Unknown Time Point Research Articles

Wildlife fecal microbiota exhibit community stability across a longitudinal semi-controlled non-invasive sampling experiment

Wildlife microbiome studies are being used to assess microbial links with animal health and habitat. The gold standard of sampling microbiomes directly from captured animals is ideal for limiting potential abiotic influences on microbiome composition, yet fails to leverage the many benefits of non-invasive sampling. Application of microbiome-based monitoring for rare, endangered, or elusive species creates a need to non-invasively collect scat samples shed into the environment. Since controlling sample age is not always possible, the potential influence of time-associated abiotic factors was assessed. To accomplish this, we analyzed partial 16S rRNA genes of fecal metagenomic DNA sampled non-invasively from Rocky Mountain elk (Cervus canadensis) near Yellowstone National Park. We sampled pellet piles from four different elk, then aged them in a natural forest plot for 1, 3, 7, and 14 days, with triplicate samples at each time point (i.e., a blocked, repeat measures (longitudinal) study design). We compared fecal microbiota of each elk through time with point estimates of diversity, bootstrapped hierarchical clustering of samples, and a version of ANOVA–simultaneous components analysis (ASCA) with PCA (LiMM-PCA) to assess the variance contributions of time, individual and sample replication. Our results showed community stability through days 0, 1, 3 and 7, with a modest but detectable change in abundance in only 2 genera (Bacteroides and Sporobacter) at day 14. The total variance explained by time in our LiMM-PCA model across the entire 2-week period was not statistically significant (p>0.195) and the overall effect size was small (<10% variance) compared to the variance explained by the individual animal (p<0.0005; 21% var.). We conclude that non-invasive sampling of elk scat collected within one week during winter/early spring provides a reliable approach to characterize fecal microbiota composition in a 16S rDNA survey and that sampled individuals can be directly compared across unknown time points with minimal bias. Further, point estimates of microbiota diversity were not mechanistically affected by sample age. Our assessment of samples using bootstrap hierarchical clustering produced clustering by animal (branches) but not by sample age (nodes). These results support greater use of non-invasive microbiome sampling to assess ecological patterns in animal systems.

Maximum likelihood estimation of a change point for Poisson distributed data

In this study we develop a change point methodology to identify and estimate changes in the parameter of a Poisson distribution. The proposed methodology considers the case when the Poisson parameter changes abruptly at an unknown point of time. For this case, the maximum likelihood estimate of the change point and its asymptotic distribution are pursued. Mainly, we carry out a large scale simulation study for evaluating the appropriateness of the asymptotic distribution of the mle from the view point of finite samples, and also for evaluating the closeness under known and unknown parameters. The simulations study also compares the mle with that of a Bayesian estimate. Then, the methodology is applied to three examples. First, we uncover changes in the number of homicides in California using monthly data from January 2002 until December 2020. Secondly, data about deaths of females caused by stomach cancer is considered to detect possible changes in the numbers recorded from 1930 to 2011. Thirdly, British coal mining disasters from 1851 to 1962 in which more than 10 men were killed are analyzed.

The state of cumulative sum sequential changepoint testing 70 years after Page

Abstract Quality control charts aim at raising an alarm as soon as sequentially obtained observations of an underlying random process no longer seem to be within stochastic fluctuations prescribed by an in-control scenario. Such random processes can often be modelled using the concept of stationarity, or even independence as in most classical works. An important out-of-control scenario is the changepoint alternative, for which the distribution of the process changes at an unknown point in time. In his seminal 1954 Biometrika paper, E. S. Page introduced the famous cumulative sum control charts for changepoint monitoring. Innovatively, decision rules based on cumulative sum procedures took the full history of the process into account, whereas previous procedures were based only on a fixed and typically small number of the most recent observations. The extreme case of using only the most recent observation, often referred to as the Shewhart chart, is more akin to serial outlier than changepoint detection. Page’s cumulative sum approach, introduced seven decades ago, is ubiquitous in modern changepoint analysis, and his original paper has led to a multitude of follow-up papers in different research communities. This review is focused on a particular subfield of this research, namely nonparametric sequential, or online, changepoint tests that are constructed to maintain a desired Type-1 error as opposed to the more traditional approach seeking to minimize the average run length of the procedures. Such tests have originated at the intersection of econometrics and statistics. We trace the development of these tests and highlight their properties, mostly using a simple location model for clarity of exposition, but we also review more complex situations such as regression and time series models.

