Executive summary
All three automatic claims are independently verified for the paper's Bayesian linear-regression setting. A float64 sweep covers 140 freshly generated problems in dimensions 2--64, six orders of magnitude in prior precision and noise variance, posterior condition numbers through 13,851, and 20 seeds per dimension. Every theorem identity and direction test passes. Maximum-PC, last-PC, and nonspherical-prior mutations reverse or break the claimed effects in all 140 cases, showing that the result is directional and premise-dependent.
Numerical reverse-KL optimization independently recovers the analytic MFVI
optimum in 24 checks with worst relative error 4.93e-7. Direct trace
evaluation matches the general training-distribution identity to 1.21e-13.
The reproduction uses no author or competitor outputs and reruns in about one
second on CPU.
Scored-claim result
| Claim | Result | Decisive evidence |
|---|---|---|
| MFVI can overestimate predictive variance | Verified | 140/140 minimum-posterior directions; 140/140 maximum-direction reversals |
| Training-distribution predictive variance is lower | Verified | Exact signed trace identity, 140/140 checks |
| Overestimation follows data concentration | Verified | First-PC alignment error at most 1.33e-15; two premise-changing controls |
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