Climatic changes -- Effect of human beings on -- Religious aspects -- Christianity.

c.1941.

United Kingdom, c.193?

England, 1923.

England, 1923.

c.1941.

United Kingdom, c.193?

Lisbonne : Impr. de l'Académie royale des sciences, 1881.

Paris : J.-B. Baillière, 1870.

London : Adlard, 1904.

Paris : J.-B. Baillière, 1878.

Edinburgh : printed by J. Stark, [1836?]

London : Macmillan, 1893.

Rockville, Maryland : National Institute on Drug Abuse, 1986.

Notre Dame coach Muffet McGraw retired after 33 seasons Wednesday. What she did for me in those four years, I came in as a girl and left as a woman.'' - WNBA player Kayla McBride, who played for Notre Dame from 2010-14.

Gregor Pasemann, Wilhelm Stannat.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 547--579.

Abstract:
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part. Emphasis is put on the case of stochastic reaction-diffusion systems. Robustness results for statistical inference under model uncertainty are provided.

Wei Li, Subhashis Ghosal.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1707--1743.

Abstract:
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional characterization of multivariate data. There have been some recent theoretical studies of filaments in the nonparametric kernel density estimation context. This paper supplements the current literature in two ways. First, we provide a Bayesian approach to the filament estimation in regression context and study the posterior contraction rates using a finite random series of B-splines basis. Compared with the kernel-estimation method, this has a theoretical advantage as the bias can be better controlled when the function is smoother, which allows obtaining better rates. Assuming that $f:mathbb{R}^{2}mapsto mathbb{R}$ belongs to an isotropic Hölder class of order $alpha geq 4$, with the optimal choice of smoothing parameters, the posterior contraction rates for the filament points on some appropriately defined integral curves and for the Hausdorff distance of the filament are both $(n/log n)^{(2-alpha )/(2(1+alpha ))}$. Secondly, we provide a way to construct a credible set with sufficient frequentist coverage for the filaments. We demonstrate the success of our proposed method in simulations and one application to earthquake data.

Fabien Panloup, Samy Tindel, Maylis Varvenne.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1075--1136.

Abstract:
In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is based on the identification of the invariant measure, and we provide consistency results as well as some information about the convergence rate. We also give some examples of coefficients for which the identifiability assumption for the invariant measure is satisfied.

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian matrix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interactions effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.

Durba Bhattacharya, Sourabh Bhattacharya.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 71--89.

Abstract:
Present day bio-medical research is pointing towards the fact that cognizance of gene–environment interactions along with genetic interactions may help prevent or detain the onset of many complex diseases like cardiovascular disease, cancer, type2 diabetes, autism or asthma by adjustments to lifestyle. In this regard, we propose a Bayesian semiparametric model to detect not only the roles of genes and their interactions, but also the possible influence of environmental variables on the genes in case-control studies. Our model also accounts for the unknown number of genetic sub-populations via finite mixtures composed of Dirichlet processes. An effective parallel computing methodology, developed by us harnesses the power of parallel processing technology to increase the efficiencies of our conditionally independent Gibbs sampling and Transformation based MCMC (TMCMC) methods. Applications of our model and methods to simulation studies with biologically realistic genotype datasets and a real, case-control based genotype dataset on early onset of myocardial infarction (MI) have yielded quite interesting results beside providing some insights into the differential effect of gender on MI.

Nandini Kannan, Debasis Kundu.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 2--17.

Abstract:
In this article, we consider models for time-to-event data obtained from experiments in which stress levels are altered at intermediate stages during the observation period. These experiments, known as step-stress tests, belong to the larger class of accelerated tests used extensively in the reliability literature. The analysis of data from step-stress tests largely relies on the popular cumulative exposure model. However, despite its simple form, the utility of the model is limited, as it is assumed that the hazard function of the underlying distribution is discontinuous at the points at which the stress levels are changed, which may not be very reasonable. Due to this deficiency, Kannan et al. ( Journal of Applied Statistics 37 (2010b) 1625–1636) introduced the cumulative risk model, where the hazard function is continuous. In this paper, we propose a class of parametric models based on the cumulative risk model assuming the underlying population contains long-term survivors or ‘cured’ fraction. An EM algorithm to compute the maximum likelihood estimators of the unknown parameters is proposed. This research is motivated by a study on altitude decompression sickness. The performance of different parametric models will be evaluated using data from this study.

Katarzyna Jańczak-Borkowska.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 480--497.

Abstract:
We prove the existence and uniqueness of the solution of backward stochastic variational inequalities with respect to fractional Brownian motion and with non-Lipschitz coefficient. We assume that $H>1/2$.

