A generalized mixture integer-valued GARCH model

Flexible binomial AR(1) processes using copulas

Emerging targeted therapies have shown benefits such as less toxicity and higher effectiveness in specific types of cancer treatment; however, the accessibility of these advantages may rely on correct identification of suitable patients, which remains highly immature. We assume that copy number profiles, being accessible genomic data via microarray techniques, can provide useful information regarding drug response and shed light on personalized therapy. Based on the mechanism of action (MOA) of trastuzumab in the HER2 signaling pathway, a Bayesian network model in which copy number alterations (CNAs) serve as latent parents modifying signal transduction is applied. Two model parameters M-score and R -value which stand for the qualitative and quantitative effects of CNAs on drug effectiveness and are functions of conditional probabilities (CPs), are defined. An expectation-maximization (EM) algorithm is developed for estimating CPs, M-scores, and R-values from continuous measures, such as microarray data. We show through simulations that the EM algorithm can outperform classical threshold-based methods in the estimation of CPs and thereby provide improved performance for the detection of unfavorable CNAs. Several candidates of unfavorable CNAs to the trastuzumab therapy in breast cancer are provided in a real data example.

In cluster-specific studies, ordinary logistic regression and conditional logistic regression for binary outcomes provide maximum likelihood estimator (MLE) and conditional maximum likelihood estimator (CMLE), respectively. In this paper, we show that CMLE is approaching to MLE asymptotically when each individual data point is replicated infinitely many times. Our theoretical derivation is based on the observation that a term appearing in the conditional average log-likelihood function is the coefficient of a polynomial, and hence can be transformed to a complex integral by Cauchy’s differentiation formula. The asymptotic analysis of the complex integral can then be performed using the classical method of steepest descent. Our result implies that CMLE can be biased if individual weights are multiplied with a constant, and that we should be cautious when assigning weights to cluster-specific studies.

This paper introduces a non-negative integer-valued autoregressive (INAR) process with seasonal structure of first order, which is an extension of the standard INAR(1) model proposed by Al-Osh and Alzaid [First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261–275]. The main properties of the model are derived such as its stationarity and autocorrelation function (ACF), among others. The conditional least squares and conditional maximum likelihood estimators of the model parameters are studied and their asymptotic properties are established. Some detailed discussion is dedicated to the case where the marginal distribution of the process is Poisson. A Monte Carlo experiment is conducted to evaluate and compare the performances of these estimators for finite sample sizes. The standard Yule–Walker approach is also considered for comparison purposes. The empirical results indicate that, in general, the conditional maximum likelihood estimator presents much better performance in terms of bias and mean square error. The model is illustrated using a real data set.

This paper considers the autoregressive modelling problem of ‐valued time series of counts, whose counting sequence consists of −1, 0 and 1. Most existing methods are based on the signed binomial thinning operator and its some extensions, in which the counting sequence consists of 0 and 1, that is, the cases of −1 is ignored. To fill this gap, we first construct the trinomial difference thinning operator and then propose the trinomial difference Z‐valued autoregressive (TDZAR) model and give some stochastic properties. An attractive merit of the TDZAR model is that the incorporated trinomial difference thinning operator makes the conditional maximum likelihood estimate more wieldy and easy. Second, we discuss the two‐step conditional least squares estimate and the conditional maximum likelihood estimate and establish their asymptotic properties of the estimators. Third, the performances of these estimators are compared via simulation study. Finally, we apply the proposed model to a real data set.

A new estimator of the common odds ratio in one-to-one matched case-control studies is proposed. The connection between this estimator and the James-Stein estimating procedure is highlighted through the argument of estimating functions. Comparisons are made between this estimator, the conditional maximum likelihood estimator, and the estimator ignoring the matching in terms of finite sample bias, mean squared error, coverage probability, and length of confidence interval. In many situations, the new estimator is found to be more efficient than the conditional maximum likelihood estimator without being as biased as the estimator that ignores matching. The extension to multiple risk factors is also outlined.

Hybrid censoring schemes are commonly used in life-testing experiments to reduce the experimental time and the cost. A Type-II progressive hybrid censoring scheme (PHCS) was introduced by Kundu and Joarder (Comput Stat Data Anal 50:2509–2528, 2006) that combines progressive Type-II censoring and Type-I censoring. In this paper, we consider the statistical inference of a two-parameter exponential distribution under the Type-II PHCS. The conditional maximum likelihood estimates (MLEs) of the model parameters and their joint and marginal conditional moment generating functions are derived. Based on these exact conditional moments, bias-reduced estimators are proposed and their distributions are discussed. Confidence intervals of the model parameters based on exact and asymptotic distributions of the MLEs and bias-reduced estimators are developed. The performances of the point and interval estimation procedures are evaluated and compared through exact calculations and Monte Carlo simulations. Recommendations are made based on these results and an illustrative example is presented.