Detecting an intermittent change of unknown duration

Oftentimes, in practice, the observed process changes statistical properties at an unknown point in time and the duration of a change is substantially finite, in which case one says that the change is intermittent or transient. We provide an overview of existing approaches for intermittent change detection and advocate in favor of a particular setting driven by the intermittent nature of the change. We propose a novel optimization criterion that is more appropriate for many applied areas such as the detection of threats in physical computer systems, near-Earth space informatics, epidemiology, pharmacokinetics, etc. We argue that controlling the local conditional probability of a false alarm, rather than the familiar average run length to a false alarm, and maximizing the local conditional probability of detection is a more reasonable approach versus a traditional quickest change detection approach that requires minimizing the expected delay to detection. We adopt the maximum likelihood (ML) approach with respect to the change duration and show that several commonly used detection rules (cumulative sum [CUSUM], window-limited [WL]-CUSUM, and finite moving average [FMA]) are equivalent to the ML-based stopping times. We discuss how to choose design parameters for these rules and provide a comprehensive simulation study to corroborate intuitive expectations.

Assessing ice sheet models against the landform record: The Likelihood of Accordant Lineations Analysis (LALA) tool

AbstractPalaeo‐ice sheets leave behind a rich database regarding their past behaviour, recorded in the landscape in the form of glacial geomorphology. The most numerous landform created by these ice sheets are subglacial lineations, which generate snapshots of the direction of ice flow at fixed (yet typically unknown) points in time. Despite their relative density within the landform record, the information provided by subglacial lineations is currently underutilised in tests of numerical ice sheet models. To some extent, this is a consequence of ongoing debate regarding lineation formation, but predominantly, it reflects the lack of rigorous model‐data comparison techniques that would enable lineation information to be properly integrated. Here, we present the Likelihood of Accordant Lineations Analysis (LALA) tool. LALA provides a statistically rigorous measure of the log‐likelihood of a supplied ice sheet simulation through comparison of simulation output with both the location and direction of observed lineations. Given an ensemble of ice sheet simulations, LALA provides a formal, and statistically underpinned, quantitative assessment of each simulation's quality‐of‐fit to mapped lineations. This enables a comparison of each simulation's relative plausibility, including identification of the most likely ice sheet simulations amongst the ensemble. This is achieved by modelling lineation formation as a marked Poisson point process and comparison of observed to modelled flow directions using the von Mises distribution. LALA is flexible—users can adapt parameters to account for differing assumptions regarding lineation formation, and for variations in the level of precision required for differing model‐data comparison experiments. We provide guidelines and rationale for assigning parameter values, including an assessment of the variability between users when mapping lineations. Finally, we demonstrate the utility of LALA through application to an ensemble of simulations of the last British‐Irish Ice Sheet. This comparison highlights the benefits of LALA over previous tools and demonstrates some of the considerations of experimental design required when identifying the fit between ice sheet model simulations and the landform record.

Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution

We study revenue management for an online retailer that offers a single product to customers with a time-varying willingness-to-pay (WTP) distribution. When the WTP distribution changes at an unknown time point (i.e., the change point), the original price quoted to customers may not be optimal. The retailer’s objective is to minimize his revenue loss by determining when to quote a new price to incoming customers and what the new price is. We formulate the problem as an optimization model, which is challenging to solve due to the presence of the unknown change point. To overcome this challenge, we first characterize the probability distribution of the estimated change point using maximum likelihood estimation. We then develop two pricing algorithms to solve the model by leveraging the characterized distribution. Lastly, through numerical studies, we illustrate the effectiveness of the proposed algorithms in identifying change points and recommending optimal post-change selling prices. The numerical results suggest that the proposed pricing algorithms significantly reduce the frequency of false change detection in the early stages of a selling season. The proposed pricing algorithms also outperform the benchmark pricing algorithm in reducing the retailer’s revenue loss.

Þrymskviða, Þrymlur, and Tord af Havsgaard—a Case of Early Antiquarianism?

<i>Þrymskviða</i>, <i>Þrymlur</i>, and <i>Tord af Havsgaard</i>—a Case of Early Antiquarianism?

Subsampling ratio tests for structural changes in time series with heavy-tailed AR(p) errors

In this article, we consider that issues related to the mean and trend of heavy-tailed AR(p) series are possibly subject to change at most once at some unknown point in time. Under the inspiration of Shao (J. Time Ser. Anal., 2011, 32, 598–606), two ratio statistics are constructed to test whether unknown changes have occurred. It is shown that asymptotic distributions of these test statistics under the no-change null hypothesis are functional for Lévy processes and their consistencies are given under the alternative. To avoid the nuisance parameter, we provide a subsampling method that returns more accurate critical values for these tests. The validity of the subsampling algorithm is proved. A simulation study shows the subsampling-based ratio tests achieve the correct empirical sizes and comparable empirical powers in large samples. Finally, two practical applications using real data set are presented.

