Package jline.api.pfqn.nc

Class Pfqn_ble

java.lang.Object

jline.api.pfqn.nc.Pfqn_ble

public final class Pfqn_ble
extends Object

Field Summary

Fields

Modifier and Type	Field	Description
static final double	BLE_CORRECTION	The eps->0 bias in nats per Laplaced direction.

Method Summary

Modifier and Type	Method	Description
static Ret.pfqnNc	pfqn_ble(Matrix L, Matrix N)
static Ret.pfqnNc	pfqn_ble(Matrix L, Matrix N, Matrix Z)	Logistic expansion with an additive (1-log(2*pi)/2) bias correction per Gaussian direction the branch actually takes.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

BLE_CORRECTION

public static final double BLE_CORRECTION

The eps->0 bias in nats per Laplaced direction.

Method Details

pfqn_ble

public static Ret.pfqnNc pfqn_ble(Matrix L,
 Matrix N,
 Matrix Z)

Logistic expansion with an additive (1-log(2*pi)/2) bias correction per Gaussian direction the branch actually takes. Cas17 Theorem 4.1 holds for eps >= eps_N > 0; the K(1+eps*N) self-looping populations are what make the integrand concentrate. Evaluated at eps->0, as pfqn_le does, the curvature at the saddle tends to 1 rather than growing with N, so Laplace's method has no asymptotic regime there and carries an O(1) relative bias of e/sqrt(2*pi) PER LAPLACED DIRECTION. The count is the exponent on sqrt(2*pi) in the branch taken: M-1 with Z=0, where the radial integral is exact as Gamma(N+M), and M with Z>0, where the radius is Laplaced too. Measured over the 1562 models of the Cas17 dataset (Zenodo 546873, sec5.3.1, sigma=100), the Z>0 deficit is M to within 0.01 units. The published expansion is NOT in error and the correction is empirical; see _kb/03-api-layer.md.

pfqn_ble

public static Ret.pfqnNc pfqn_ble(Matrix L,
 Matrix N)