Author response: Environmental dynamics shape human learning: change points versus random walks

Stationarity of annual flood peaks during 1951–2010 in the Pearl River basin, China

As the result of legal construction, market trading mechanism, transaction body,investor psychology immature and other reasons, China stock market, as an emerging market is vulnerable to the influence of external factors and presents large fluctuations. In the framework of Bayesian theory of econometrics, this article for the first time introduced the binomial distribution to AR (p) model with structure change in its lag coefficients, considering the mean mutation and variance mutation, and comprehensively analyzed the mutations of the time trend, intercept,lag coefficient and variance. Based on Bayesian theory, this paper constructed likelihood function, and at the same time introduced the hierarchical prior distribution by using a priori information and sample information. Then we used Gibbs sampling and MH algorithm to complete the judgment of change point number and location. After introducing the method, this paper discussed the structure change point of the Shanghai index. The results showed that in May 1992 to April 2012, the Shanghai index had 14 structural breaks:4 mean-variance change points, 1 mean change point, 9 variance change points.

Economic system mathematical model often contains multiple variance change points about structure model. In the same mean, we combine the Bayesian method with the maximum likelihood method on the detection of the variance multiple change points. With Bayesian method, we can eliminate extra parameters first, and then use maximum likelihood method to find the change position. So we both can eliminate extra parameters and can avoid the change point on the prior distribution unknown problem. In addition, the benefit of the maximum likelihood method is just needed to find out likelihood density function of the maximal solution in the solution space, thus the variance of multiple change point detection problem is resolved. By making substantial analysis with an example from commodity house prices in Wuhan, three changes of variance are found in all. They correspond to the major structure changes of contemporary property market in Wuhan city. The method is practical and effective as the final results shown. It also has a certain practical significance.

In this dissertation a new model for the description of cell organelle movement is defined and a test and change point detection algorithm for changes in the model parameters is proposed. The description of movement patterns can be important for the understanding of various biological processes on multiple scales. One of the primary goals is to understand the causes of change between movement patterns. On the micro scale, movement patterns of cell organelles and swimming micro-organisms such as cells are investigated. To learn more about the different movement types of cell organelles, as well as the changes between these types, we analyse the movement of two specific types of cell organelles in the root of the plant Arabidopsis thaliana, Plastids and Peroxisomes. Interestingly, while all tracks were recorded in three dimensions, over 90% of the tracks show more than 95% of their movement variability in only two dimensions. We therefore focus on the two-dimensional projection of the movements, allowing comparability to approaches for animal movement pattern analysis. In this data set of organelle movement we observe visually prominent, linear movement structures with seemingly piecewise constant movement direction and speed. Since the different sections of the movement could be associated with different movement mechanisms such as movement through cytoplasmic streaming or transport along intracellular filaments, it is of interest to detect the change points (CPs) in the direction and speed of the movement. The most widely used time discrete models are variants of the random walk. Most often used, particularly in animal studies, are so-called correlated random walks, which are parametrised by a random turning angle relative to the previous direction. Correlated random walks are useful to model movement where the difference between highly directed and undirected movement is of interest. By fitting HMM models to the observed organelle movement we show that a biased random walk (BRW), parametrised via absolute directions, may be more appropriate to model sections of different but constant movement direction. The BRW is therefore used as a reference model. However, our findings indicate that a BRW shows a higher variability in the movement direction and may thus move less strictly along a linear structure than can be observed in many organelle tracks. Therefore, we define a new model termed linear walk (LW) with less variability around an expected position. Both models, the BRW and LW, have the same process of expected positions, which is parametrised by two parameters, the movement direction and the step length, where the direction is the angle relative to the x-axis. The models differ in regard to the variability around the expected position. In the BRW, independent random increments are summed up, while in the LW an independent, random error is added to each expected position. Due to this definition the changes in movement direction and step length can be described independently. The expectation of the increments in both models can be parameterised by the movement direction and step length or alternatively by a two dimensional expectation. The maximum likelihood estimators of the model parameters in both models and proof of their strong consistency is provided. Note that for the expectation of the increments in the BRW the estimator is the classical mean, while in the LW the estimator is a weighted average. In the context of the BRW model a known MOSUM approach for the bivariate detection of change points is easily adapted to our setting. In this approach a double window is shifted over the movement track. The difference of the bivariate expectation of increments in the left and right window half is estimated, leading to a process of differences that fluctuates around the origin, but shows systematic deviation in the neighborhood around a CP. Therefore the maximum deviation of the process of differences from the origin is used as a test statistic. The rejection threshold is obtained via simulation of a limit process. CPs are estimated successively by identifying local deviations of the process of differences from the origin. In the LW model the MOSUM has inconvenient properties due to the dependency structure of the increments. Therefore a moving kernel approach is proposed where the maximum likelihood estimators for the expectation in the LW model are used instead of the classical mean. For this approach the proof of the weak convergence of the process of differences assuming the true variance is provided. For both approaches simulation studies concerning the test power and precision are provided. Since the CPs in both approaches are detected within the expectation, we propose a graphical technique to classify the detected change points into CPs in movement direction and step length and apply this technique to the observed organelle movement.

