Examples of moderate deviation principle for diffusion processes

Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a family $$S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH(X_s)ds, \ t\to\infty$$ for an ergodic diffusion process $X_t$ under $0.5<\kappa<1$ and appropriate $H$. We mean a decomposition with ``corrector'': $$\frac{1}{t^\kappa}\int_0^tH(X_s)ds={\rm corrector}+\frac{1}{t^\kappa}\underbrace{M_t}_{\rm martingale}.$$ and show that, as in the CLT analysis, the corrector is negligible but in the MD scale, and the main contribution in the MD brings the family ``$\frac{1}{t^\kappa}M_t, t\to\infty.$'' Starting from Bayer and Freidlin, \cite{BF}, and finishing by Wu's papers \cite{Wu1}-\cite{WuH}, in the MD study Laplace's transform dominates. In the paper, we replace the Laplace technique by one, admitting to give the conditions, providing the MD, in terms of ``drift-diffusion'' parameters and $H$. However, a verification of these conditions heavily depends on a specificity of a diffusion model. That is why the paper is named ``Examples ...''

Transportation cost-information inequalities and applications to random dynamical systems and diffusions

We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000053

Moderate deviations for particle filtering

Consider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and (Y_t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations (Y_1,...,Y_t). The particle filtering method gives an approximation of the law L(X_t|Y_1,...,Y_t) by an empirical measure \frac{1}{n}\sum_1^n\delta_{x_{i,t}}. In this paper we establish the moderate deviation principle for the empirical mean \frac{1}{n}\sum_1^n\psi(x_{i,t}) (centered and properly rescaled) when the number of particles grows to infinity, enhancing the central limit theorem. Several extensions and examples are also studied.Comment: Published at http://dx.doi.org/10.1214/105051604000000657 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Convergence of adaptive mixtures of importance sampling schemes

In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for adaptive mixtures of population Monte Carlo algorithms and show that Rao--Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions do not benefit from repeated updating.Comment: Published at http://dx.doi.org/10.1214/009053606000001154 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

How long should arthroscopic clavicular resection be in acromioclavicular arthropathy? A radiological-clinical study (with computed tomography) of 18 cases at a mean 4 years’ follow-up

AbstractIntroductionEndoscopic clavicular resection is a common procedure, but few studies have analyzed predictive factors for outcome.Hypotheses1) Computed tomography (CT) of clavicular resection is reproductible; 2) Functional outcome correlates with resection length; 3) Other factors also influence outcome.Material and methodsPatients operated on between 2005 and 2010 were called back to establish functional scores (Constant, Simple Shoulder Test [SST], satisfaction) and undergo low-dose bilateral comparative computed tomography (CT) centered on the acromioclavicular joints. The assessment criteria were resection edge parallelism and resection length, measured using OsiriX® software. Radiological and clinical data were correlated.Results18 out of 21 patients (85%: 3 female, 15 male) were assessed. Mean age at surgery was 49 years (range, 40–62 yrs); mean follow-up was 4.2 years (1.6–7.2 yrs). Mean Constant score rose from 57.7 (25–85) to 70.2 (30–96); mean postoperative SST was 9.3 (3–12). 11 patients had very good and 4 poor results. CT resection length was reproducible, with intraclass, intra- and interobserver correlation coefficients >95%. There was no significant correlation between articular resection length on CT and functional scores (P=0.2). Functional scores were negatively influenced by an occupational pathologic context (P<0.01) and by associated tendinopathy.Discussion and conclusionLow-dose CT enabled reproducible analysis of clavicular resection. The hypothesized correlation between resection length and functional result was not confirmed. Work accidents and occupational disease emerged as risk factors.Level of evidenceSingle-center retrospective analytic cohort study. Level 4, guideline grade C

Entrapment and traumatic neuropathies of the elbow and hand: An imaging approach

AbstractUltrasound and magnetic resonance imaging currently offer a detailed analysis of the peripheral nerves. Compressive and traumatic nerve injuries are the two main indications for imaging investigation of nerves with several publications describing the indications, technique and diagnostic capabilities of imaging signs. Investigation of entrapment neuropathies has three main goals, which are to confirm neuronal distress, search for the cause of nerve compression and exclude a differential diagnosis on the entire nerve. For traumatic nerve injuries, imaging, predominantly ultrasound, occasionally provides essential information for management including the type of nerve lesion, its exact site and local extension

Specific boundaries between the causal agents of the soybean stem canker

Pathogens within the Diaporthe complex cause seed decay, stem blight and stem canker on soybean, representing a serious threat for this crop species. We herein utilize worldwide sequence data retrieved from Genbank in order to assess the species boundaries between the soybean stem canker causal agents, and define whether or not they should be regarded as members of the same biological species. These studies were complemented with compatibility tests, in order to validate our findings from a biological standpoint. Species delimitation assays supported the occurrence of a speciation event between D. caulivora and D. phaseolourm var. meridionalis. A speciation hypothesis between D. aspalathi and D. phaseolourm var. meridionalis was also supported, based on three reciprocally monophyletic substitutions at locus EF1-α. Compatibility tests further validated species delimitation assays indicating that D. caulivora has developed barriers to gene exchange with D. phaseolorum var. meridionalis. Clarification of the specific boundaries of the SSC pathogens and related entities will be an important asset to future research in soybean pathology, epidemiology and breeding.Fil: Guillin, Eduardo A.. Instituto Nacional de Tecnología Agropecuaria. Centro de Investigación en Ciencias Veterinarias y Agronómicas. Instituto de Genética; ArgentinaFil: Grijalba, Pablo Enrique. Universidad de Buenos Aires. Facultad de Agronomia; ArgentinaFil: Oliveira, Luiz Orlando de. Universidade Federal de Viçosa; BrasilFil: Gottlieb, Alexandra Marina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Ecología, Genética y Evolución de Buenos Aires; Argentin

Convergence of adaptive sampling schemes

International audienceIn the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performances of a given kernel can clarify how adequate it is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is quite complex and most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for a wide class of population Monte Carlo algorithms and show that Rao-Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions simply do not benefit from repeated updating