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Many testing problems are readily amenable to randomized tests, such as those employing data splitting. However, despite their usefulness in principle, randomized tests have obvious drawbacks. Firstly, two analyses of the same dataset may lead to different results. Secondly, the test typically loses power because it does not fully utilize the entire sample. As a remedy to these drawbacks, we study how to combine the test statistics or p -values resulting from multiple random realizations, such as through random data splits. We develop rank-transformed subsampling as a general method for delivering large-sample inference about the combined statistic or p -value under mild assumptions. We apply our methodology to a wide range of problems, including testing unimodality in high-dimensional data, testing goodness-of-fit of parametric quantile regression models, testing no direct effect in a sequentially randomized trial and calibrating cross-fit double machine learning confidence intervals. In contrast to existing p -value aggregation schemes that can be highly conservative, our method enjoys Type I error control that asymptotically approaches the nominal level. Moreover, compared to using the ordinary subsampling, we show that our rank transform can remove the first-order bias in approximating the null under alternatives and greatly improve power. [ABSTRACT FROM AUTHOR]

It is important to improve the localization accuracy of the unmanned surface vehicle (USV) for ensuring safe navigation in an inland waterway scenario. However, the localization accuracy of the USV is affected by the limited availability of global navigation satellite system signals, the sparsity of feature points, and the high scene similarity in inland waterway scenarios. Therefore, this paper proposes a laser-based simultaneous localization and mapping (SLAM) algorithm for accurate localization and mapping in inland waterway scenarios. Inertial measurement unit (IMU) data are integrated with lidar data to address motion distortion caused by the frequent motion of the USV. Subsequently, a generalized iterative closest point (GICP) algorithm incorporating rejection sampling is integrated to enhance the accuracy of point cloud matching, involving a two-phase filtering process to select key feature points for matching. Additionally, a mixed global descriptor is constructed by combining point cloud intensity and distance information to improve the accuracy of loop closure detection. Experiments are conducted on the USV-Inland datasets to evaluate the performance of the proposed algorithm. The experimental results show that the proposed algorithm generates accurate mapping and significantly improves localization accuracy by 25.6%, 18.5%, and 23.6% compared to A-LOAM, LeGO-LOAM, and ISC-LOAM, respectively. These results demonstrate that the proposed algorithm achieves accurate localization and mapping in an inland waterway scenario. [ABSTRACT FROM AUTHOR]

Inverse transform sampling is a general method to generate non-uniform-distributed random numbers, but it can be unstable when simulating extremely truncated distributions. Many famous probability distributions are log-concave; this feature is preserved under truncation, so Devroye's automatic rejection sampler is available for this task. This method is more stable than inverse transform sampling and uses a very simple envelope with an acceptance rate greater than 20%, independent of the distribution. The aim of this paper is threefold: firstly, to warn the public against incorrect simulation of truncated distributions; secondly, to motivate a more extensive use of rejection sampling to mitigate these issues; lastly, to propose Devroye's automatic sampler as a practical standard for log-concave distributions. We illustrate the proposal with simulations based on Tweedie distributions due to their relevance in regression analysis. The proposed sampler is shown to work under more extreme truncations than the inverse transform method. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we present two efficient methods for sampling from the Watson distribution in arbitrary dimensions. The first method adapts the rejection sampling algorithm from Kent, Ganeiber, and Mardia, 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, 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. [ABSTRACT FROM AUTHOR]

Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution's parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Frontiers of Computer Science & Technology is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution’s parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions.

