Adaptive Rejection Research Articles

Efficient Sampling From the Watson Distribution in Arbitrary Dimensions

In this paper, we present two efficient methods for sampling from the Watson distribution in arbitrary dimensions. The first method adapts the rejection sampling algorithm from Kent et al. (2018), originally designed for Bingham distributions, using angular central Gaussian envelopes. For the Watson distribution, we derive a closed-form expression for the parameters that maximize sampling efficiency, which is further investigated and bounded by asymptotic results. This approach avoids the curse of dimensionality through a smart matrix inversion, enabling fast runtimes even in high dimensions. The second method, based on Saw (1978), employs adaptive rejection sampling from a projected distribution. This algorithm is also effective in all dimensions and offers rapid sampling capabilities. Finally, our simulation study compares the two main methods, revealing that each excels under different conditions: the first method is more efficient for small samples or large dimensions, while the second performs better with larger samples and more concentrated distributions. Both algorithms are available in the R package watson on CRAN. Supplementary materials for this article are available online.

Systematic Control Design for Adaptive Rejection of Narrow-Band Disturbances Based on a Novel Resonant Generalized Extended State Observer

In this paper, the adaptive rejection of multiple narrow-band disturbances with time-varying frequencies is investigated. A systematic control approach based on a resonant generalized extended state observer (RGESO) is proposed. The frequency response of the RGESO is shaped into a desired form to reject the total disturbance, including the wide-band uncertainties and the narrow-band disturbances. The state-space realization of the RGESO is also provided to estimate both the states and the total disturbance. To handle the time-varying frequencies of the narrow-band disturbances, a direct frequency estimation approach based on the Levenberg–Marquardt method and an online supervision strategy is presented to improve convergence and reliability, and the estimations are then used to adapt the RGESO parameters. Parameter tuning and stability robustness analysis methods are also developed for the proposed scheme to facilitate its application. Finally, extensive simulations are conducted to demonstrate the effectiveness of our method.

Automated generation of initial points for adaptive rejection sampling of log-concave distributions

Automated generation of initial points for adaptive rejection sampling of log-concave distributions

Wheeled Robot Formation Control under Uncertainty Including Adaptive Rejection of Harmonic Disturbances with Arbitrary Frequencies

This work addresses an adaptive regulation problem for formation control of uncertain unicycle-like dynamical robots. The control goal is to drive a finite number of robots to a prescribed formation despite the presence of multi-sinusoidal input disturbances of unknown frequencies and despite uncertainties in the unicycle model, (mass and inertia’s are unknown). Numerical Simulations were done to illustrate the viability of the suggested strategy. The only measurements available for control are the orientation of the unicycles and the relative positions and velocities according to a given connectivity graph.

Concave-Convex PDMP-based Sampling

Recently nonreversible samplers based on simulating piecewise deterministic Markov processes (PDMPs) have shown potential for efficient sampling in Bayesian inference problems. However, there remains a lack of guidance on how to best implement these algorithms. If implemented poorly, the computational costs of simulating event times can outweigh the statistical efficiency of the nonreversible dynamics. Drawing on the adaptive rejection literature, we propose the concave-convex adaptive thinning approach for simulating a piecewise deterministic Markov process, which we call CC-PDMP. This approach provides a general guide for constructing bounds that may be used to facilitate PDMP-based sampling. A key advantage of this method is its additive structure—adding concave-convex decompositions yields a concave-convex decomposition. This makes the construction of bounds modular, as given a concave-convex decomposition for a class of likelihoods and a family of priors, they can be combined to construct bounds for the posterior. We show that constructing our bounds is simple and leads to computationally efficient thinning. Our approach is well suited to local PDMP simulation where conditional independence of the target can be exploited for potentially huge computational gains. We provide an R package and compare with existing approaches to simulating events in the PDMP literature. Supplementary materials for this article are available online.

Generalized gamma distribution based on the Bayesian approach with application to investment modelling

