The Pipeline
Evidence is defined through the Feynman–Kac representation. Wick rotation and Euler's formula bridge quantum amplitudes to statistics. Bayesian updating yields beliefs given evidence. Stability is governed by the ∆/β principle with Abel-type convergence and Jacobian correction.
Worked Example: How Many Words Remain Unseen?
Given a finite sample of text, how many distinct words have not yet appeared? The data-as-evidence approach uses the frequency of frequencies fj from n word tokens. The Quantostats route models the sample with the Chinese Restaurant Process with parameter θ (the measurable ∆ of Chapter 4). The expected number of new types among the next m tokens is θ [ψ(n + m + θ) − ψ(n + θ)] → θ log(1 + m/n).
Unlike the raw series, this formula remains finite and stable at every m, growing only logarithmically.
The Toolkit
A unified pipeline drawing on statistical theory, complex analysis, stochastic calculus and quantum formalism.
The Central Conjecture
Does β Add Anything?
Local Asymptotic Normality
Obstruction from Spectral Geometry
Cross-Domain Claims
Classical Results, Cited Correctly
Quantostats builds on established theory: the Feynman–Kac formula, Bayes' theorem, Cauchy's residue theorem, Abel's theorem, Whittle likelihood, conformal prediction's coverage guarantee, Le Cam's lemmas, Girsanov's theorem, Wilks' theorem, Weyl's law, the James–Stein estimator, and Schwartz's posterior-consistency theorem. Every classical result is attributed to its source, and the book distinguishes rigorously between what is proven in the literature and what is proposed here. This transparency is foundational: a research programme earns trust by naming its debts and its conjectures clearly.
Heuristic Arguments and Open Questions
Sections labeled 'Stability Sketch' present the case for ∆/β-type correction. They are not derivations and are set off in a shaded box. Chapter 4 is the one grounded case: it defines ∆ as the Ewens sampling parameter θ of population genetics, estimable directly from allele-count data, for example from the number of distinct alleles or from sample homozygosity, the quantity behind the Ewens–Watterson test (Watterson, 1978). Elsewhere, ∆ remains an analogy. Chapter 16 lists the open problems frankly: no jointly established (∆, β) pair with proven uniform stability, the unresolved contribution of β in the non-parametric setting, the gap in local asymptotic normality proofs, the obstruction from isospectral non-isometric domains in spectral geometry, and the illustrative (not structural) status of cross-domain case studies. Honest labeling is the book's signature move.
The Book
'Quantum Bayesianism and Beyond: Statistical and Bayesian Inference in Complex Quantum Systems' (Expanded Edition, 2026)
This 93-page PDF, typeset in LaTeX, offers a rigorous exploration of quantum inference. Each chapter opens with an epigraph from the Sherlock Holmes stories. The Expanded Edition enriches the original with formal results, proof sketches, and worked examples: a non-linear path-dependent Jacobian via Girsanov's theorem (§8), explicit quadratic-mean-differentiability for spectral families (§11), connections between non-parametric methods and Schwartz's theorem (§7), and a complete applied demonstration (Chapter 15).
About the Author
Join the Research Conversation
Who Is It For?
Researchers in quantum physics and quantum information who want stronger statistical tools for their experimental and theoretical work.
Statisticians interested in quantum-inspired inference and how quantum mechanics reshapes classical frameworks for probability and estimation.
Graduate students looking for a research-level text with worked examples that bridge pedagogical clarity and cutting-edge methodology.
Readers who want to see how a speculative framework can be labeled honestly without overstating its current empirical reach.
Comments on the open problems in Chapter 16 are especially welcome.
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