The network security assessment instrument is a comprehensive set of tools that can be used individually or collectively to ensure the security of network aware software applications and systems. Using the various tools collectively provide a distinct advantage for assuring the security of software and systems. Each tool's resulting output provides feedback into the other tools. Thus, more comprehensive assessment results are attained through the leverage each tool provides to the other when they are employed in concert. Previous portions of this work were presented at the IEEE Wet Ice 2000 and 2001 Workshops and are printed in those proceedings. This paper presents a portion of an overall research project on the generation of the network security assessment instrument to aid developers in assessing and assuring the security of software in the development and maintenance lifecycles. This portion, the flexible modeling framework (FMF), focuses on modeling requirements and early lifecycle designs to discover vulnerabilities that result from interaction between system components that are either under development in a new system or proposed as additions to an existing system. There are early indications that this new approach, the flexible modeling framework (FMF), has promise in the areas of network security as well as other critical areas such as system safety. Information about the overall research effort regarding network security is available at http://security.jpl.nasa.gov/rssr.

We propose signed compound Poisson integer-valued GARCH processes for the modeling of the difference of count time series data. We investigate the theoretical properties of these processes and we state their ergodicity and stationarity under mild conditions. We discuss the conditional maximum likelihood estimator when the series appearing in the difference are INGARCH with geometric distribution and explore its finite sample properties in a simulation study. Two real data examples illustrate this methodology.

Abstract. Despite showing great success of applications in many commercial fields, machine learning and data science models generally show limited success in many scientific fields, including hydrology (Karpatne et al., 2017). The approach is often criticized for its lack of interpretability and physical consistency. This has led to the emergence of new modelling paradigms, such as theory-guided data science (TGDS) and physics-informed machine learning. The motivation behind such approaches is to improve the physical meaningfulness of machine learning models by blending existing scientific knowledge with learning algorithms. Following the same principles in our prior work (Chadalawada et al., 2020), a new model induction framework was founded on genetic programming (GP), namely the Machine Learning Rainfall–Runoff Model Induction (ML-RR-MI) toolkit. ML-RR-MI is capable of developing fully fledged lumped conceptual rainfall–runoff models for a watershed of interest using the building blocks of two flexible rainfall–runoff modelling frameworks. In this study, we extend ML-RR-MI towards inducing semi-distributed rainfall–runoff models. The meaningfulness and reliability of hydrological inferences gained from lumped models may tend to deteriorate within large catchments where the spatial heterogeneity of forcing variables and watershed properties is significant. This was the motivation behind developing our machine learning approach for distributed rainfall–runoff modelling titled Machine Induction Knowledge Augmented – System Hydrologique Asiatique (MIKA-SHA). MIKA-SHA captures spatial variabilities and automatically induces rainfall–runoff models for the catchment of interest without any explicit user selections. Currently, MIKA-SHA learns models utilizing the model building components of two flexible modelling frameworks. However, the proposed framework can be coupled with any internally coherent collection of building blocks. MIKA-SHA's model induction capabilities have been tested on the Rappahannock River basin near Fredericksburg, Virginia, USA. MIKA-SHA builds and tests many model configurations using the model building components of the two flexible modelling frameworks and quantitatively identifies the optimal model for the watershed of concern. In this study, MIKA-SHA is utilized to identify two optimal models (one from each flexible modelling framework) to capture the runoff dynamics of the Rappahannock River basin. Both optimal models achieve high-efficiency values in hydrograph predictions (both at catchment and subcatchment outlets) and good visual matches with the observed runoff response of the catchment. Furthermore, the resulting model architectures are compatible with previously reported research findings and fieldwork insights of the watershed and are readily interpretable by hydrologists. MIKA-SHA-induced semi-distributed model performances were compared against existing lumped model performances for the same basin. MIKA-SHA-induced optimal models outperform the lumped models used in this study in terms of efficiency values while benefitting hydrologists with more meaningful hydrological inferences about the runoff dynamics of the Rappahannock River basin.

In this article, we introduce a new random coefficients self-exciting threshold integer-valued autoregressive process. The autoregressive coefficients are driven by a logistic regression structure, so that the explanatory variables can be included. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators, as well as the asymptotic properties of the estimators, are discussed. The nonlinearity test of the model and existence test of explanatory variables are also addressed. As an illustration, we evaluate our estimates through a simulation study. Finally, we apply our method to the data sets of sexual offences in Ballina, New South Wales (NSW), Australia, with two covariates of temperature and drug offences. The result reveals that the proposed model fits the data sets well.

ABSTRACTThe paper presents 3D diffraction imaging based on the spectral decomposition of a different combination of selective or partial images. These images are obtained by the pre‐stack asymmetric migration procedure, which is weighted data summation. Spectral decomposition is done in the Fourier domain with respect to spatial dip and azimuth angles. Numerical examples with the application of different workflows for the synthetic and real data examples demonstrate detailed reliable reconstruction of the fractured zones and reliable reconstruction of fracture orientation on synthetic and real 3D data examples.

Classical and Bayesian inferential approaches using Lomax model under progressively type-I hybrid censoring

ABSTRACTIn this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation–maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.

Some biomedical studies lead to mixture data. When a discrete covariate defining subgroup membership is missing for some of the subjects in a study, the distribution of the outcome follows a mixture distribution of the subgroup-specific distributions. Taking into account the uncertain distribution of the group membership and the covariates, we model the relation between the disease onset time and the covariates through transformation models in each sub-population, and develop a nonparametric maximum likelihood based estimation implemented through EM algorithm along with its inference procedure. We further propose methods to identify the covariates that have different effects or common effects in distinct populations, which enables parsimonious modeling and better understanding of the difference across populations. The methods are illustrated through extensive simulation studies and a real data example.