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Deathly deception : the real story of Operation Mincemeat
In the pre-dawn darkness of April 30, 1943, the body of a Royal Marine Major washed ashore on the south-western coast of Spain, part of an incredible plot to mislead the German High Command about the Allies' impending Mediterranean invasion. What made this ruse unique--and macabre--was that the \"Major\" was actually a deceased Welsh laborer, who drifted lifelessly ashore carrying false documents indicating that the Allies were set to launch an attack on Greece, rather than Sicily. In this accurate and in-depth retelling of the story behind the operation, Denis Smyth draws on a vast collection of previously unavailable documentary sources to expertly bring all phases of \"Mincemeat\" to life. He reveals how the architects of the plan navigated a maze of medical, technical, and logistical issues to deceive the enemy at the highest strategic levels.--From publisher description.
Book
The Ubiquitous Ewens Sampling Formula
Ewens's sampling formula exemplifies the harmony of mathematical theory, statistical application, and scientific discovery. The formula not only contributes to the foundations of evolutionary molecular genetics, the neutral theory of biodiversity, Bayesian nonparametrics, combinatorial stochastic processes, and inductive inference but also emerges from fundamental concepts in probability theory, algebra, and number theory. With an emphasis on its far-reaching influence throughout statistics and probability, we highlight these and many other consequences of Ewens's seminal discovery.
Journal Article
Using Theatrical Intimacy Practices to Create Vocal Health Boundaries
[...]she suffered \"symptoms of recurrent hoarseness, discomfort, and imbalance in her singing voice\" due to vocal fold lesions and a vascular polyp,3 which eventually necessitated surgery \"to rescue her singing voice. Borrowing the FRIES acronym established by Planned Parenthood, consent must be Freely given, Reversible, Informed, Enthusiastic/Engaged/Embodied, and Specific.6 In a consent-based environment, actors are encouraged to come to rehearsals with a clear understanding of their boundaries-physically, personally, professionally, culturally, and, we would argue, vocally. Actors in this situation who use the opportunity to work on the request as homework can solicit the advice of their full \"voice team,\" which may include a voice teacher, a vocal coach, and even health professionals at a voice clinic, like speech-language pathologists and/or laryngologists. Actors are shown choreography in rehearsals, then spend what may amount to hours of their own time outside of company rehearsals practicing the sequences in order to get them into their minds and bodies. [...]there is precedent for actors requiring outside time or designated closed rehearsals to work out particular challenges of the performance material.
Journal Article
Another view of sequential sampling in the birth process with immigration
We explore properties of the family sizes arising in a linear birth process with immigration (BI). In particular, we study the correlation of the number of families observed during consecutive disjoint intervals of time. Letting S(a, b) be the number of families observed in (a, b), we study the expected sample variance and its asymptotics for p consecutive sequential samples Sp=(S(t0,t1),⋯,S(tp-1,tp)), for 0=t0
Journal Article
A BERRY–ESSEEN THEOREM FOR PITMAN’S α-DIVERSITY
This paper contributes to the study of the random number Kn
of blocks in the random partition of {1, . . . , n} induced by random sampling from the celebrated two parameter Poisson–Dirichlet process. For any α ∈ (0, 1) and θ > −α Pitman (Combinatorial Stochastic Processes (2006) Springer, Berlin) showed that n
−α
n
−
α
K
n
→
a
.s
.
S
α
,
θ
as n → +∞, where the limiting random variable, referred to as Pitman’s α-diversity, is distributed according to a polynomially scaled Mittag–Leffler distribution function. Our main result is a Berry–Esseen theorem for Pitman’s α-diversity Sα,θ
, namely we show that
sup
x
≥
0
|
P
[
K
n
n
α
≤
x
]
−
P
[
S
α
,
θ
≤
x
]
|
≤
C
(
α
,
θ
)
n
α
holds for every n ∈ ℕ with an explicit constant term C(α, θ), for α ∈ (0, 1) and θ > 0. The proof relies on three intermediate novel results which are of independent interest: (i) a probabilistic representation of the distribution of Kn
in terms of a compound distribution; (ii) a quantitative version of the Laplace’s approximation method for integrals; (iii) a refined quantitative bound for Poisson approximation. An application of our Berry–Esseen theorem is presented in the context of Bayesian nonparametric inference for species sampling problems, quantifying the error of a posterior approximation that has been extensively applied to infer the number of unseen species in a population.
Journal Article
On Bernoulli trials with unequal harmonic success probabilities
A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and the time to the first success. Large sample asymptotics, statistical parameter estimation, and relations to Sibuya distributions and Yule–Simon distributions are discussed. This toy model is relevant in several applications including reliability, species sampling problems, record values breaking and random walks with disasters.
Journal Article
STEIN’S METHOD FOR THE POISSON–DIRICHLET DISTRIBUTION AND THE EWENS SAMPLING FORMULA, WITH APPLICATIONS TO WRIGHT–FISHER MODELS
We provide a general theorem bounding the error in the approximation of a random measure of interest—for example, the empirical population measure of types in a Wright–Fisher model—and a Dirichlet process, which is a measure having Poisson–Dirichlet distributed atoms with i.i.d. labels from a diffuse distribution. The implicit metric of the approximation theorem captures the sizes and locations of the masses, and so also yields bounds on the approximation between the masses of the measure of interest and the Poisson–Dirichlet distribution. We apply the result to bound the error in the approximation of the stationary distribution of types in the finite Wright–Fisher model with infinite-alleles mutation structure (not necessarily parent independent) by the Poisson–Dirichlet distribution. An important consequence of our result is an explicit upper bound on the total variation distance between the random partition generated by sampling from a finite Wright–Fisher stationary distribution, and the Ewens sampling formula. The bound is small if the sample size n is much smaller than N
1/6 log(N)−1/2, where N is the total population size. Our analysis requires a result of separate interest, giving an explicit bound on the second moment of the number of types of a finite Wright–Fisher stationary distribution. The general approximation result follows from a new development of Stein’s method for the Dirichlet process, which follows by viewing the Dirichlet process as the stationary distribution of a Fleming–Viot process, and then applying Barbour’s generator approach.
Journal Article
Involution factorizations of Ewens random permutations
An involution is a bijection that is its own inverse. Given a permutation $σ$ of $[n],$ let $\\mathsf{invol}(σ)$ denote the number of ways $σ$ can be expressed as a composition of two involutions of $[n].$ We prove that the statistic $\\mathsf{invol}$ is asymptotically lognormal when the symmetric groups $\\mathfrak{S}_n$ are each equipped with Ewens Sampling Formula probability measures of some fixed positive parameter $θ.$ This paper strengthens and generalizes previously determined results about the limiting distribution of $\\log(\\mathsf{invol})$ for uniform random permutations, i.e. the specific case of $θ= 1$. We also investigate the first two moments of $\\mathsf{invol}$ itself, detailing the phase transition in asymptotic behavior at $θ= 1,$ and provide a functional refinement and a convergence rate for the Gaussian limit law which is demonstrably optimal when $θ= 1.$
Journal Article
On nested infinite occupancy scheme in random environment
We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem for the cumulative occupancy counts as the number of balls approaches infinity. In the case of fragmentation driven by a homogeneous residual allocation model our result generalises the functional central limit theorem for the block counts in Ewens’ and more general regenerative partitions.
Journal Article