Prediction of Time-Series Transcriptomic Gene Expression Based on Long Short-Term Memory with Empirical Mode Decomposition.

RNA degradation can significantly affect the results of gene expression profiling, with subsequent analysis failing to faithfully represent the initial gene expression level. It is urgent to have an artificial intelligence approach to better utilize the limited data to obtain meaningful and reliable analysis results in the case of data with missing destination time. In this study, we propose a method based on the signal decomposition technique and deep learning, named Multi-LSTM. It is divided into two main modules: One decomposes the collected gene expression data by an empirical mode decomposition (EMD) algorithm to obtain a series of sub-modules with different frequencies to improve data stability and reduce modeling complexity. The other is based on long short-term memory (LSTM) as the core predictor, aiming to deeply explore the temporal nonlinear relationships embedded in the sub-modules. Finally, the prediction results of sub-modules are reconstructed to obtain the final prediction results of time-series transcriptomic gene expression. The results show that EMD can efficiently reduce the nonlinearity of the original data, which provides reliable theoretical support to reduce the complexity and improve the robustness of LSTM models. Overall, the decomposition-combination prediction framework can effectively predict gene expression levels at unknown time points.

Pregnancy outcomes of women with multiple sclerosis treated with ocrelizumab in Canada: A descriptive analysis of real-world data

ObjectivesTo report and describe the real-world use of ocrelizumab in women with multiple sclerosis (MS) in Canada before and/or during pregnancy as well as their fetal outcomes. MethodsWe identified retrospective and prospective Canadian pregnancy exposure cases from the Roche Global Safety Database from November 5, 2008 until March 31, 2021, and linked these cases to information within the Canadian Roche Patient Support Program (COMPASS). The analysis only included spontaneous reports or those from a non-interventional program. Details of the pregnancy exposures, fetal outcomes, as well as relevant patient characteristics, were collected. ResultsA total of 107 cases of maternal exposures were retrieved, with 104 (97.2%) being prescribed ocrelizumab for relapsing-remitting MS (RRMS) and 105 (98.1%) being reported from the COMPASS program. Of these cases, 85 (79.4%) were prospective and 22 (20.6%) retrospective. Cases were pooled (n = 65), and unknown/lost to follow-up outcomes and ongoing pregnancies were excluded. All cases reporting an outcome were analyzed, including 47 (72.3%) live births (44.7% full term, 8.5% preterm, 46.8% unknown gestational age), 13 (20.0%) spontaneous abortions, 2 (3.1%) therapeutic abortions/elective terminations, and 3 (4.6%) ectopic pregnancies. One major congenital anomaly of the limb (polydactyly) was reported; however, multiple confounders were likely contributors. Of the total maternal exposures (n = 107), 50 cases (46.6%) were not exposed to ocrelizumab in utero, with 32 of these (64.0%) receiving their last ocrelizumab infusion >3 but ≤6 months prior to conception, 17 (34.0%) receiving it >6 months prior to conception and 1 case receiving it at an unknown time point not in utero. Among the 37 (34.6%) maternal exposure cases exposed in utero, 22 (59.5%) received their last ocrelizumab infusion ≤3 months prior to conception. ConclusionThe data presented, although not without limitations, continues to suggest no increased risk of congenital anomalies and are consistent with ocrelizumab global pregnancy safety data and epidemiological rates.

ЛИНЕЙНАЯ ДИФФЕРЕНЦИАЛЬНАЯ ИГРА УДЕРЖАНИЯ С ПОЛОМКОЙ

A linear simple motion constraint differential game is considered. This game is considered from the part of the first player, who needs to keep the state of the system in a given convex terminal set throughout the game, despite the possible glitch and control of the second player. A glitch is understood as an instantaneous stop of the first player at a previously unknown point in time; after a certain time he will eliminate the glitch and will continue his motion. The player control vectograms are n-dimensional convex compacts that depend on time. To construct a u-stable bridge, the second method of L.S. Pontryagin is used. This is how a multi-valued mapping is constructed on the basis of the alternating integral of L.S. Pontryagin. After that, it is proved that the constructed mapping is a u-stable bridge for the game under consideration if a number of conditions are satisfied. At the end of the article, a simple example on the plane is considered, where the vectors of the players are circles centered at the origin and with a constant radius, while the radius of the circle of the first player is strictly greater than the second. In this example, a u-stable bridge is built according to the method proposed in the article, and an extremal strategy is found for the first player on the constructed u-stable bridge.