It is important to improve the localization accuracy of the unmanned surface vehicle (USV) for ensuring safe navigation in an inland waterway scenario. However, the localization accuracy of the USV is affected by the limited availability of global navigation satellite system signals, the sparsity of feature points, and the high scene similarity in inland waterway scenarios. Therefore, this paper proposes a laser-based simultaneous localization and mapping (SLAM) algorithm for accurate localization and mapping in inland waterway scenarios. Inertial measurement unit (IMU) data are integrated with lidar data to address motion distortion caused by the frequent motion of the USV. Subsequently, a generalized iterative closest point (GICP) algorithm incorporating rejection sampling is integrated to enhance the accuracy of point cloud matching, involving a two-phase filtering process to select key feature points for matching. Additionally, a mixed global descriptor is constructed by combining point cloud intensity and distance information to improve the accuracy of loop closure detection. Experiments are conducted on the USV-Inland datasets to evaluate the performance of the proposed algorithm. The experimental results show that the proposed algorithm generates accurate mapping and significantly improves localization accuracy by 25.6%, 18.5%, and 23.6% compared to A-LOAM, LeGO-LOAM, and ISC-LOAM, respectively. These results demonstrate that the proposed algorithm achieves accurate localization and mapping in an inland waterway scenario.

A prominent problem in analysing genetic information has been a lack of mathematical frameworks for doing so. This article offers some new statistical methods to model and analyse information content in proteins, protein families, and their sequences. We discuss how to understand the qualitative aspects of genetic information, how to estimate the quantitative aspects of it, and implement a statistical model where the qualitative genetic function is represented jointly with its probabilistic metric of self-information. The functional information of protein families in the Cath and Pfam databases are estimated using a method inspired by rejection sampling. Scientific work may place these components of information as one of the fundamental aspects of molecular biology. [ABSTRACT FROM AUTHOR]

Random variate generation has been widely used in various engineering applications and model frameworks. The introduction of the proposal distribution makes this kind of methods can deal with more general sampling problems with complex probability density representation. However, the design of proposal distribution is usually difficult, especially when the target distribution is so complex that it contains asymmetric, multimodal and skewed, or even unsmooth, heavy tailed and illegal density, the sampling performance and efficiency will be greatly affected. In this paper, a novel parameter optimization method with efficient self-tuning strategy is proposed in order to automatically construct the optimal proposal distribution for any complex target density, which treats the design of proposal distribution as a parameter search process and search the optimal solution in an infeasible region by evaluating the loss of solution. The significant advantage of the proposed method is that the search based on infeasible region can converge to a good solution with only a few iterations, making our method far superior to other existing methods in efficiency, which is very suitable for the complex target distribution model with time-consuming density calculation process. Experimental results show the advantages of the proposed method in terms of search strategy, optimal solution performance, search efficiency and robustness.

Abstract Gaussian sampling over the integers is one of the fundamental building blocks of lattice-based cryptography. Among the extensively used trapdoor sampling algorithms, it is ineluctable until now. Under the influence of numerous side-channel attacks, it is still challenging to construct a Gaussian sampler that is generic, efficient, and resistant to timing attacks. In this paper, our contribution is three-fold. First, we propose a secure, efficient exponential Bernoulli sampling algorithm. It can be applied to Gaussian samplers based on rejection samplings. We apply it to FALCON, a candidate of round 3 of the NIST post-quantum cryptography standardization project, and reduce its signature generation time by 13–14%. Second, we develop an isochronous Gaussian sampler based on rejection sampling. Our Algorithm can securely sample from Gaussian distributions with different standard deviations and arbitrary centers. We apply it to PALISADE (S&P 2018), an open-source lattice-based cryptography library. During the online phase of trapdoor sampling, the running time of the G-lattice sampling algorithm is reduced by 44.12% while resisting timing attacks. Third, we improve the efficiency of the COSAC sampler (PQC 2020). The new COSAC sampler is 1.46x–1.63x faster than the original and has the lowest expected number of trials among all Gaussian samplers based on rejection samplings. But it needs a more efficient algorithm sampling from the normal distribution to improve its performance.