The Generalized Gamma Distribution (GGD) is one of the most popular distributions in analyzing real lifetime datasets. Estimating the parameters of a high dimensional probability distribution is challenging due to the complexities associated with the resulting objectives function. When traditional estimation techniques fail due to complexity in the model objectives function, other powerful computational approaches are employed. In this study, a Bayesian approach to Generalized Gamma Distribution (GGD) based on Markov Chain Monte-Carlo (MCMC) has been employed to estimate model parameters. This study considers the Bayesian approach to GGD parameters using the Adaptive Rejection Metropolis Sampling (ARMS) technique of random variable generation within the Gibbs sampler. The MCMC approach has been used for estimating the multi-dimensional objectives function distribution. The results of the ARMS were compared to the existing Simulated annealing (SA) algorithm and Method of Moment (MM) based on modified internal rate of return data (MIRR). The performances of various derived estimators were recorded using the Markov chain Monte Carlo simulation technique for different sample sizes. The study reveals that ARMS's performance is marginally better than the existing SA and MA approaches. The efficiency of ARMS does not require a larger sample size as the SA does, in the case of simulated data. The performances of ARMS and SA are similar comparing them to the MM as an initial assumption in the case of real MIRR data. However, ARMS gives an acceptable estimated parameter for the different sample sizes due to its ability to evaluate the conditional distributions easily and sample from them exactly.

Sampling methods for the concentration parameter and discrete baseline of the Dirichlet Process

Abstract There are many models in the current statistical literature for making inferences based on samples selected from a finite population. Parametric models may be problematic because statistical inference is sensitive to parametric assumptions. The Dirichlet process (DP) prior is very flexible and determines the complexity of the model. It is indexed by two hyper-parameters: the baseline distribution and concentration parameter. We address two distinct problems in the article. Firstly, we review the current sampling methods for the concentration parameter, which use the continuous baseline distribution. We compare three different methods: the adaptive rejection method, the mixture of Gammas method and the grid method. We also propose a new method based on the ratio of uniforms. Secondly, in practice, some survey responses are known to be discrete. If a continuous distribution is adopted as the baseline distribution, the model is misspecified and standard inference may be invalid. We propose a discrete baseline approach to the DP prior and sample the unobserved responses from the finite population both using a Polya urn scheme and a Multinomial distribution. We applied our discrete baseline approach to a Phytophthora data set.

An adaptive rejection sampler for sampling from the Wiener diffusion model.

The Wiener diffusion model with two absorbing boundaries is one of the most frequently applied models for jointly modeling responses and response latencies in psychological research. We consider four methods for sampling from the model with and without variability in drift rate, starting point, and non-decision time: Inverse transform sampling, rejection sampling, and two new methods based on adaptive rejection sampling (ARS). We implement these four methods in an R package, validate the methods, and compare their sampling speed in different settings. All four implemented methods provide samples that follow the intended distributions. The ARS-based methods, however, outperform the other methods in sampling speed as the requested sample size increases. We provide guidelines for when using ARS is more efficient than using traditional methods and vice versa.

Adaptive Rejection of a Sinusoidal Disturbance with Unknown Frequency in a Flexible Rotor with Lubricated Journal Bearings

Frequency-dependent adaptive noise cancellation-based tracking controller (ANC-TC) is a known technique for the stabilization of several nonlinear dynamical systems. In recent years, this control strategy has been introduced and applied for the stabilization of a flexible rotor supported on full-lubricated journal bearings. This paper proposes a theoretical investigation, based on robust immersion and invariance (I&I) theory, of a novel ANC-frequency estimation (FE) technique designed to stabilize a flexible rotor shaft affected by self-generated sinusoidal disturbances, generalized to the case of unknown frequency. A structural proof, under assumptions on closed-loop output signals, shows that the sinusoidal disturbance rejection is exponential. Numerical simulations are presented to validate the mathematical results in silico. The iterative Inexact Newton method is applied to the disturbance frequency and phase estimation error point series. The data fitting confirms that the phase estimation succession has an exponential convergence behavior and that the asymptotical frequency estimation is a warm-up phase of the overall close-loop disturbance estimation process. In two different operating conditions, the orders of convergence obtained by phase and frequency estimate timeseries are pφ=1, pω,unc=0.9983 and pω,cav=1.005. Rejection of the rotor dynamic disturbance occurs approximately 76% before in the cavitated than in the uncavitated condition, 2 (s) and 8.5 (s), respectively.

Exact Simulation of Max-Infinitely Divisible Processes

Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions drawn from a Poisson point process defined on a suitable function space. Simulating from a max-id process is often difficult due to its complex stochastic structure, while calculating its joint density in high dimensions is often numerically infeasible. Therefore, exact and efficient simulation techniques for max-id processes are useful tools for studying the characteristics of the process and for drawing statistical inferences. Inspired by the simulation algorithms for max-stable processes, theory and algorithms to generalize simulation approaches tailored for certain flexible (existing or new) classes of max-id processes are presented. Efficient simulation for a large class of models can be achieved by implementing an adaptive rejection sampling scheme to sidestep a numerical integration step in the algorithm. The results of a simulation study highlight that our simulation algorithm works as expected and is highly accurate and efficient, such that it clearly outperforms customary approximate sampling schemes. As a by-product, new max-id models, which can be represented as pointwise maxima of general location-scale mixtures and possess flexible tail dependence structures capturing a wide range of asymptotic dependence scenarios, are also developed.