A wavelet method for panel models with jump discontinuities in the parameters

While a substantial literature on structural break change point analysis exists for univariate time series, research on large panel data models has not been as extensive. In this paper, a novel method for estimating panel models with multiple structural changes is proposed. The breaks are allowed to occur at unknown points in time and may affect the multivariate slope parameters individually. Our method adapts Haar wavelets to the structure of the observed variables in order to detect the change points of the parameters consistently. We also develop methods to address endogenous regressors within our modeling framework. The asymptotic property of our estimator is established. In our application, we examine the impact of algorithmic trading on standard measures of market quality such as liquidity and volatility over a time period that covers the financial meltdown that began in 2007. We are able to detect jumps in regression slope parameters automatically without using ad-hoc subsample selection criteria.

A simple test for stability of a spatial model

ABSTRACT This paper suggests a simple test to check if a spatial model’s specifications hold for the entire sample period, that is, to see if the model is stable. Our test is general in that it allows for possible unknown changes, one or more times, in the weighting matrix, in the exogenous variables and/or in the parameters. These changes may occur cross-sectionally or at unknown points in time. The test also allows for additional endogenous regressors, and the error terms are non-parametrically specified. However, if instabilities are detected, our test does not indicate which set of model components is responsible for it. Our Monte Carlo results suggest that the test has extremely high power for almost all the experiments considered. However, the size of the test is low for small sample sizes when additional endogenous regressors are part of the model.

Dynamic memory to alleviate catastrophic forgetting in continual learning with medical imaging

Medical imaging is a central part of clinical diagnosis and treatment guidance. Machine learning has increasingly gained relevance because it captures features of disease and treatment response that are relevant for therapeutic decision-making. In clinical practice, the continuous progress of image acquisition technology or diagnostic procedures, the diversity of scanners, and evolving imaging protocols hamper the utility of machine learning, as prediction accuracy on new data deteriorates, or models become outdated due to these domain shifts. We propose a continual learning approach to deal with such domain shifts occurring at unknown time points. We adapt models to emerging variations in a continuous data stream while counteracting catastrophic forgetting. A dynamic memory enables rehearsal on a subset of diverse training data to mitigate forgetting while enabling models to expand to new domains. The technique balances memory by detecting pseudo-domains, representing different style clusters within the data stream. Evaluation of two different tasks, cardiac segmentation in magnetic resonance imaging and lung nodule detection in computed tomography, demonstrate a consistent advantage of the method.

Estimating change-point latent factor models for high-dimensional time series

We consider estimating a factor model for high-dimensional time series that contains structural breaks in the factor loading space at unknown time points. We first study the case when there is one change point in factor loadings, and propose a consistent estimator for the structural break location, whose convergence rate is shown to depend on an interplay between the dimension of the observed time series and the strength of the underlying factor structure. Our results reveal that the asymptotic behavior of the proposed estimator can be asymmetric in the sense that a larger estimation error can occur toward the regime with weaker factor strength. Based on the proposed estimator for the structural break location, we also consider the problem of estimating the factor loading spaces before and after the structural break. We show that the proposed estimators for change-point location and loading spaces are consistent when the numbers of factors are correctly estimated or overestimated. The algorithm for multiple change-point detection is also developed in the paper. Compared with existing results on change-point factor analyses of high-dimensional time series, a distinguished feature of the current paper is that the noise process is not necessarily assumed to be idiosyncratic and as a result we allow the noise process with potentially strong cross-sectional dependence. Another advantage for the proposed method is that it is specifically designed for the changes in the factor loading space and the stationarity assumption is not imposed on either the factor or noise process, while most existing methods for change-point detection of high-dimensional time series with/without a factor structure require the data to be stationary or ’close’ to a stationary process between two change points, which is rather restrictive. Numerical experiments including a Monte Carlo simulation and a real data application are presented to illustrate the proposed estimators perform well.

Optimal Sequential Detection of Signals With Unknown Appearance and Disappearance Points in Time

The paper addresses a sequential changepoint detection problem, assuming that the duration of change may be finite and unknown. This problem is of importance for many applications, e.g., for signal and image processing where signals appear and disappear at unknown points in time or space. In contrast to the conventional optimality criterion in quickest change detection that requires minimization of the expected delay to detection for a given average run length to a false alarm, we focus on a reliable maximin change detection criterion of maximizing the minimal probability of detection in a given time (or space) window for a given local maximal probability of false alarm in the prescribed window. We show that the optimal detection procedure is a modified CUSUM procedure. We then compare operating characteristics of this optimal procedure with popular in engineering the Finite Moving Average (FMA) detection algorithm and the ordinary CUSUM procedure using Monte Carlo simulations, which show that typically the later algorithms have almost the same performance as the optimal one. At the same time, the FMA procedure has a substantial advantage -- independence to the intensity of the signal, which is usually unknown. Finally, the FMA algorithm is applied to detecting faint streaks of satellites in optical images.

