The very first case of corona-virus illness was recorded on 30 January 2020, in India and the number of infected cases, including the death toll, continues to rise. In this paper, we present short-term forecasts of COVID-19 for 28 Indian states and five union territories using real-time data from 30 January to 21 April 2020. Applying Holt's second-order exponential smoothing method and autoregressive integrated moving average (ARIMA) model, we generate 10-day ahead forecasts of the likely number of infected cases and deaths in India for 22 April to 1 May 2020. Our results show that the number of cumulative cases in India will rise to 36335.63 [PI 95% (30884.56, 42918.87)], concurrently the number of deaths may increase to 1099.38 [PI 95% (959.77, 1553.76)] by 1 May 2020. Further, we have divided the country into severity zones based on the cumulative cases. According to this analysis, Maharashtra is likely to be the most affected states with around 9787.24 [PI 95% (6949.81, 13757.06)] cumulative cases by 1 May 2020. However, Kerala and Karnataka are likely to shift from the red zone (i.e. highly affected) to the lesser affected region. On the other hand, Gujarat and Madhya Pradesh will move to the red zone. These results mark the states where lockdown by 3 May 2020, can be loosened.

In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in literature.

Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which extit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is straightforward to show that they have the same $mathcal{O}(1/sqrt{N})$ convergence rate as standard importance samplers, where $N$ is the number of Monte Carlo samples, the behaviour of adaptive importance samplers over the number of iterations has been left relatively unexplored. In this work, we investigate an adaptation strategy based on convex optimisation which leads to a class of adaptive importance samplers termed extit{optimised adaptive importance samplers} (OAIS). These samplers rely on the iterative minimisation of the $chi^2$-divergence between an exponential-family proposal and the target. The analysed algorithms are closely related to the class of adaptive importance samplers which minimise the variance of the weight function. We first prove non-asymptotic error bounds for the mean squared errors (MSEs) of these algorithms, which explicitly depend on the number of iterations and the number of samples together. The non-asymptotic bounds derived in this paper imply that when the target belongs to the exponential family, the $L_2$ errors of the optimised samplers converge to the optimal rate of $mathcal{O}(1/sqrt{N})$ and the rate of convergence in the number of iterations are explicitly provided. When the target does not belong to the exponential family, the rate of convergence is the same but the asymptotic $L_2$ error increases by a factor $sqrt{ ho^star} > 1$, where $ ho^star - 1$ is the minimum $chi^2$-divergence between the target and an exponential-family proposal.

The ability of intelligent agents to learn and remember multiple tasks sequentially is crucial to achieving artificial general intelligence. Many continual learning (CL) methods have been proposed to overcome catastrophic forgetting. Catastrophic forgetting notoriously impedes the sequential learning of neural networks as the data of previous tasks are unavailable. In this paper we focus on class incremental learning, a challenging CL scenario, in which classes of each task are disjoint and task identity is unknown during test. For this scenario, generative replay is an effective strategy which generates and replays pseudo data for previous tasks to alleviate catastrophic forgetting. However, it is not trivial to learn a generative model continually for relatively complex data. Based on recently proposed orthogonal weight modification (OWM) algorithm which can keep previously learned input-output mappings invariant approximately when learning new tasks, we propose to directly generate and replay feature. Empirical results on image and text datasets show our method can improve OWM consistently by a significant margin while conventional generative replay always results in a negative effect. Our method also beats a state-of-the-art generative replay method and is competitive with a strong baseline based on real data storage.

We present SmartExchange, an algorithm-hardware co-design framework to trade higher-cost memory storage/access for lower-cost computation, for energy-efficient inference of deep neural networks (DNNs). We develop a novel algorithm to enforce a specially favorable DNN weight structure, where each layerwise weight matrix can be stored as the product of a small basis matrix and a large sparse coefficient matrix whose non-zero elements are all power-of-2. To our best knowledge, this algorithm is the first formulation that integrates three mainstream model compression ideas: sparsification or pruning, decomposition, and quantization, into one unified framework. The resulting sparse and readily-quantized DNN thus enjoys greatly reduced energy consumption in data movement as well as weight storage. On top of that, we further design a dedicated accelerator to fully utilize the SmartExchange-enforced weights to improve both energy efficiency and latency performance. Extensive experiments show that 1) on the algorithm level, SmartExchange outperforms state-of-the-art compression techniques, including merely sparsification or pruning, decomposition, and quantization, in various ablation studies based on nine DNN models and four datasets; and 2) on the hardware level, the proposed SmartExchange based accelerator can improve the energy efficiency by up to 6.7$ imes$ and the speedup by up to 19.2$ imes$ over four state-of-the-art DNN accelerators, when benchmarked on seven DNN models (including four standard DNNs, two compact DNN models, and one segmentation model) and three datasets.