As the key technology of the new generation air traffic control, automatic dependent surveillance-broadcast (ADS-B) has been deployed in most airspace around the world. The existing ADS-B message authentication schemes mainly utilize traditional public key cryptosystem to achieve data security, which are complex for computation and vulnerable to the quantum attack. We apply latticebased cryptography to ADS-B communication security for the first time, and propose a hierarchical certificateless message authentication scheme supporting message recovery and batch verification simultaneously. The ADS-B airborne equipments are not required to manage certificates, and there is no key escrow problem. The ADS-B messages do not need to be transmitted with the signature, but can be recovered during verification. By utilizing rejection sampling and trapdoor-free technology, the proposed scheme requires just some computationally simple linear operations to realize message authentication. Our scheme is provably secure in the random oracle model under the assumption of the small integer solution (SIS). Experimental results of performance evaluation indicate that this scheme has significant performance improvement in saving computing overhead compared with related works under the same bit security level. It is very suitable for typical aeronautic electronic devices with limited computational resources. [ABSTRACT FROM AUTHOR]

Stochastic programming has been widely used in various application scenarios and theoretical research works. However, these excellent methods depend on specific explicit probability modeling with complete knowledge of uncertainty, which is very limited in practical problem since there is usually no way to abstract complex uncertainties into the commonly used known probability models. In this paper, a novel generative model named the Adaptive Discrete Approximation Rejection Sampling is proposed for stochastic programming with incomplete knowledge of uncertainty, which can not only simulate uncertain scenarios from a complex explicit probability model that cannot meet the constraints of existing sampling methods, but also even simulate scenarios from a sample set related to uncertainty when the specific explicit probability model of uncertainty is missing or unavailable. The method is to establish the easy-to-sample proposal distribution by approximately transforming the complex hard-to-sample target probability model, to make the proposal distribution close enough to the target distribution, so as to achieve an efficient sampling while ensuring the performance of the model. On this basis, combining the Monte Carlo method and heuristic optimization, an uncertain optimization model for stochastic programming with incomplete knowledge of uncertainty is further constructed, to solve the unavailability of the existing stochastic programming methods in the absence of explicit probability model of uncertainty. Experimental results show the advantages of the proposed method in terms of applicability, adaptability, accuracy, efficiency and model performance. [ABSTRACT FROM AUTHOR]

We develop efficient methods for simulating processes of Ornstein–Uhlenbeck type related to the class of p-tempered α -stable ( TS α p ) distributions. Our results hold for both the univariate and multivariate cases and we consider both the case where the TS α p distribution is the stationary law and where it is the distribution of the background driving Lévy process. In the latter case, we also derive an explicit representation for the transition law as this was previous known only in certain special cases and only for p = 1 and α ∈ [ 0 , 1) . Simulation results suggest that our methods work well in practice. [ABSTRACT FROM AUTHOR]

In engineering practice, the bus powertrain mounting system (BPMS) may have both epistemic and aleatory uncertainty under the influence of manufacturing, measurement, and assembly errors. The hybrid uncertainty in BPMS may result in over-design or insufficient design. Therefore, the probability box (p-box) model, which can handle both aleatory and epistemic variables, is introduced into the uncertainty analysis of BPMS. Considering the elastic connection between the compressor and powertrain, a 12-degree-of-freedom dynamic model is constructed to calculate the inherent characteristic of BPMS. A rejection sampling method based on the fast envelope function (RSMBFEF) is proposed to propagate the hybrid uncertainties. Then double-loop Monte Carlo method is used to be compared with RSMBFEF. To reduce the number of uncertainty analyses, a two-step uncertainty optimisation method is proposed. Finally, the proposed method's efficacy and accuracy are verified through a numerical case. The applicability of the p-box model is illustrated by comparing it with the BPMS model with only pure aleatory or pure interval variables. [ABSTRACT FROM AUTHOR]

A discrete Gaussian distribution over the integers is a Gaussian distribution restricted so that its support is the set of all the integers. This paper studies the problem of sampling exactly from discrete Gaussian distributions over the integers. It is required to generate integers according to a given discrete Gaussian distribution without any statistical discrepancy. In 2016, Karney proposed an exact sampling algorithm for discrete Gaussian distributions whose parameters are rational numbers. This algorithm uses rejection sampling, and it is a discretization of his algorithm for sampling exactly from the standard normal distribution. In this paper, we give a rigorous and complete analysis of the rejection rate of this algorithm, which was not given by Karney, and show that it cannot generate integers efficiently in the case where the standard deviation of the distribution is very small (e.g. much smaller than 1/2). Then, we present an alternative algorithm for this special case, which can sample exactly and efficiently from discrete Gaussian distributions with very small standard deviations. [ABSTRACT FROM AUTHOR]

