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Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.

In the U.S. Forest Service’s Forest Inventory and Analysis (FIA) program, as in other natural resource surveys, many auxiliary variables are available for use in model-assisted inference about finite population parameters. Some of this auxiliary information may be extraneous, and therefore model selection is appropriate to improve the efficiency of the survey regression estimators of finite population totals. A model-assisted survey regression estimator using the lasso is presented and extended to the adaptive lasso. For a sequence of finite populations and probability sampling designs, asymptotic properties of the lasso survey regression estimator are derived, including design consistency and central limit theory for the estimator and design consistency of a variance estimator. To estimate multiple finite population quantities with the method, lasso survey regression weights are developed, using both a model calibration approach and a ridge regression approximation. The gains in efficiency of the lasso estimator over the full regression estimator are demonstrated through a simulation study estimating tree canopy cover for a region in Utah.

Variational approximations provide fast, deterministic alternatives to Markov Chain Monte Carlo for Bayesian inference on the parameters of complex, hierarchical models. Variational approximations are often limited in practicality in the absence of conjugate posterior distributions. Recent work has focused on the application of variational methods to models with only partial conjugacy, such as in semiparametric regression with heteroskedastic errors. Here, both the mean and log variance functions are modeled as smooth functions of covariates. For this problem, we derive a mean field variational approximation with an embedded Laplace approximation to account for the non-conjugate structure. Empirical results with simulated and real data show that our approximate method has significant computational advantages over traditional Markov Chain Monte Carlo; in this case, a delayed rejection adaptive Metropolis algorithm. The variational approximation is much faster and eliminates the need for tuning parameter selection, achieves good fits for both the mean and log variance functions, and reasonably reflects the posterior uncertainty. We apply the methods to log-intensity data from a small angle X-ray scattering experiment, in which properly accounting for the smooth heteroskedasticity leads to significant improvements in posterior inference for key physical characteristics of an organic molecule.

The general projected normal distribution is a simple and intuitive model for directional data in any dimension: a multivariate normal random vector divided by its length is the projection of that vector onto the surface of the unit hypersphere. Observed data consist of the projections, but not the lengths. Inference for this model has been restricted to the two-dimensional (circular) case, using Bayesian methods with data augmentation to generate the latent lengths and a Metropolis-within-Gibbs algorithm to sample from the posterior. We describe a new parameterization of the general projected normal distribution that makes inference in any dimension tractable, including the important three-dimensional (spherical) case, which has not previously been considered. Under this new parameterization, the full conditionals of the unknown parameters have closed forms, and we propose a new slice sampler to draw the latent lengths without the need for rejection. Gibbs sampling with this new scheme is fast and easy, leading to improved Bayesian inference; for example, it is now feasible to conduct model selection among complex mixture and regression models for large data sets. Our parameterization also allows straightforward incorporation of covariates into the covariance matrix of the multivariate normal, increasing the ability of the model to explain directional data as a function of independent regressors. Circular and spherical cases are considered in detail and illustrated with scientific applications. For the circular case, seasonal variation in time-of-day departures of anglers from recreational fishing sites is modeled using covariates in both the mean vector and covariance matrix. For the spherical case, we consider paired angles that describe the relative positions of carbon atoms along the backbone chain of a protein. We fit mixtures of general projected normals to these data, with the best-fitting mixture accurately describing biologically meaningful structures including helices, $\beta$ -sheets, and coils and turns. Finally, we show via simulation that our methodology has satisfactory performance in some 10-dimensional and 50-dimensional problems.

Small-angle X-ray scattering (SAXS) is a technique for obtaining low-resolution structural information about biological macromolecules, by exposing a dilute solution to a high-intensity X-ray beam and capturing the resulting scattering pattern on a two-dimensional detector. The two-dimensional pattern is reduced to a one-dimensional curve through radial averaging; that is, by averaging across annuli on the detector plane. Subsequent analysis of structure relies on these one-dimensional data. This paper reviews the technique of SAXS and investigates autocorrelation structure in the detector plane and in the radial averages. Across a range of experimental conditions and molecular types, spatial autocorrelation in the detector plane is present and is well-described by a stationary kernel convolution model. The corresponding autocorrelation structure for the radial averages is non-stationary. Implications of the autocorrelation structure for inference about macromolecular structure are discussed.

Many environmental data sets have a continuous domain, in time and/or space, and complex features that may be poorly modelled with a stationary (in space and time) Gaussian process (GP). We adapt stochastic volatility modelling to this context, resulting in a stochastic heteroscedastic process (SHP), which is unconditionally stationary and non-Gaussian. Conditional on a latent GP, the SHP is a heteroscedastic GP with non-stationary (in space and time) covariance structure. The realizations from SHP are versatile and can represent spatial inhomogeneities. The unconditional correlation functions of SHP form a rich isotropic class that can allow for a smoothed nugget effect. We apply an importance sampling strategy to implement pseudo maximum likelihood parameter estimation for the SHP. To predict the process at unobserved locations, we develop a plug-in best predictor. We extend the single-realization SHP model to handle replicates across time of SHP realizations in space. Empirical results with simulated data show that SHP is nearly as efficient as a stationary GP in out-of-sample prediction when the true process is a stationary GP, and outperforms a stationary GP substantially when the true process is SHP. The SHP methodology is applied to enhanced vegetation index data and US NO3 deposition data for illustration.