Effective property prediction methods can help accelerate the search for COVID-19 antivirals either through accurate in-silico screens or by effectively guiding on-going at-scale experimental efforts. However, existing prediction tools have limited ability to accommodate scarce or fragmented training data currently available. In this paper, we introduce a novel approach to learn predictors that can generalize or extrapolate beyond the heterogeneous data. Our method builds on and extends recently proposed invariant risk minimization, adaptively forcing the predictor to avoid nuisance variation. We achieve this by continually exercising and manipulating latent representations of molecules to highlight undesirable variation to the predictor. To test the method we use a combination of three data sources: SARS-CoV-2 antiviral screening data, molecular fragments that bind to SARS-CoV-2 main protease and large screening data for SARS-CoV-1. Our predictor outperforms state-of-the-art transfer learning methods by significant margin. We also report the top 20 predictions of our model on Broad drug repurposing hub.

The next seminar in the 2017–18 History of Pre-Modern Medicine seminar series takes place on Tuesday 16 January. Speaker: Dr Catherine Rider (University of Exeter) Medieval Ideas about Infertility and Old Age Abstract: When they discussed fertility and reproductive disorders it was common… Continue reading

InBios International, Inc. announces the U.S. Food and Drug Administration (FDA) issued an emergency use authorization (EUA) for its diagnostic test that can be used immediately by CLIA...

(PRWeb April 08, 2020)

Read the full story at https://www.prweb.com/releases/inbios_receives_emergency_use_authorization_for_its_smart_detect_sars_cov_2_rrt_pcr_kit_for_detection_of_the_virus_causing_covid_19/prweb17036897.htm

Harvested produce crops feed Florida Department of Corrections’ (FDC) more than 87,000 inmates; action saves food costs while reducing COVID-19 related supply chain impacts.

(PRWeb April 20, 2020)

Read the full story at https://www.prweb.com/releases/new_partnerships_emerge_for_covid_19_relief_dade_county_farm_bureau_teams_with_state_leaders_to_launch_farm_to_inmate_program/prweb17052045.htm

Defendant’s Motion to Exclude Expert Testimony regarding evidence generated by STRmix denied.

(PRWeb May 08, 2020)

Read the full story at https://www.prweb.com/releases/colorado_court_rules_strmix_is_relevant_and_reliable_practice_for_interpreting_likelihood_ratios/prweb17101548.htm

Jere Koskela, Paul A. Jenkins, Adam M. Johansen, Dario Spanò.

Source: The Annals of Statistics, Volume 48, Number 1, 560--583.

Abstract:
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman $n$-coalescent in the infinite system size limit in the sense of finite-dimensional distributions. Thus, the tractable $n$-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well. Our conditions for convergence are strong, but we show by simulation that they do not appear to be necessary.

Guangyu Zhu, Zhihua Su.

Source: The Annals of Statistics, Volume 48, Number 1, 161--182.

Abstract:
Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keleş ( J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this paper, we propose a new version of SPLS, called the envelope-based SPLS, using a connection between envelope models and partial least squares (PLS). We establish the consistency, oracle property and asymptotic normality of the envelope-based SPLS estimator. The large-sample scenario and high-dimensional scenario are both considered. We also develop the envelope-based SPLS estimators under the context of generalized linear models, and discuss its theoretical properties including consistency, oracle property and asymptotic distribution. Numerical experiments and examples show that the envelope-based SPLS estimator has better variable selection and prediction performance over the SPLS estimator ( J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25).

Steffen Grønneberg, Benjamin Holcblat.

Source: The Annals of Statistics, Volume 47, Number 6, 3216--3243.