Exact penalty functions in the problem of choosing the optimal wholesale order in the face of rapid fluctuations in demand

The current article discusses a different situation in the market, when there is a rush demand for a new product followed by a sharp drop in demand. The trading company uses the following scheme for the wholesale order of goods. The ordered product is divided into two parts, and the first batch of goods arrives immediately, it is sold over a certain period of time (0, Z,]. The second batch of goods is delivered at the time 7’, but at the time interval [0, 7]. This batch is sold at a discount and is completely sold out. Time T' corresponds to the end of the sale of the entire product. The time points 7), T' are selected by the trading firm from the condition of maximizing income. The need to consider such a wholesale order scheme is related to the fact that, firstly, the warehouses of the trading firms have limited capacity and cannot accommodate all the ordered goods, and secondly, a manufacturer may not offer the entire ordered batch of goods, since not all goods can be produced at the initial (zero) point of time immediately after receiving the order. At the time 71, the trading company completely sells the first batch of goods and receives financial resources, part of which is paid to the manufacturer. At the moment of time Т', Ме сотр/ефе sale of all purchased goods is completed. The choice of time points 7; and T' allow to determine the volume of the first batch of ordered goods and the total volume of product ordered from the manufacturer. In the article, a mathematical model is proposed that makes it possible to choose the optimal ordering strategy for a trading company in the conditions of excessive growth of demand for the new product in time 71,72 at some unknown point in time and т. Е [73,74], and the subsequent sharp drop in demand in the period of time [73, 74] due to the saturation of the market with a new product. Four possible variants of optimization problems are considered. A method of exact penalty function is suggested, which allows one to find their solutions.

Mosum: A Package for Moving Sums in Change-Point Analysis

Time series data, i.e., temporally ordered data, is routinely collected and analysed in in many fields of natural science, economy, technology and medicine, where it is of importance to verify the assumption of stochastic stationarity prior to modeling the data. Nonstationarities in the data are often attributed to structural changes with segments between adjacent change-points being approximately stationary. A particularly important, and thus widely studied, problem in statistics and signal processing is to detect changes in the mean at unknown time points. In this paper, we present the R package mosum, which implements elegant and mathematically well-justified procedures for the multiple mean change problem using the moving sum statistics.

Inference of Break-Points in High-Dimensional Time Series

We consider a new procedure for detecting structural breaks in mean for high-dimensional time series. We target breaks happening at unknown time points and locations. In particular, at a fixed time point our method is concerned with either the biggest break in one location or aggregating simultaneous breaks over multiple locations. We allow for both big or small sized breaks, so that we can 1), stamp the dates and the locations of the breaks, 2), estimate the break sizes and 3), make inference on the break sizes as well as the break dates. Our theoretical setup incorporates both temporal and cross-sectional dependence, and is suitable for heavy-tailed innovations. We derive the asymptotic distribution for the sizes of the breaks by extending the existing powerful theory on local linear kernel estimation and high dimensional Gaussian approximation to allow for trend stationary time series with jumps. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the US unemployment rate is considered to illustrate the usefulness of our method.

An algorithm for outlier detection in a time series model using backpropagation neural network

Outliers are commonplace in many real-life experiments. The presence of even a few anomalous data can lead to model misspecification, biased parameter estimation, and poor forecasts. Outliers in a time series are usually generated by dynamic intervention models at unknown points of time. Therefore, detecting outliers is the cornerstone before implementing any statistical analysis. In this paper, a multivariate outlier detection algorithm is given to detect outliers in time series models. A univariate time series is transformed to bivariate data based on the estimate of robust lag. The proposed algorithm is designed by using robust measures of location and dispersion matrix. Feed forward neural network is used for designing time series models. Number of hidden units in the network is determined based on the standard error of the forecasting error. A comparison study between the proposed algorithm and the widely used algorithms is given based on three real-data sets. The results demonstrated that the proposed algorithm outperformed the existing algorithms due to its non-requirement of a priori knowledge of the time series and its control of both masking and swamping effects. We also discussed an efficient method to deal with unexpected jumps or drops on share prices due to stock split and commodity prices near contract expiry dates.