A new continuous-time Markov chain rate change formula is proven. This theorem is used to derive existence and uniqueness of novel filtering equations akin to the Duncan–Mortensen–Zakai equation and the Fujisaki–Kallianpur–Kunita equation but for Markov signals with general continuous-time Markov chain observations. The equations in this second theorem have the unique feature of being driven by both the observations and the process counting the observation transitions. A direct method of solving these filtering equations is also derived. Most results apply as special cases to the continuous-time Hidden Markov Models (CTHMM), which have become important in applications like disease progression tracking, The corresponding CTHMM results are stated as corollaries. Finally, application of our general theorems to Markov chain importance sampling, rejection sampling and branching particle filtering algorithms is also explained and these are illustrated by way of disease tracking simulations. [ABSTRACT FROM AUTHOR]

The multivariate skew-t distribution plays an important role in statistics since it combines skewness with heavy tails, a very common feature in real-world data. A generalization of this distribution is the truncated multivariate skew-t distribution which contains the truncated multivariate t distribution and the truncated multivariate skew-normal distribution as special cases. In this article, we study several distributional properties of the truncated multivariate skew-t distribution involving affine transformations, marginalization, and conditioning. The generation of random samples from this distribution is described. [ABSTRACT FROM AUTHOR]

Genotyping of single nucleotide variants (SNVs) has enabled the assessment of disease-related risk factors and significantly improved the potency of diagnosis and prognosis. Meanwhile, genotyping of SNVs is challenging due to the high sequence similarity between wild-type (WT) and SNV. To increase the discrimination between WT and SNV, probes are modified with nucleic acid analogues such as locked nucleic acid (LNA), or deliberate mismatches are introduced to the probe sequence. However, nucleic acid analogues have limitation in high cost and complexity in their synthesis. And a generalized methodology has not been proposed for determining the position and type of deliberate mismatches at the designated experimental conditions to the best of our knowledge. Herein, we propose a reliable workflow for designing mismatch-introduced probes (MIPs) based on nucleic acid thermodynamic analysis and rejection sampling. The theoretical hybridization state of MIP was calculated using nucleic acid thermodynamics, and the detectability was estimated by rejection sampling that simulates the errors from experimental environments. We fabricated MIPs for SNVs in epidermal growth factor receptor, and experimentally demonstrated optimized detectability. The detectability increased up to 7.19-fold depending on the position and type of mismatch; moreover, the optimized MIP showed higher detectability than the LNA probe. This indicates that the workflow can be broadly applied to the optimization of probe sequence for the detection of various disease-related SNVs. [ABSTRACT FROM AUTHOR]

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.

In this note, we develop a novel algorithm for generating random numbers from a distribution with a probability density function proportional to sin k (x) , x ∈ (0 , π) and k ≥ 1. Our algorithm is highly efficient and is based on rejection sampling where the envelope distribution is an appropriately chosen beta distribution. An example application illustrating how the new algorithm can be used to generate random correlation matrices is discussed. [ABSTRACT FROM AUTHOR]