Bayesian Estimation of The Ex-Gaussian Distribution

Fitting of the exponential modified Gaussian distribution to model reaction times and drawing conclusions from its estimated parameter values is one of the most popular method used in psychology. This paper aims to develop a Bayesian approach to estimate the parameters of the ex-Gaussian distribution. Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method. Applications on simulated data and on real data are provided to compare this method to the standard maximum likelihood estimation method as well as the quantile maximum likelihood estimation. Results shows the effectiveness of the proposed Bayesian method by computing the root mean square error of the estimated parameters using the three methods.

Adaptive rejection of narrow-band disturbances in the presence of plant uncertainties—A dual Youla–Kucera approach

The stability of adaptive disturbance rejection schemes using Youla–Kucera (YK) parametrization and the internal model principle (IMP) in the presence of plant model uncertainties is investigated. The problem is approached by using the dual Youla–Kucera parametrization for the description of the plant model uncertainties. The known disturbance case is discussed first, emphasizing the need of over parametrization of the Youla–Kucera filter used for control in order to both solving the IMP and the stability problems. Then this solution is extended for the case of unknown disturbances leading to the use of a parameter adaptation algorithm with projection. A stability analysis of the adaptive scheme is provided. Simulation results on relevant examples and experimental evaluation on an active noise attenuation system illustrate the possibilities of this approach for handling significant plant-model mismatch.

Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo

For modeling multivariate financial time series a single factor copula model with stochastic volatility margins is proposed. It generalizes single factor models based on the multivariate normal distribution by allowing for symmetric and asymmetric tail dependence. A joint Bayesian approach using Hamiltonian Monte Carlo (HMC) within Gibbs sampling is developed. Thus, the information loss caused by the two-step approach for margins and dependence is avoided. Further, the Bayesian approach is tractable in high dimensional parameter spaces in addition to uncertainty quantification through credible intervals. By introducing indicators for different copula families the copula families are selected automatically in the Bayesian framework. In a first simulation study the performance of HMC for the copula part is compared to a procedure based on adaptive rejection Metropolis sampling within Gibbs sampling. It is shown that HMC considerably outperforms this alternative approach in terms of effective sample size per minute. In a second simulation study satisfactory performance is seen for the full HMC within Gibbs procedure. The approach is illustrated for a portfolio of financial assets with respect to one-day ahead value at risk forecasts. Comparison to a two-step estimation procedure and to relevant benchmark models, such as a multivariate factor stochastic volatility model, shows superior performance of the proposed approach.

Anti-swing strategy of overhead cranes based on prescribed performance PID control

How to ensure anti-swing and adaptive control for cranes when used in complex outdoor environment such as docks is a difficult problem. Although the traditional PID control can solve the problem of robust adaptive and disturbance rejection very well, the quality of PID parameters depends too much on the experience of adjusting parameters or requires a lot of trial and error, so a new non-linear PID control method is proposed in this paper. The theory of prescribed performance control is introduced, and a non-linear closed-loop PID controller is designed based on the idea of performance function and error conversion of prescribed performance control. As the parameter adjustment is more flexible, the system has better robustness, adaptability and immunity to disturbance. Experiment results show that using the designed anti-swing strategy can effectively realise the anti-swing and it has excellent anti-interference ability.

Bayesian Survival Analysis for Generalized Pareto Distribution Under Progressively Type II Censored Data

In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented.

An Ultra-Compact Low Power Self-Capacitive Touch Screen Readout IC Embedding Reconfigurable Noise Immunity and Current-Driven Capacitance Compensation

This brief presents the design of a readout IC for dot-matrix, self-capacitive touch screen system. To accommodate only a capacitive change with large base capacitance of electrodes, it employs an encoded multiple sensing method as well as current- driven offset compensator (OC), that strike circuit complexity, power consumption and handling range of the base capacitance. The current-driven OC can provide compensation current up to 300 $\boldsymbol {\mu }\text{A}$ with a 4-bit tunable magnitude and mismatch calibration between source and sink currents. It can also perform adaptive noise rejection for in-band as well as out-band interferences by introducing hybrid touch screen panel (TSP) drive scheme. The measurement results show that it achieves 47.2 dB signal-to-noise ratio and 31 dB in-band noise rejection with 220 kHz TSP drive frequency and 330 Hz scan rate when a 4 mm metal pillar is used. The proposed front end circuit, fabricated on a 130-nm CMOS technology, occupies an area of 0.128 mm2 and consumes 1.04 mW of power for 16 channels 1.3-in, dot-matrix On-cell TSP for rigid OLED.