A statistical model of wind -prediction uncertainty is developed for investigating the impact of wind -predic tion uncertainty on aircraft trajectory prediction accuracy. The model seeks to capture properties of the wind uncertainty that are likely to have an impact on Air Traffic Management applications relying on trajectory prediction. The model ensures that th e distribution of errors is consistent with observations, not just in an RMS sense, but with respect to the frequency of occurrence of large errors. Spatial and temporal correlations of uncertainties are preserved, including the correlation across altitud es. Inclusion of the altitude correlation allows wind -shear error, an important contributor to climb/descent behavior, to be modeled in accordance with observation. The model applies errors at three length scales commensurate with three types of wind -pre diction errors described in the literature. The model is subsequently applied to flights in cruise and transition to investigate the impact of wind uncertainty on prediction according to this model. The aircraft dynamical response is considered to act as a low -pass filter on the wind error to yield the ground speed. It is shown that precise knowledge of initial conditions can significantly improve the along -track prediction error due to wind uncertainty for shorter look -ahead horizons. Along -track error is a weak function of operational conditions such as weight, speed and aircraft type. The altitude error in transition is shown to be small in th e average case, although the existence of large errors correlated in space and time may result in large error s occurring with some persistence.

How is new information organized in memory? According to latent state theories, this is determined by the level of surprise, or prediction error, generated by the new information: small prediction error leads to updating of existing memory, large prediction error leads to encoding of a new memory. We tested this idea using a protocol in which rats were first conditioned to fear a stimulus paired with shock. The stimulus was then gradually extinguished by progressively reducing the shock intensity until the stimulus was presented alone. Consistent with latent state theories, this gradual extinction protocol (small prediction errors) was better than standard extinction (large prediction errors) in producing long-term suppression of fear responses; and the benefit of gradual extinction was due to updating of the conditioning memory with information about extinction. Thus, prediction error determines how new information is organized in memory, and latent state theories adequately describe the ways in which this occurs.

Most of the trend analysis that has been conducted has not considered the existence of a change point in the time series analysis. If these occurred, then the trend analysis will not be able to detect an obvious increasing or decreasing trend over certain parts of the time series. Furthermore, the lack of discussion on the possible factors that influenced either the decreasing or the increasing trend in the series needs to be addressed in any trend analysis. Hence, this study proposes to investigate the trends, and change point detection of mean, maximum and minimum temperature series, both annually and seasonally in Peninsular Malaysia and determine the possible factors that could contribute to the significance trends. In this study, Pettitt and sequential Mann–Kendall (SQ–MK) tests were used to examine the occurrence of any abrupt climate changes in the independent series. The analyses of the abrupt changes in temperature series suggested that most of the change points in Peninsular Malaysia were detected during the years 1996, 1997 and 1998. These detection points captured by Pettitt and SQ–MK tests are possibly related to climatic factors, such as El Nino and La Nina events. The findings also showed that the majority of the significant change points that exist in the series are related to the significant trend of the stations. Significant increasing trends of annual and seasonal mean, maximum and minimum temperatures in Peninsular Malaysia were found with a range of 2–5 °C/100 years during the last 32 years. It was observed that the magnitudes of the increasing trend in minimum temperatures were larger than the maximum temperatures for most of the studied stations, particularly at the urban stations. These increases are suspected to be linked with the effect of urban heat island other than El Nino event.