Gaussian sampling over the integers is one of the fundamental building blocks of lattice-based cryptography. Among the extensively used trapdoor sampling algorithms, it is ineluctable until now. Under the influence of numerous side-channel attacks, it is still challenging to construct a Gaussian sampler that is generic, efficient, and resistant to timing attacks. In this paper, our contribution is three-fold. First, we propose a secure, efficient exponential Bernoulli sampling algorithm. It can be applied to Gaussian samplers based on rejection samplings. We apply it to FALCON, a candidate of round 3 of the NIST post-quantum cryptography standardization project, and reduce its signature generation time by 13–14%. Second, we develop an isochronous Gaussian sampler based on rejection sampling. Our Algorithm can securely sample from Gaussian distributions with different standard deviations and arbitrary centers. We apply it to PALISADE (S&P 2018), an open-source lattice-based cryptography library. During the online phase of trapdoor sampling, the running time of the G-lattice sampling algorithm is reduced by 44.12% while resisting timing attacks. Third, we improve the efficiency of the COSAC sampler (PQC 2020). The new COSAC sampler is 1.46x–1.63x faster than the original and has the lowest expected number of trials among all Gaussian samplers based on rejection samplings. But it needs a more efficient algorithm sampling from the normal distribution to improve its performance. [ABSTRACT FROM AUTHOR]

In 2016, Karney proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney's algorithm requires the access to an infinite sequence of independently and uniformly random deviates over the range (0, 1). We give a theoretical estimate of the expected number of uniform deviates used by this algorithm until it completes, and present an improved algorithm with lower uniform deviate consumption. The experimental results also shows that our improved algorithm has better performance than Karney's algorithm. [ABSTRACT FROM AUTHOR]

Well before large-scale quantum computers will be available, traditional cryptosystems must be transitioned to post-quantum (PQ) secure schemes. The NIST PQC competition aims to standardize suitable cryptographic schemes. Candidates are evaluated not only on their formal security strengths, but are also judged based on the security with regard to resistance against side-channel attacks. Although round 3 candidates have already been intensively vetted with regard to such attacks, one important attack vector has hitherto been missed: PQ schemes often rely on rejection sampling techniques to obtain pseudorandomness from a specific distribution. In this paper, we reveal that rejection sampling routines that are seeded with secretdependent information and leak timing information result in practical key recovery attacks in the code-based key encapsulation mechanisms HQC and BIKE. Both HQC and BIKE have been selected as alternate candidates in the third round of the NIST competition, which puts them on track for getting standardized separately o the finalists. They have already been specifically hardened with constant-time decoders to avoid side-channel attacks. However, in this paper, we show novel timing vulnerabilities in both schemes: (1) Our secret key recovery attack on HQC requiresonly approx. 866,000 idealized decapsulation timing oracle queries in the 128-bit security setting. It is structurally different from previously identified attacks on the scheme: Previously, exploitable side-channel leakages have been identified in the BCH decoder of a previously submitted HQC version, in the ciphertext check as well as in the pseudorandom function of the Fujisaki-Okamoto transformation. In contrast, our attack uses the fact that the rejection sampling routine invoked during the deterministic re-encryption of the decapsulation leaks secret-dependent timing information, which can be efficiently exploited to recover the secret key when HQC is instantiated with the (now constant-time) BCH decoder, as well as with the RMRS decoder of the current submission. (2) From the timing information of the constant weight word sampler in the BIKE decapsulation, we demonstrate how to distinguish whether the decoding step is successful or not, and how this distinguisher is then used in the framework of the GJS attack to derive the distance spectrum of the secret key, using 5.8 x 107 idealized timing oracle queries. We provide details and analyses of the fully implemented attacks, as well as a discussion on possible countermeasures and their limits.

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Three new rejection sampling methods for generating samples from the adjoint Klein-Nishina cross section are discussed: the two-branch rejection sampling procedure, the three-branch linear rejection sampling procedure and the three-branch inverse rejection sampling procedure. These methods have all been implemented in the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). The efficiency and sample generation rate of each of these methods are evaluated to characterize the methods and to make recommendations regarding their use. The use of these methods in realistic transport simulations is also evaluated by incorporating a scattering function into the sampling process. The results of an infinite medium problem are presented to verify that the sampling procedure can be used in an adjoint Monte Carlo simulation to generate results that are in agreement with an equivalent forward simulation. [ABSTRACT FROM AUTHOR]