The cube method proposed by Deville and Tille (2004) enables the selection of balanced samples: that is, samples such that the Horvitz–Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the cube method generally proceeds in two steps: a “flight phase” in which exact balance is maintained, and a “landing phase” in which the final sample is selected while respecting the balance conditions as closely as possible. Deville and Tille (2005) derive a variance approximation for balanced sampling that takes account of the flight phase only, whereas the landing phase can prove to add non-negligible variance. This paper uses a martingale difference representation of the cube method to construct an efficient simulation-based method for calculating approximate second-order inclusion probabilities. The approximation enables nearly unbiased variance estimation, where the bias is primarily due to the limited number of simulations. In a Monte Carlo study, the proposed method has significantly less bias than the standard variance estimator, leading to improved confidence interval coverage.

We consider an autoregressive regime-switching model for the dynamic mean structure of a univariate time series. The model allows for a variety of stationary and nonstationary alternatives, and includes the possibility of approximate long-memory behavior. The proposed model includes as special cases white noise, first-order autoregression, and random walk models as well as regime-switching models and the random level-shift model proposed by Chen and Tiao, Journal of Business and Economic Statistics, 8 (1990) p. 83. We describe properties of the model, focusing on its resemblance to long-memory under a certain asymptotic parameterization. We develop a reversible-jump Markov chain Monte Carlo method for Bayesian inference on unknown model parameters and apply the methodology to the Nile River data.

The estimation of the distribution functon of a random variable X measured with error is studied. Let the i-th observation on X be denoted by YiXi+ei where ei is the measuremen error. Let {Yi} (i=1,2,…,n) be a sample of independent observations. It is assumed that {Xi} and {∈i} are mutually independent and each is identically distributed. As is standard in the literature for this problem, the distribution of e is assumed known in the development of the methodology. In practice, the measurement error distribution is estimated from replicate observations. The proposed semiparametric estimator is derived by estimating the quantises of X on a set of n transformed V-values and smoothing the estimated quantiles using a spline function. The number of parameters of the spline function is determined by the data with a simple criterion, such as AIC. In a simulation study, the semiparametric estimator dominates an optimal kernel estimator and a normal mixture estimator for a wide class of densities. The proposed est...

We consider bootstrap construction and calibration of prediction intervals for nonGaussian autoregressions. In particular, we address the question of prediction conditioned on the last p observations of the process, for which we offer an exact simulation technique and an approximate bootstrap approach. In simulations for a variety of first-order autoregressions, we compare various nonparametric prediction intervals and find that calibration gives reasonably narrow prediction intervals with the lowest coverage probability mean squared error among the methods used.

Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the superpopulation model. The selection is informative in the sense that the sample responses, given that they were selected, are not i.i.d. f. In general, the informative selection mechanism may induce dependence among the selected observations. The impact of such dependence on the empirical cumulative distribution function (c.d.f.) is studied. An asymptotic framework and weak conditions on the informative selection mechanism are developed under which the (unweighted) empirical c.d.f. converges uniformly, in $L_2$ and almost surely, to a weighted version of the superpopulation c.d.f. This yields an analogue of the Glivenko-Cantelli theorem. A series of examples, motivated by real problems in surveys and other observational studies, shows that the conditions are verifiable for specified designs., Published in at http://dx.doi.org/10.3150/11-BEJ369 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram., Published at http://dx.doi.org/10.1214/009053606000001316 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The first-order moving average model or MA(1) is given by $X_t=Z_t-\theta_0Z_{t-1}$, with independent and identically distributed $\{Z_t\}$. This is arguably the simplest time series model that one can write down. The MA(1) with unit root ($\theta_0=1$) arises naturally in a variety of time series applications. For example, if an underlying time series consists of a linear trend plus white noise errors, then the differenced series is an MA(1) with unit root. In such cases, testing for a unit root of the differenced series is equivalent to testing the adequacy of the trend plus noise model. The unit root problem also arises naturally in a signal plus noise model in which the signal is modeled as a random walk. The differenced series follows a MA(1) model and has a unit root if and only if the random walk signal is in fact a constant. The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root case and nearly unit root case ($\theta=1+\beta/n,\beta\le0$). Unlike standard $1/\sqrt{n}$-asymptotics, these estimation procedures have $1/n$-asymptotics and a so-called pile-up effect, in which P$(\hat{\theta}=1)$ converges to a positive value. One explanation for this pile-up phenomenon is the lack of identifiability of $\theta$ in the Gaussian case. That is, the Gaussian likelihood has the same value for the two sets of parameter values $(\theta,\sigma^2)$ and $(1/\theta,\theta^2\sigma^2$). It follows that $\theta=1$ is always a critical point of the likelihood function. In contrast, for non-Gaussian noise, $\theta$ is identifiable for all real values. Hence it is no longer clear whether or not the same pile-up phenomenon will persist in the non-Gaussian case. In this paper, we focus on limiting pile-up probabilities for estimates of $\theta_0$ based on a Laplace likelihood. In some cases, these estimates can be viewed as Least Absolute Deviation (LAD) estimates. Simulation results illustrate the limit theory., Comment: Published at http://dx.doi.org/10.1214/074921706000000923 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

An autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the case of Laplacian (two-sided exponential) noise yields a modified absolute deviations criterion, which can be used even if the underlying noise is not Laplacian. Asymptotic normality for least absolute deviation estimators of the model parameters is established under general conditions. Behavior of the estimators in finite samples is studied via simulation. The methodology is applied to exchange rate returns to show that linear all-pass models can mimic “nonlinear” behavior, and is applied to stock market volume data to illustrate a two-step procedure for fitting noncausal autoregressions.

We propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility (LMSV) model. The LMSV model is constructed by incorporating an ARFIMA process in a standard stochastic volatility scheme. Strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the Gaussian likelihood. The finite sample properties of the spectral likelihood estimator are analyzed by means of a Monte Carlo study. An empirical example with a long time series of stock prices demonstrates the superiority of the LMSV model over existing (short-memory) volatility models. info:eu-repo/semantics/publishedVersion