Predictive Constructions Based on Measure-Valued Pólya Urn Processes

Measure-valued Pólya urn processes (MVPP) are Markov chains with an additive structure that serve as an extension of the generalized k-color Pólya urn model towards a continuum of pos- sible colors. We prove that, for any MVPP $(\mu_n)_{n ≥ 0}$ on a Polish space $\mathbb{X}$, the normalized sequence $( \mu_n / \mu_n (\mathbb{X}) )_{n \ge 0}$ agrees with the marginal predictive distributions of some random process $(X_n)_{n \ge 1}$. Moreover, $\mu_n = \mu_{n − 1} + R_{X_n}, \ n \ge 1$, where $x \mapsto R_x$ is a random transition kernel on $\mathbb{X}$; thus, if $\mu_{n − 1}$ represents the contents of an urn, then X n denotes the color of the ball drawn with distribution $\mu_{n − 1} / \mu_{n − 1}(\mathbb{X})$ and $R_{X_{n}}$ - the subsequent reinforcement. In the case $R_{X_{n}} = W_n\delta_{X_n}$, for some non-negative random weights $W_1, \ W_2, \$ ... , the process $( X_n )_{n \ge 1}$ is better understood as a randomly reinforced extension of Blackwell and MacQueen’s Pólya sequence. We study the asymptotic properties of the predictive distributions and the empirical frequencies of $( X_n )_{n \ge 1}$ under different assumptions on the weights. We also investigate a generalization of the above models via a randomization of the law of the reinforcement

Registros destacados de Spilogale angustifrons en la Reserva de la Biosfera Calakmul

Spilogale angustifrons has a wide distribution in southeastern Mexico, however, knowledge is scarce for the Calakmul region. New spotted records are reported S. angustifrons in the Calakmul region, Campeche, Mexico. With a cumulative effort of 9000 trap-nights, 18 photographs of southern spotted skunks corresponding to 15 independent events were obtained at four photo-trapping stations in the Calakmul region. At the photo-trapping stations, four photographic events were recorded in which solitary male individuals were observed, but it was not possible to identify whether the records correspond to one or more individuals. The few records of S. angustifrons in the Yucatan Peninsula may be due to the lack of mastozoological surveys in the region. The records reported in this note provide knowledge on the distribution, habitat, use of artificial watering places and interspecific relationships of S. angustifrons. Being a carnivore, it is likely that the ecological role of S. angustifrons in the Calakmul region is relevant, however the population and ecological aspects of the species are unknown, so it is necessary to conduct studies focused on the status of the populations of S. angustifrons.Spilogale angustifrons cuenta con una amplia distribución en el sureste de México, sin embargo, para la región de Calakmul el conocimiento es escaso. Se reportan nuevos registros de S. angustifrons en la región de Calakmul, Campeche, México. Con un esfuerzo acumulado de 9000 noches-trampa, se obtuvieron 18 fotografías de S. angustifrons que corresponden a 15 eventos independientes, en cuatro estaciones de fototrampeo colocadas en la región de Calakmul. En las estaciones de fototrampeo se registraron cuatro eventos fotográficos en los que se observan a individuos machos, solitarios, pero no fue posible identificar si los registros corresponden a uno o más individuos. Los pocos registros de S. angustifrons en la Península de Yucatán puede deberse a la falta de prospecciones mastozoológicas en la región. Los registros reportados en esta nota, aportan conocimiento sobre la distribución, hábitat, uso de bebederos artificiales y relaciones interespecíficas de S. angustifrons. Al ser un carnívoro es probable que el papel ecológico de S. angustifrons en la región de Calakmul sea relevante, sin embargo los aspectos poblacionales y ecológicos de la especie se desconocen, por lo que es necesario realizar estudios enfocados a conocer el estado de las poblaciones de S. angustifron

Persistent C-peptide secretion in Type 1 diabetes and its relationship to the genetic architecture of diabetes