Abstract:
We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and provide a general algorithm to obtain pivot statistics for CUSUM tests.

Long Feng, Cun-Hui Zhang.

Source: The Annals of Statistics, Volume 47, Number 6, 3069--3098.

Abstract:
The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and estimation, the bias of the Lasso can be also reduced by taking a smaller penalty level than what selection consistency requires, but such smaller penalty level depends on the sparsity of the true coefficient vector. The sorted $ell_{1}$ penalized estimation (Slope) was proposed for adaptation to such smaller penalty levels. However, the advantages of concave PLSE and Slope do not subsume each other. We propose sorted concave penalized estimation to combine the advantages of concave and sorted penalizations. We prove that sorted concave penalties adaptively choose the smaller penalty level and at the same time benefits from signal strength, especially when a significant proportion of signals are stronger than the corresponding adaptively selected penalty levels. A local convex approximation for sorted concave penalties, which extends the local linear and quadratic approximations for separable concave penalties, is developed to facilitate the computation of sorted concave PLSE and proven to possess desired prediction and estimation error bounds. Our analysis of prediction and estimation errors requires the restricted eigenvalue condition on the design, not beyond, and provides selection consistency under a required minimum signal strength condition in addition. Thus, our results also sharpens existing results on concave PLSE by removing the upper sparse eigenvalue component of the sparse Riesz condition.

Heng Lian, Kaifeng Zhao, Shaogao Lv.

Source: The Annals of Statistics, Volume 47, Number 5, 2922--2949.

Abstract:
In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to the nonparametric part. We propose a novel approach for estimation of the nonparametric function and establish the local asymptotics of the estimator. The result is useful for massive data with possibly different linear coefficients in each subpopulation but common nonparametric function. Some numerical illustrations are also presented.

Didier Chételat, Martin T. Wells.

Source: The Annals of Statistics, Volume 47, Number 5, 2639--2670.

Abstract:
We study the behavior of a real $p$-dimensional Wishart random matrix with $n$ degrees of freedom when $n,p ightarrowinfty$ but $p/n ightarrow0$. We establish the existence of phase transitions when $p$ grows at the order $n^{(K+1)/(K+3)}$ for every $Kinmathbb{N}$, and derive expressions for approximating densities between every two phase transitions. To do this, we make use of a novel tool we call the $mathcal{F}$-conjugate of an absolutely continuous distribution, which is obtained from the Fourier transform of the square root of its density. In the case of the normalized Wishart distribution, this represents an extension of the $t$-distribution to the space of real symmetric matrices.

Matey Neykov, Han Liu.

Source: The Annals of Statistics, Volume 47, Number 5, 2472--2503.

Abstract:
This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom property tests can be statistically and/or computationally more efficient than graph recovery based algorithms. Understanding the statistical complexity of property testing requires the distinction of ferromagnetic (i.e., positive interactions only) and general Ising models. Using combinatorial constructs such as graph packing and strong monotonicity, we characterize how target properties affect the corresponding minimax upper and lower bounds within the realm of ferromagnets. On the other hand, by studying the detection of an antiferromagnetic (i.e., negative interactions only) Curie–Weiss model buried in Rademacher noise, we show that property testing is strictly more challenging over general Ising models. In terms of methodological development, we propose two types of correlation based tests: computationally efficient screening for ferromagnets, and score type tests for general models, including a fast cycle presence test. Our correlation screening tests match the information-theoretic bounds for property testing in ferromagnets in certain regimes.

Qian Qin, James P. Hobert.

Source: The Annals of Statistics, Volume 47, Number 4, 2320--2347.

Abstract:
The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales with sample size, $n$, and/or number of covariates, $p$. This article provides a thorough convergence complexity analysis of Albert and Chib’s [ J. Amer. Statist. Assoc. 88 (1993) 669–679] data augmentation algorithm for the Bayesian probit regression model. The main tools used in this analysis are drift and minorization conditions. The usual pitfalls associated with this type of analysis are avoided by utilizing centered drift functions, which are minimized in high posterior probability regions, and by using a new technique to suppress high-dimensionality in the construction of minorization conditions. The main result is that the geometric convergence rate of the underlying Markov chain is bounded below 1 both as $n ightarrowinfty$ (with $p$ fixed), and as $p ightarrowinfty$ (with $n$ fixed). Furthermore, the first computable bounds on the total variation distance to stationarity are byproducts of the asymptotic analysis.