In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either momentarily unavailable or too expensive in terms of computation time. It therefore needs to be replaced by an approximation procedure. As was previously the case, the ambitious exact simulation of first exit times for diffusion processes was unreachable though it concerns many applications in different fields like mathematical finance, neuroscience or reliability. The usual way to describe first exit times was to use discretization schemes, that are of course approximation procedures. Recently, Herrmann and Zucca (Herrmann and Zucca, 2020) proposed a new algorithm, the so-called GDET-algorithm (General Diffusion Exit Time), which permits to simulate exactly the first exit time for one-dimensional diffusions. The only drawback of exact simulation methods using an acceptance-rejection sampling is their time consumption. In this paper the authors highlight an acceleration procedure for the GDET-algorithm based on a multi-armed bandit model. The efficiency of this acceleration is pointed out through numerical examples. [ABSTRACT FROM AUTHOR]

Purpose: Bayesian inference has become popular. It offers several pragmatic approaches to account for uncertainty in inference decision-making. Various estimation methods have been introduced to implement Bayesian methods. Although these algorithms are powerful, they are not always easy to grasp for non-statisticians. This paper aims to provide an intuitive framework of four essential Bayesian computational methods for epidemiologists and other health researchers. We do not cover an extensive mathematical discussion of these approaches, but instead offer a non-quantitative description of these algorithms and provide some illuminating examples. Materials and methods: Bayesian computational methods, namely importance sampling, rejection sampling, Markov chain Monte Carlo, and data augmentation are presented. Results and conclusions: The substantial amount of research published on Bayesian inference has highlighted its popularity among researchers, while the basic concepts are not always straightforward for interested learners. We show that alternative approaches such as a weighted prior approach, which are intuitively appealing and easy-to-understand, work well in the case of low-dimensional problems and appropriate prior information. Otherwise, MCMC is a trouble-free tool in those cases.

In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that Δ4=O(m), where Δ is the maximal degree and m is the number of edges, the algorithm runs in expected time O(m). Our algorithm significantly improves the previously most efficient uniform sampler, which runs in expected time O(m2Δ2) for the same family of degree sequences. Our method uses a novel ingredient which progressively relaxes restrictions on an object being generated uniformly at random, and we use this to give fast algorithms for uniform sampling of graphs with other degree sequences as well. Using the same method, we also obtain algorithms with expected run time which is (i) linear for power‐law degree sequences in cases where the previous best was O(n4.081), and (ii) O(nd + d4) for d‐regular graphs when d=o(n), where the previous best was O(nd3). [ABSTRACT FROM AUTHOR]

Bayesian inference for models with intractable likelihood functions represents a challenging suite of problems in modern statistics. In this work we analyse the Conway-Maxwell-Poisson (COM-Poisson) distribution, a two parameter generalisation of the Poisson distribution. COM-Poisson regression modelling allows the flexibility to model dispersed count data as part of a generalised linear model (GLM) with a COM-Poisson response, where exogenous covariates control the mean and dispersion level of the response. The major difficulty with COMPoisson regression is that the likelihood function contains multiple intractable normalising constants and is not amenable to standard inference and Markov Chain Monte Carlo (MCMC) techniques. Recent work by Chanialidis et al. (2018) has seen the development of a sampler to draw random variates from the COM-Poisson likelihood using a rejection sampling algorithm. We provide a new rejection sampler for the COM-Poisson distribution which significantly reduces the central processing unit (CPU) time required to perform inference for COM-Poisson regression models. An extension of this work shows that for any intractable likelihood function with an associated rejection sampler it is possible to construct unbiased estimators of the intractable likelihood which proves useful for model selection or for use within pseudo-marginal MCMC algorithms (Andrieu and Roberts, 2009). We demonstrate all of these methods on a real-world dataset of takeover bids. [ABSTRACT FROM AUTHOR]

We investigate the properties of a Wright-Fisher diffusion process starting at frequency x at time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge. Bridges arise naturally in the analysis of selection acting on standing variation and in the inference of selection from allele frequency time series. We establish a number of results about the distribution of neutral Wright-Fisher bridges and develop a novel rejection-sampling scheme for bridges under selection that we use to study their behavior.