Background: The objective of this cross-sectional study was to explore the relationship of detectable C-peptide secretion in type 1 diabetes to clinical features and to the genetic architecture of diabetes. Methods: C-peptide was measured in an untimed serum sample in the SDRNT1BIO cohort of 6076 Scottish people with clinically diagnosed type 1 diabetes or latent autoimmune diabetes of adulthood. Risk scores at loci previously associated with type 1 and type 2 diabetes were calculated from publicly available summary statistics. Results: Prevalence of detectable C-peptide varied from 19% in those with onset before age 15 and duration greater than 15 years to 92% in those with onset after age 35 and duration less than 5 years. Twenty-nine percent of variance in C-peptide levels was accounted for by associations with male gender, late age at onset and short duration. The SNP heritability of residual C-peptide secretion adjusted for gender, age at onset and duration was estimated as 26%. Genotypic risk score for type 1 diabetes was inversely associated with detectable C-peptide secretion: the most strongly associated loci were the HLA and INS gene regions. A risk score for type 1 diabetes based on the HLA DR3 and DQ8-DR4 serotypes was strongly associated with early age at onset and inversely associated with C-peptide persistence. For C-peptide but not age at onset, there were strong associations with risk scores for type 1 and type 2 diabetes that were based on SNPs in the HLA region but not accounted for by HLA serotype. Conclusions: Persistence of C-peptide secretion varies widely in people clinically diagnosed as type 1 diabetes. C-peptide persistence is influenced by variants in the HLA region that are different from those determining risk of early-onset type 1 diabetes. Known risk loci for diabetes account for only a small proportion of the genetic effects on C-peptide persistence

Comparative Transmissibility of SARS-CoV-2 Variants Delta and Alpha in New England, USA

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Delta variant quickly rose to dominance in mid-2021, displacing other variants, including Alpha. Studies using data from the United Kingdom and India estimated that Delta was 40-80% more transmissible than Alpha, allowing Delta to become the globally dominant variant. However, it was unclear if the ostensible difference in relative transmissibility was due mostly to innate properties of Delta\u27s infectiousness or differences in the study populations. To investigate, we formed a partnership with SARS-CoV-2 genomic surveillance programs from all six New England US states. By comparing logistic growth rates, we found that Delta emerged 37-163% faster than Alpha in early 2021 (37% Massachusetts, 75% New Hampshire, 95% Maine, 98% Rhode Island, 151% Connecticut, and 163% Vermont). We next computed variant-specific effective reproductive numbers and estimated that Delta was 58-120% more transmissible than Alpha across New England (58% New Hampshire, 68% Massachusetts, 76% Connecticut, 85% Rhode Island, 98% Maine, and 120% Vermont). Finally, using RT-PCR data, we estimated that Delta infections generate on average ∼6 times more viral RNA copies per mL than Alpha infections. Overall, our evidence indicates that Delta\u27s enhanced transmissibility could be attributed to its innate ability to increase infectiousness, but its epidemiological dynamics may vary depending on the underlying immunity and behavior of distinct populations

Comparative transmissibility of SARS-CoV-2 variants Delta and Alpha in New England, USA.

The SARS-CoV-2 Delta variant rose to dominance in mid-2021, likely propelled by an estimated 40%-80% increased transmissibility over Alpha. To investigate if this ostensible difference in transmissibility is uniform across populations, we partner with public health programs from all six states in New England in the United States. We compare logistic growth rates during each variant\u27s respective emergence period, finding that Delta emerged 1.37-2.63 times faster than Alpha (range across states). We compute variant-specific effective reproductive numbers, estimating that Delta is 63%-167% more transmissible than Alpha (range across states). Finally, we estimate that Delta infections generate on average 6.2 (95% CI 3.1-10.9) times more viral RNA copies per milliliter than Alpha infections during their respective emergence. Overall, our evidence suggests that Delta\u27s enhanced transmissibility can be attributed to its innate ability to increase infectiousness, but its epidemiological dynamics may vary depending on underlying population attributes and sequencing data availability

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon

Predictive characterization of mixtures of Markov chains

Predictive constructions are a powerful way of characterizing the probability laws of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are available, the predictive characterization implicitly defines the prior distribution, starting from assumptions on the observables; moreover, it often helps in designing efficient computational strategies. In this paper we give necessary and sufficient conditions on the sequence of predictive distributions such that they characterize a Markov exchangeable probability law for a discrete valued process \bX. Under recurrence, Markov exchangeable processes are mixtures of Markov chains. Our predictive conditions are in some sense minimal sufficient conditions for Markov exchangeability; we also provide predictive conditions for recurrence. We illustrate their application in relevant examples from the literature and in novel constructions

Prediction-based uncertainty quantification for exchangeable sequences

Prediction has a central role in the foundations of Bayesian statistics and is now the main focus in many areas of machine learning, in contrast to the more classical focus on inference. We discuss that, in the basic setting of random sampling - that is, in the Bayesian approach, exchangeability - uncertainty expressed by the posterior distribution and credible intervals can indeed be understood in terms of prediction. The posterior law on the unknown distribution is centered on the predictive distribution and we prove that it is marginally asymptotically Gaussian with variance depending on the predictive updates, i.e. on how the predictive rule incorporates information as new observations become available. This allows to obtain asymptotic credible intervals only based on the predictive rule (without having to specify the model and the prior law), sheds light on frequentist coverage as related to the predictive learning rule, and, we believe, opens a new perspective towards a notion of predictive efficiency that seems to call for further research