Digital identity standards group. Set up at the instigation of Sun Microsystems in 2001, the Liberty Alliance Project is a consortium of technology vendors and consumer-facing enterprises formed "to establish an open standard for federated network identity." It aims to make it easier for consumers to access networked services from multiple suppliers while safeguarding security and privacy. Its specifications have been published in three phases: the Identity Federation Framework (ID-FF) came first; the Identity Web Services Framework (ID-WSF) followed in November 2003; and work is in progress on the Identity Services Interface Specifications (ID-SIS). Liberty Alliance specifications are closely linked to the SAML single sign-on standard, and overlap with elements of WS-Security.

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.

Wenjie Wang, Robert Aseltine, Kun Chen, Jun Yan.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 51--73.

Abstract:
The concept of integrating data from disparate sources to accelerate scientific discovery has generated tremendous excitement in many fields. The potential benefits from data integration, however, may be compromised by the uncertainty due to incomplete/imperfect record linkage. Motivated by a suicide risk study, we propose an approach for analyzing survival data with uncertain event times arising from data integration. Specifically, in our problem deaths identified from the hospital discharge records together with reported suicidal deaths determined by the Office of Medical Examiner may still not include all the death events of patients, and the missing deaths can be recovered from a complete database of death records. Since the hospital discharge data can only be linked to the death record data by matching basic patient characteristics, a patient with a censored death time from the first dataset could be linked to multiple potential event records in the second dataset. We develop an integrative Cox proportional hazards regression in which the uncertainty in the matched event times is modeled probabilistically. The estimation procedure combines the ideas of profile likelihood and the expectation conditional maximization algorithm (ECM). Simulation studies demonstrate that under realistic settings of imperfect data linkage the proposed method outperforms several competing approaches including multiple imputation. A marginal screening analysis using the proposed integrative Cox model is performed to identify risk factors associated with death following suicide-related hospitalization in Connecticut. The identified diagnostics codes are consistent with existing literature and provide several new insights on suicide risk, prediction and prevention.

Jennifer E. Starling, Jared S. Murray, Carlos M. Carvalho, Radek K. Bukowski, James G. Scott.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 28--50.

Abstract:
This article introduces BART with Targeted Smoothing, or tsBART, a new Bayesian tree-based model for nonparametric regression. The goal of tsBART is to introduce smoothness over a single target covariate $t$ while not necessarily requiring smoothness over other covariates $x$. tsBART is based on the Bayesian Additive Regression Trees (BART) model, an ensemble of regression trees. tsBART extends BART by parameterizing each tree’s terminal nodes with smooth functions of $t$ rather than independent scalars. Like BART, tsBART captures complex nonlinear relationships and interactions among the predictors. But unlike BART, tsBART guarantees that the response surface will be smooth in the target covariate. This improves interpretability and helps to regularize the estimate. After introducing and benchmarking the tsBART model, we apply it to our motivating example—pregnancy outcomes data from the National Center for Health Statistics. Our aim is to provide patient-specific estimates of stillbirth risk across gestational age $(t)$ and based on maternal and fetal risk factors $(x)$. Obstetricians expect stillbirth risk to vary smoothly over gestational age but not necessarily over other covariates, and tsBART has been designed precisely to reflect this structural knowledge. The results of our analysis show the clear superiority of the tsBART model for quantifying stillbirth risk, thereby providing patients and doctors with better information for managing the risk of fetal mortality. All methods described here are implemented in the R package tsbart .

Jason Xu, Samson Koelle, Peter Guttorp, Chuanfeng Wu, Cynthia Dunbar, Janis L. Abkowitz, Vladimir N. Minin.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2091--2119.