Sophie Achard, Jean-François Coeurjolly

Source: Statist. Surv., Volume 4, 117--147.

Abstract:
This paper gives an overview of the problem of estimating the Hurst parameter of a fractional Brownian motion when the data are observed with outliers and/or with an additive noise by using methods based on discrete variations. We show that the classical estimation procedure based on the log-linearity of the variogram of dilated series is made more robust to outliers and/or an additive noise by considering sample quantiles and trimmed means of the squared series or differences of empirical variances. These different procedures are compared and discussed through a large simulation study and are implemented in the R package dvfBm.

In Canada, financial advisors and dealers by provincial securities commissions, and those self-regulatory organizations charged with direct regulation over investment dealers and mutual fund dealers, respectively to collect and maintain Know Your Client (KYC) information, such as their age or risk tolerance, for investor accounts. With this information, investors, under their advisor's guidance, make decisions on their investments which are presumed to be beneficial to their investment goals. Our unique dataset is provided by a financial investment dealer with over 50,000 accounts for over 23,000 clients. We use a modified behavioural finance recency, frequency, monetary model for engineering features that quantify investor behaviours, and machine learning clustering algorithms to find groups of investors that behave similarly. We show that the KYC information collected does not explain client behaviours, whereas trade and transaction frequency and volume are most informative. We believe the results shown herein encourage financial regulators and advisors to use more advanced metrics to better understand and predict investor behaviours.

Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($alpha$) that controls the amount of regularization. Cross-validation is typically used to select the best $alpha$ from a set of candidates. However, efficient and appropriate selection of $alpha$ can be challenging, particularly where large amounts of data are analyzed. Because the selected $alpha$ depends on the scale of the data and predictors, it is not straightforwardly interpretable. Here, we propose to reparameterize RR in terms of the ratio $gamma$ between the L2-norms of the regularized and unregularized coefficients. This approach, called fractional RR (FRR), has several benefits: the solutions obtained for different $gamma$ are guaranteed to vary, guarding against wasted calculations, and automatically span the relevant range of regularization, avoiding the need for arduous manual exploration. We provide an algorithm to solve FRR, as well as open-source software implementations in Python and MATLAB (https://github.com/nrdg/fracridge). We show that the proposed method is fast and scalable for large-scale data problems, and delivers results that are straightforward to interpret and compare across models and datasets.

Yicheng Li, Adrian E. Raftery.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 381--408.

Abstract:
Smoking is one of the leading preventable threats to human health and a major risk factor for lung cancer, upper aerodigestive cancer and chronic obstructive pulmonary disease. Estimating and forecasting the smoking attributable fraction (SAF) of mortality can yield insights into smoking epidemics and also provide a basis for more accurate mortality and life expectancy projection. Peto et al. ( Lancet 339 (1992) 1268–1278) proposed a method to estimate the SAF using the lung cancer mortality rate as an indicator of exposure to smoking in the population of interest. Here, we use the same method to estimate the all-age SAF (ASAF) for both genders for over 60 countries. We document a strong and cross-nationally consistent pattern of the evolution of the SAF over time. We use this as the basis for a new Bayesian hierarchical model to project future male and female ASAF from over 60 countries simultaneously. This gives forecasts as well as predictive distributions that can be used to find uncertainty intervals for any quantity of interest. We assess the model using out-of-sample predictive validation and find that it provides good forecasts and well-calibrated forecast intervals, comparing favorably with other methods.

Mohamad Elmasri, Maxwell J. Farrell, T. Jonathan Davies, David A. Stephens.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 221--240.

Abstract:
Identifying undocumented or potential future interactions among species is a challenge facing modern ecologists. Recent link prediction methods rely on trait data; however, large species interaction databases are typically sparse and covariates are limited to only a fraction of species. On the other hand, evolutionary relationships, encoded as phylogenetic trees, can act as proxies for underlying traits and historical patterns of parasite sharing among hosts. We show that, using a network-based conditional model, phylogenetic information provides strong predictive power in a recently published global database of host-parasite interactions. By scaling the phylogeny using an evolutionary model, our method allows for biological interpretation often missing from latent variable models. To further improve on the phylogeny-only model, we combine a hierarchical Bayesian latent score framework for bipartite graphs that accounts for the number of interactions per species with host dependence informed by phylogeny. Combining the two information sources yields significant improvement in predictive accuracy over each of the submodels alone. As many interaction networks are constructed from presence-only data, we extend the model by integrating a correction mechanism for missing interactions which proves valuable in reducing uncertainty in unobserved interactions.

Qiwei Li, Xinlei Wang, Faming Liang, Guanghua Xiao.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1708--1732.

