 2 1 = . 1 (so the variance ratio is still h$_{z}$ = . 80 ). 8. Same as Model 4, but the random factors U and V in (7) and (8) have contaminated Normal distributions (1 − ε ) N (0 , γ$_{1}$ )+ εN (0 , kγ$_{1}$ ) and (1 − ε ) N (0 , λ 1 )+ εN (0 , kλ 1 ) respectively, with ε = . 10 and k = 5 (the variance ratio is still h$_{z}$ = . 80 ). 9. Two-component models (7) and (8), with φ$_{1}$ ( t ) = ψ$_{1}$ ( t ) = ϕ ( t, . 3 , . 1) / 1 . 68 , φ$_{2}$ ( t ) = ψ$_{2}$ ( t ) = ( ϕ ( t, . 6 , . 1) / 1 . 68 − . 105 φ$_{1}$ ( t )) /. 99 (so that each pc is associated with am- plitude variation at each peak), variances γ$_{1}$ = . 2 $^{2}$, γ$_{2}$ = . 1 $^{2}$, λ 1 = . 1 $^{2}$, λ 2 = . 05 2 (so h$_{z}$ = . 80 as in previous models), and a one-knot warping process as in Model 3. 16