In this thesis we discuss concentration inequalities, relaxation to equilibrium of stochastic dynamics, and random walks in dynamic random environments. In stochastic systems one is interested in macroscopic and/or asymptotic properties as well as in fluctuations around typical behaviour. But the dependence structure induced by the interaction between the components of the system makes the analysis challenging. In order to overcome this in different settings a variety of methods are employed. Additive functionals of Markov processes play important roles in applications. In order to get exponential and moment estimates for their fluctuations a non-standard martingale approximation is used. The resulting general theorems do not require special properties like reversibility or a spectral gap. What is needed is some control on the expected evolution. That is, the difference of the evolution starting from two adjacent'' configurations has to be controlled. Coupling methods are well suited to do perform this comparison. In concrete examples couplings are used to prove the conditions of the theorems. In statistical mechanics Gibbs measures and Markov random fields play important roles. The Poincare inequality is an important property describing the regularity of the measure. We prove the Poincare inequality via a martingale telescoping argument. To control the individual increments of the martingale we use a coupling method called disagreement percolation. If the clusters of this percolation are sufficiently small we obtain the Poincare inequality. When interacting spin systems and their dynamics have a delicate connection to their ergodic measure(s) one has to take more care. We carefully study the graphical construction of the dynamics to understand how the influence of the measure can be preserved. An assumption is made that one can control how fast the system in equilibrium can compensate for a single spin flip. Under this assumption we obtain relaxation speed estimates for general functions. In attractive spin systems the condition can be reduced to the decay of auto-correlation of the spin at the origin. An application where this is of use is the low-temperature Ising model. Finally we look at random walks in dynamic random environments. Here a time-changing random environment drives the motion of a particle. The goal is to understand under which conditions the macroscopic behaviour of this random walk is like that of a Brownian motion. We use coupling to prove a law of large numbers as well as a functional central limit theorem for the position of the random walk. Only polynomial decay of correlations in time are needed for the environment, and the influence of the environment on the walk can be very general.

Graphs are commonly used in various applications such as online social networks (OSNs), E-commerce systems and social recommender systems. Random walk sampling is often used to conduct statistical estimation over such graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. A new feature of this bias reduction algorithm is that it allows the variance to increase whenever the bias can be further reduced. The increased variance may lead to a large mean square error of the estimator. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. Our algorithmic framework enables one to attain different trade-offs between the sample complexity (i.e., number of parallel random walks) and the mean square error of the statistical estimation. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. To demonstrate the versatility of the framework, we apply it to optimize the Metropolis random walk and simple random walk sampling. Extensive experiments confirm the effectiveness and efficiency of our proposed algorithmic framework.

The nonstationary hydrologic processes due to climate variability and intensification of human activities are challenging and questionable for researchers. This study investigates nonstationary partial duration series (PDS) records for the period 1971–2017 at 14 hydrological stations across the Gorganrood River Basin, Iran. The Gorganrood Basin is very diverse in terms of climate such as humid, semihumid, Mediterranean, semiarid, and arid climates. Change points are analyzed using the Pettitt technique. Trends of PDS are detected using the Mann–Kendall method. The nonstationarity of the PDS series is examined by generalized additive models for location, scale, and shape (GAMLSS). Results indicate that abrupt changes are significant for the PDS series in the Gorganrood River Basin. Change points have a considerable effect on trend detection, and these may be attributed to the fact that an abrupt increase or decrease in mean values affects trend changes. In addition, the GAMLSS results showed that the most suitable performance distribution was LNO distribution and then RGE distribution in the Gorganrood River Basin. On other hand, the GAMLSS model and the Pettitt test have good capability in detecting stationary and nonstationary PDS series.