Abstract:
Single-cell lineage tracking strategies enabled by recent experimental technologies have produced significant insights into cell fate decisions, but lack the quantitative framework necessary for rigorous statistical analysis of mechanistic models describing cell division and differentiation. In this paper, we develop such a framework with corresponding moment-based parameter estimation techniques for continuous-time, multi-type branching processes. Such processes provide a probabilistic model of how cells divide and differentiate, and we apply our method to study hematopoiesis , the mechanism of blood cell production. We derive closed-form expressions for higher moments in a general class of such models. These analytical results allow us to efficiently estimate parameters of much richer statistical models of hematopoiesis than those used in previous statistical studies. To our knowledge, the method provides the first rate inference procedure for fitting such models to time series data generated from cellular barcoding experiments. After validating the methodology in simulation studies, we apply our estimator to hematopoietic lineage tracking data from rhesus macaques. Our analysis provides a more complete understanding of cell fate decisions during hematopoiesis in nonhuman primates, which may be more relevant to human biology and clinical strategies than previous findings from murine studies. For example, in addition to previously estimated hematopoietic stem cell self-renewal rate, we are able to estimate fate decision probabilities and to compare structurally distinct models of hematopoiesis using cross validation. These estimates of fate decision probabilities and our model selection results should help biologists compare competing hypotheses about how progenitor cells differentiate. The methodology is transferrable to a large class of stochastic compartmental and multi-type branching models, commonly used in studies of cancer progression, epidemiology and many other fields.

Ahmed Aziz Ezzat, Mikyoung Jun, Yu Ding.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1484--1510.

Abstract:
Accurate short-term forecasts are indispensable for the integration of wind energy in power grids. On a wind farm, local wind conditions exhibit sizeable variations at a fine temporal resolution. Existing statistical models may capture the in-sample variations in wind behavior, but are often shortsighted to those occurring in the near future, that is, in the forecast horizon. The calibrated regime-switching method proposed in this paper introduces an action of regime dependent calibration on the predictand (here the wind speed variable), which helps correct the bias resulting from out-of-sample variations in wind behavior. This is achieved by modeling the calibration as a function of two elements: the wind regime at the time of the forecast (and the calibration is therefore regime dependent), and the runlength, which is the time elapsed since the last observed regime change. In addition to regime-switching dynamics, the proposed model also accounts for other features of wind fields: spatio-temporal dependencies, transport effect of wind and nonstationarity. Using one year of turbine-specific wind data, we show that the calibrated regime-switching method can offer a wide margin of improvement over existing forecasting methods in terms of both wind speed and power.

Sarat B. Moka, Dirk P. Kroese.

Source: Bernoulli, Volume 26, Number 3, 2082--2104.

Abstract:
We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC’17 – Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342–355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high and $Theta(1/r^{d})$ parallel processor units are available.

Adam Osękowski.

Source: Bernoulli, Volume 26, Number 3, 1912--1926.

Abstract:
Let $X=(X_{t})_{tgeq 0}in H^{1}$ and $Y=(Y_{t})_{tgeq 0}in{mathrm{BMO}} $ be arbitrary continuous-path martingales. The paper contains the proof of the inequality egin{equation*}mathbb{E}int _{0}^{infty }iglvert dlangle X,Y angle_{t}igrvert leq sqrt{2}Vert XVert _{H^{1}}Vert YVert _{mathrm{BMO}_{2}},end{equation*} and the constant $sqrt{2}$ is shown to be the best possible. The proof rests on the construction of a certain special function, enjoying appropriate size and concavity conditions.

Michael Jauch, Peter D. Hoff, David B. Dunson.

Source: Bernoulli, Volume 26, Number 2, 1560--1586.

Abstract:
Random orthogonal matrices play an important role in probability and statistics, arising in multivariate analysis, directional statistics, and models of physical systems, among other areas. Calculations involving random orthogonal matrices are complicated by their constrained support. Accordingly, we parametrize the Stiefel and Grassmann manifolds, represented as subsets of orthogonal matrices, in terms of Euclidean parameters using the Cayley transform. We derive the necessary Jacobian terms for change of variables formulas. Given a density defined on the Stiefel or Grassmann manifold, these allow us to specify the corresponding density for the Euclidean parameters, and vice versa. As an application, we present a Markov chain Monte Carlo approach to simulating from distributions on the Stiefel and Grassmann manifolds. Finally, we establish that the Euclidean parameters corresponding to a uniform orthogonal matrix can be approximated asymptotically by independent normals. This result contributes to the growing literature on normal approximations to the entries of random orthogonal matrices or transformations thereof.

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.