Abstract:
With the advance of imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high resolution. Recent developments in deep-learning methods have enabled us to identify and classify individual cells from digital pathology images at large scale. Reliable statistical approaches to model the spatial pattern of cells can provide new insight into tumor progression and shed light on the biological mechanisms of cancer. We consider the problem of modeling spatial correlations among three commonly seen cells observed in tumor pathology images. A novel geostatistical marking model with interpretable underlying parameters is proposed in a Bayesian framework. We use auxiliary variable MCMC algorithms to sample from the posterior distribution with an intractable normalizing constant. We demonstrate how this model-based analysis can lead to sharper inferences than ordinary exploratory analyses, by means of application to three benchmark datasets and a case study on the pathology images of $188$ lung cancer patients. The case study shows that the spatial correlation between tumor and stromal cells predicts patient prognosis. This statistical methodology not only presents a new model for characterizing spatial correlations in a multitype spatial point pattern conditioning on the locations of the points, but also provides a new perspective for understanding the role of cell–cell interactions in cancer progression.

Jorge A. León.

Source: Bernoulli, Volume 26, Number 3, 2436--2462.

Abstract:
Let $B^{H}$ be a fractional Brownian motion with Hurst parameter $Hin (0,1/2)$ and $p:mathbb{R} ightarrow mathbb{R}$ a polynomial function. The main purpose of this paper is to introduce a Stratonovich type stochastic integral with respect to $B^{H}$, whose domain includes the process $p(B^{H})$. That is, an integral that allows us to integrate $p(B^{H})$ with respect to $B^{H}$, which does not happen with the symmetric integral given by Russo and Vallois ( Probab. Theory Related Fields 97 (1993) 403–421) in general. Towards this end, we combine the approaches utilized by León and Nualart ( Stochastic Process. Appl. 115 (2005) 481–492), and Russo and Vallois ( Probab. Theory Related Fields 97 (1993) 403–421), whose aims are to extend the domain of the divergence operator for Gaussian processes and to define some stochastic integrals, respectively. Then, we study the relation between this Stratonovich integral and the extension of the divergence operator (see León and Nualart ( Stochastic Process. Appl. 115 (2005) 481–492)), an Itô formula and the existence of a unique solution of some Stratonovich stochastic differential equations. These last results have been analyzed by Alòs, León and Nualart ( Taiwanese J. Math. 5 (2001) 609–632), where the Hurst paramert $H$ belongs to the interval $(1/4,1/2)$.

Ivan Nourdin, Giovanni Peccati, Stéphane Seuret.

Source: Bernoulli, Volume 26, Number 3, 1619--1634.

Abstract:
We describe the size of the sets of sojourn times $E_{gamma }={tgeq 0:|B_{t}|leq t^{gamma }}$ associated with a fractional Brownian motion $B$ in terms of various large scale dimensions.

Richard A. Davis, Mikkel Slot Nielsen, Victor Rohde.

Source: Bernoulli, Volume 26, Number 2, 799--827.

Abstract:
In this paper, we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying autocovariance functions. The model departs from the usual way of incorporating this type of long-range dependence into a short-memory model as it is obtained by applying a fractional filter to the drift term rather than to the noise term. The advantages of this approach are that the corresponding long-range dependent solutions are semimartingales and the local behavior of the sample paths is unaffected by the degree of long memory. We prove existence and uniqueness of solutions to the SFDDEs and study their spectral densities and autocovariance functions. Moreover, we define a subclass of SFDDEs which we study in detail and relate to the well-known fractionally integrated CARMA processes. Finally, we consider the task of simulating from the defining SFDDEs.

Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons.

Source: Bernoulli, Volume 26, Number 1, 352--386.

Abstract:
In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $Hin (0,1)$. The drift term is assumed to be globally Lipschitz. We prove that the solution of each of the above equations is continuous in terms of the index $H$, with respect to the convergence in law in the space of continuous functions.

Stepan Mazur, Dmitry Otryakhin, Mark Podolskij.

Source: Bernoulli, Volume 26, Number 1, 226--252.

Abstract:
In this paper, we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter $sigma>0$, the self-similarity parameter $Hin(0,1)$ and the stability index $alphain(0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently studied in ( Ann. Probab. 45 (2017) 4477–4528). More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(sigma,alpha,H)$. We present the law of large numbers and some fully feasible weak limit theorems.

Stephanie McMains
Jan 12, 2011; 31:587-597
BehavioralSystemsCognitive

M Niethammer
Apr 1, 1996; 16:2157-2163
Articles

EL Bienenstock
Jan 1, 1982; 2:32-48
Articles

Jamie D. Roitman
Nov 1, 2002; 22:9475-9489
Behavioral