This paper addresses the problem of monitoring online a non-stationary process to detect abrupt changes in the process mean value. Two main challenges are addressed: First, the monitored process is non-stationary; i.e., naturally changes over time and it is necessary to distinguish those “regular” process changes from abrupt changes resulting from potential failures. Second, this paper aims at being applied for industrial processes where the performance of the detection method must be accurately controlled. A novel sequential method, based on two fixed-length windows, is proposed to detect abrupt changes with guaranteed accuracy while dealing with non-stationary process. The first window is used for estimating the non-stationary process parameters, whereas the second window is used to execute the detection. A study on the performances of the proposed method provides analytical expressions of the test statistical properties. This allows to bound the false alarm probability for a given number of observations while maximizing the detection power as a function of a given detection delay. The proposed method is then applied for wheels coating monitoring using an imaging system. Numerical results on a large set of wheel images show the efficiency of the proposed approach and the sharpness of the theoretical study.

Theories of associative learning often propose that learning is proportional to prediction error, or the difference between expected events and those that occur. Spicer et al. (2020) suggested an alternative, that humans might instead selectively attribute surprising outcomes to cues that they are not confident about, to maintain cue-outcome associations about which they are more confident. Spicer et al. reported three predictive learning experiments, the results of which were consistent with their proposal ("theory protection") rather than a prediction error account (Rescorla, 2001). The four experiments reported here further test theory protection against a prediction error account. Experiments 3 and 4 also test the proposals of Holmes et al. (2019), who suggested a function mapping learning to performance that can explain Spicer et al.'s results using a prediction-error framework. In contrast to the previous study, these experiments were based on inhibition rather than excitation. Participants were trained with a set of cues (represented by letters), each of which was followed by the presence or absence of an outcome (represented by + or -). Following this, a cue that previously caused the outcome (A+) was placed in compound with another cue (B) with an ambiguous causal status (e.g., a novel cue in Experiment 1). This compound (AB-) did not cause the outcome. Participants always learned more about B in the second training phase, despite A always having the greater prediction error. In Experiments 3 and 4, a cue with no apparent prediction error was learned about more than a cue with a large prediction error. Experiment 4 tested participants' relative confidence about the causal status of cues A and B prior to the AB- stage, producing findings that are consistent with theory protection and inconsistent with the predictions of Rescorla, and Holmes et al. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

ABSTRACTThis study aimed at identification of abrupt change points (CPs) and detection of gradual trends in 34‐year (1980–2013) annual rainfall at nine stations of an Indian arid region. TheCPswere determined by five tests and their significance was examined by two tests. Furthermore, trends were tested by three tests and their magnitudes were quantified by two tests. Novelty of the study lies in investigating significance of trends sequentially over years by applying Mann–Kendall (M–K) test. The identifiedCPswere similar for standard normal homogeneity test and cumulative deviations test at most stations. In contrast, Pettitt and Bayesian tests detectedCPin years 2002 and 2005 at six and three stations, respectively, and their significance was verified. Results of sequential M–K test did not match with other tests' results. The mean annual rainfall afterCP(350–627 mm) increased by 14–80% of the amount beforeCP(306–444 mm) with 7–42% reduction in coefficient of variation. The box–whisker plots supported these findings. Results of trend tests indicated statistically significant trends at Anjar, Bhachau, Mandvi and Rapar. Trend magnitudes by linear regression prior toCP(−6.2 to 7.1 mm year−1) showed an overall increase afterCP(4.7–40.8 mm year−1) with negative trend at one station. Sen's slope test, showing good harmony with linear regression, revealed that trend magnitudes afterCPwere 2–10 times higher than that for 34‐year period at six stations. Results of M–K test applied for sequential periods emphasized that rainfall trends are becoming stronger over time. This finding suggests that significance level of increasing rainfall trends may further increase in future. Finally, findings of this study are useful for planners and decision makers for developing policies to meet the challenges of the heightened rainfall in study area. Also, the approach used here may be adopted in other parts of the globe.

Water Accounting Plus for Water Resources Reporting and River Basin Planning

Quantifying errors in travel time and cost by latent variables