We derive an explicit representation for the transition law of a p-tempered α -stable process of Ornstein–Uhlenbeck-type and use it to develop a methodology for simulation. Our results apply in both the univariate and multivariate cases. Special attention is given to the case where p ≤ α , which is more complicated and requires developing the new class of so-called incomplete gamma distributions. [ABSTRACT FROM AUTHOR]

We derive a probability distribution for the possible number of iterations required for a SIMT (single instruction multiple thread) program using rejection sampling to finish creating a sample across all threads. This distribution is found to match a recently proposed distribution from Chakraborty and Gupta (in: Communications in statistics: theory and methods, 2015) that was shown as a good approximation of certain datasets. This work demonstrates an exact application of this distribution. The distribution can be used to evaluate the relative merit of some sampling methods on the GPU without resort to numerical tests. The distribution reduces to the expected geometric distribution in the single thread per warp limit. A simplified formula to approximate the expected number of iterations required to obtain rejection iteration samples is provided. With this new result, a simple, efficient layout for assigning sampling tasks to threads on a GPU is found as a function of the rejection probability without recourse to more complicated rejection sampling methods. [ABSTRACT FROM AUTHOR]

Viruses that infect animals regularly spill over into the human population, but individual events may lead to anything from a single case to a novel pandemic. Rapidly gaining an understanding of a spillover event is critical to calibrating a public health response. We here propose a novel method, using likelihood-free rejection sampling, to evaluate the properties of an outbreak of swine-origin influenza A(H1N2)v in the United Kingdom, detected in November 2023. From the limited data available, we generate historical estimates of the probability that the outbreak had died out in the days following the detection of the first case. Our method suggests that the outbreak could have been said to be over with 95% certainty between 19 and 29 days after the first case was detected, depending upon the probability of a case being detected. We further estimate the number of undetected cases conditional upon the outbreak still being live, the epidemiological parameter R 0 , and the date on which the spillover event itself occurred. Our method requires minimal data to be effective. While our calculations were performed after the event, the real-time application of our method has potential value for public health responses to cases of emerging viral infection.

The non-homogeneous Poisson process provides a generalised framework for the modelling of random point data by allowing the intensity of point generation to vary across its domain of interest (time or space). The use of non-homogeneous Poisson processes have arisen in many areas of signal processing and machine learning, but application is still largely limited by its intractable likelihood function and the lack of computationally efficient inference schemes, although some methods do exist for the batch data case. In this paper, we propose for the first time a sequential framework for intensity inference which combines the non-homogeneous model of Poisson data with continuous-time state-space models for their time-varying intensity. This approach enables us to design efficient online inference schemes, for which we propose a novel sequential Markov chain Monte Carlo (SMCMC) algorithm, as is demanded by many applications where point data arrive sequentially and decisions need to be made with low latency. The proposed approach is compared with competing methods on synthetic datasets and tested with high-frequency financial order book data, showing in general improved performance and better computational efficiency than the main batch-based competitor algorithm, and better performance than a simple baseline kernel estimation scheme. [ABSTRACT FROM AUTHOR]

Previous works about linguistic steganography such as synonym substitution and sampling-based methods usually manipulate observed symbols explicitly to conceal secret information, which may give rise to security risks. In this letter, in order to preclude straightforward operation on observed symbols, we explored generation-based linguistic steganography in latent space by means of encoding secret messages in the selection of implicit attributes (semanteme) of natural language. We proposed a novel framework of linguistic semantic steganography based on rejection sampling strategy. Concretely, we utilized controllable text generation model for embedding and semantic classifier for extraction. In experiments, a model based on CTRL and BERT is implemented for further quantitative assessment. Results reveal that our approach is able to achieve satisfactory efficiency as well as nearly perfect imperceptibility. Our code is available at https://github.com/YangzlTHU/Linguistic-Steganography-and-Steganalysis/tree/master/Steganography/Linguistic-Semantic-Steganography. [ABSTRACT FROM AUTHOR]