Features of atmospheric tide according to the Geophysical observatory Mikhnevo

Atmospheric tides refer to those oscillations in the atmosphere whose periods are integral fractions of a lunar or solar day. Atmospheric tides are, in small measure, gravitationally forced, they are primarily forced by daily variations in solar insolation. Based on the results of instrumental observations of micropulsations of atmospheric pressure, the main waves of the lunar-solar tide in the Earth’s atmosphere are identified. The registration of micropulsations is obtained in the range from 0.1 MHz to 10 Hz in the Geophysical observatory Mikhnevo of Institute of Geosphere Dynamics of Russian Academy of Sciences located in the Moscow region in period 2008-2016. An estimate of the spectral characteristics of micropulsations was carried out using the maximum entropy method. In order to increase the level of discrimination related to the frequencies of tidal waves, the adaptive rejection filtering method was applied. It is shown that the spectral amplitudes with frequencies that coincide with the frequencies of the tidal waves change with time with a periodicity of about 29 days. The characteristics of modulation of the solar elliptic wave S1 and the main solar wave S2 by periods of 13.66, 27.55 days are obtained; as well as ∼ 0.3, 0.5 and 1 year.

Clutter Parameter Estimation Based on Indirect Algorithms

Indirect algorithms for clutter parameter estimation using linear transformations of initial data have been synthesized by the maximum likelihood method. The likelihood function was introduced for the input samples transformed in accordance with the sum-difference algorithms. The estimation algorithms of the interperiod correlation and Doppler phase shift coefficients derived by solving the appropriate likelihood equations do not contain the traditional complex multiplication operation over input data. The functional block diagram of the estimator of appropriate clutter parameters that can be used in adaptive rejection filters is presented. The estimation accuracy analysis of required parameters of clutter is performed depending on the size of training sample and correlation properties of clutter. The comparison of simulation and calculation results for indirect and direct algorithms revealed their complete match and confirmed the asymptotic efficiency of resultant estimates and the equivalence of indirect and direct algorithms.

A nonparametric Bayesian continual reassessment method in single-agent dose-finding studies

BackgroundThe main purpose of dose-finding studies in Phase I trial is to estimate maximum tolerated dose (MTD), which is the maximum test dose that can be assigned with an acceptable level of toxicity. Existing methods developed for single-agent dose-finding assume that the dose-toxicity relationship follows a specific parametric potency curve. This assumption may lead to bias and unsafe dose escalations due to the misspecification of parametric curve.MethodsThis paper relaxes the parametric assumption of dose-toxicity relationship by imposing a Dirichlet process prior on unknown dose-toxicity curve. A hybrid algorithm combining the Gibbs sampler and adaptive rejection Metropolis sampling (ARMS) algorithm is developed to estimate the dose-toxicity curve, and a two-stage Bayesian nonparametric adaptive design is presented to estimate MTD.ResultsFor comparison, we consider two classical continual reassessment methods (CRMs) (i.e., logistic and power models). Numerical results show the flexibility of the proposed method for single-agent dose-finding trials, and the proposed method behaves better than two classical CRMs under our considered scenarios.ConclusionsThe proposed dose-finding procedure is model-free and robust, and behaves satisfactorily even in small sample cases.

Repeated responses in misclassification binary regression: A Bayesian approach

Binary regression models generally assume that the response variable is measured perfectly. However, in some situations, the outcome is subject to misclassification: a success may be erroneously classified as a failure or vice versa. Many methods, described in existing literature, have been developed to deal with misclassification, but we demonstrate that these methods may lead to serious inferential problems when only a single evaluation of the individual is taken. Thus, this study proposes to incorporate repeated and independent responses in misclassification binary regression models, considering the total number of successes obtained or even the simple majority classification. We use subjective prior distributions, as our conditional means prior, to evaluate and compare models. A data augmentation approach, Gibbs sampling, and Adaptive Rejection Metropolis Sampling are used for posterior inferences. Simulation studies suggested that repeated measures significantly improve the posterior estimates, in that these estimates are closer to those obtained in a case with no misclassifications with a lower standard deviation. Finally, we illustrate the usefulness of the new methodology with the analysis about defects in eyeglass lenses.