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Logarithmic scale heatmap representing the value of the ξ-ratio for the additivity of the Fisher information on an Ising chain. Notice the difference between the ferromagnetic and the anti-ferromagnetic regimes. The emerging feature of a particularly high ξ from B /J = −2 to B /J → ∞ (zeroderivative curve) is discussed in the main text. As described in the main text, F1(T ) → ∞ for B → 0, hence leading to a divergence of the ξ ratio. In the plot, all areas with ξ > 10 10 are shaded in white.
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Many real-world tasks include some kind of parameter estimation, i.e., determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic process with temporal correlations, the random variables that constitute it are identically distributed but not...
Contexts in source publication
Context 1
... behaviour corresponds to ξ > 1, and subadditive to ξ < 1; independent random variables yield a perfectly additive behaviour with ξ = 1. The value of ξ for a wide choice of parameters is represented in Figure 4. It is apparent that there is a significant difference between the behaviours in the ferromagnetic and the antiferromagnetic regimes: the first gives ξ 1 almost everywhere, corresponding to a slightly sub-additive Fisher information. ...
Context 2
... perspective allows us also to interpret the emerging curve labeled as zero-derivative curve in Figure 4 in the anti-ferromagnetic region. The curve corresponds to point of maximum or minimum of the one-site probability P (↑) with respect to the temperature; consequently, they have zero derivative and zero one-site thermal Fisher information, hence causing a divergence of the ξ ratio. ...
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