Many physical systems exhibit limit-cycle oscillations that can typically be modeled as stochastically driven self-oscillators. In this work, we focus on a self-oscillator model where the nonlinearity is on the damping term. In various applications, it is crucial to determine the nonlinear damping term and the noise intensity of the driving force. This article presents a novel approach that employs a deep operator network (DeepONet) for parameter identification of self-oscillators. We build our work upon a system identification methodology based on the adjoint Fokker–Planck formulation, which is robust to the finite sampling interval effects. We employ DeepONet as a surrogate model for the operator that maps the first Kramers–Moyal (KM) coefficient to the first and second finite-time KM coefficients. The proposed approach can directly predict the finite-time KM coefficients, eliminating the intermediate computation of the solution field of the adjoint Fokker–Planck equation. Additionally, the differentiability of the neural network readily facilitates the use of gradient-based optimizers, further accelerating the identification process. The numerical experiments demonstrate that the proposed methodology can recover desired parameters with a significant reduction in time while maintaining an accuracy comparable to that of the classical finite-difference approach. The low computational time of the forward path enables Bayesian inference of the parameters. Metropolis-adjusted Langevin algorithm is employed to obtain the posterior distribution of the parameters. The proposed method is validated against numerical simulations and experimental data obtained from a linearly unstable turbulent combustor.

The age at first calving (AFC) is an important trait to be considered in breeding programmes of dairy buffaloes, where new approaches and technologies, such as genomic selection, are constantly applied. Thus, the objective of this study was to compare the predictive ability of different genomic single-step methods using AFC information from Murrah buffaloes. From a pedigree file containing 3320 buffaloes, 2247 cows had AFC records and 553 animals were genotyped. The following models were performed: pedigree-based BLUP (PBLUP), single-step GBLUP (ssGBLUP), weighted single-step GBLUP (WssGBLUP), and single-step Bayesian regression methods (ssBR-BayesA, BayesBπ, BayesCπ, Bayes-Lasso, and BayesRR). To compare the methodologies, the accuracy and dispersion of (G)EBVs were assessed using the LR method. Accuracy estimates for the genotyped animals ranged from 0.30 (PBLUP) to 0.39 (WssGBLUP). Predictions with the traditional model (PBLUP) were very dispersed from what was expected, while BayesCπ (0.99) and WssGBLUP (1.00) obtained the lowest dispersion. The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation/deflation of predictions compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and single-step BayesA were the most advantageous methods to be used in the genomic evaluation of AFC of buffaloes from this population.

This article introduces a comprehensive framework that effectively combines experience rating and exposure rating approaches in reinsurance for both short-tail and long-tail businesses. The generic framework applies to all nonlife lines of business and products emphasizing nonproportional treaty business. The approach is based on three pillars that enable a coherent usage of all available information. The first pillar comprises an exposure-based generative model that emulates the generative process leading to the observed claims experience. The second pillar encompasses a standardized reduction procedure that maps each high-dimensional claim object to a few weakly coupled reduced random variables. The third pillar comprises calibrating the generative model with retrospective Bayesian inference. The derived calibration parameters are fed back into the generative model, and the reinsurance contracts covering future cover periods are rated by projecting the calibrated generative model to the cover period and applying the future contract terms.

When researchers design an experiment, they usually hold potentially relevant features of the experiment constant. We call these details the “topic” of the experiment. For example, researchers studying the impact of party cues on attitudes must inform respondents of the parties’ positions on a particular policy. In doing so, researchers implement just one of many possible designs . Clifford, Leeper, and Rainey (2023. “Generalizing Survey Experiments Using Topic Sampling: An Application to Party Cues.” Forthcoming in Political Behavior. https://doi.org/10.1007/s11109-023-09870-1) argue that researchers should implement many of the possible designs in parallel—what they call “topic sampling”—to generalize to a larger population of topics. We describe two estimators for topic-sampling designs: First, we describe a nonparametric estimator of the typical effect that is unbiased under the assumptions of the design; and second, we describe a hierarchical model that researchers can use to describe the heterogeneity. We suggest describing the heterogeneity across topics in three ways: (1) the standard deviation in treatment effects across topics, (2) the treatment effects for particular topics, and (3) how the treatment effects for particular topics vary with topic-level predictors. We evaluate the performance of the hierarchical model using the Strengthening Democracy Challenge megastudy and show that the hierarchical model works well.

There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise deterministic Markov processes. However, existing algorithms can only be used if the target distribution of interest is differentiable everywhere. The key to adapting these algorithms so that they can sample from densities with discontinuities is to define appropriate dynamics for the process when it hits a discontinuity. We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the bouncy particle sampler, the coordinate sampler, and the zigzag process. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the zigzag process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise deterministic Markov process with boundaries may be of independent interest.

Combining experts’ subjective probability estimates is a fundamental task with broad applicability in domains ranging from finance to public health. However, it is still an open question how to combine such estimates optimally. Since the beta distribution is a common choice for modeling uncertainty about probabilities, here we propose a family of normative Bayesian models for aggregating probability estimates based on beta distributions. We systematically derive and compare different variants, including hierarchical and non-hierarchical as well as asymmetric and symmetric beta fusion models. Using these models, we show how the beta calibration function naturally arises in this normative framework and how it is related to the widely used Linear-in-Log-Odds calibration function. For evaluation, we provide the new Knowledge Test Confidence data set consisting of subjective probability estimates of 85 forecasters on 180 queries. On this and another data set, we show that the hierarchical symmetric beta fusion model performs best of all beta fusion models and outperforms related Bayesian fusion models in terms of mean absolute error.

Psychologists and neuroscientists extensively rely on computational models for studying and analyzing the human mind. Traditionally, such computational models have been hand-designed by expert researchers. Two prominent examples are cognitive architectures and Bayesian models of cognition. Although the former requires the specification of a fixed set of computational structures and a definition of how these structures interact with each other, the latter necessitates the commitment to a particular prior and a likelihood function that – in combination with Bayes' rule – determine the model's behavior. In recent years, a new framework has established itself as a promising tool for building models of human cognition: the framework of meta-learning. In contrast to the previously mentioned model classes, meta-learned models acquire their inductive biases from experience, that is, by repeatedly interacting with an environment. However, a coherent research program around meta-learned models of cognition is still missing to date. The purpose of this article is to synthesize previous work in this field and establish such a research program. We accomplish this by pointing out that meta-learning can be used to construct Bayes-optimal learning algorithms, allowing us to draw strong connections to the rational analysis of cognition. We then discuss several advantages of the meta-learning framework over traditional methods and reexamine prior work in the context of these new insights.

Exploiting high-energy electron beams colliding into high-intensity laser pulses brings an opportunity to reach high values of the dimensionless rest-frame acceleration $\chi$ and thereby invoke processes described by strong-field quantum electrodynamics (SFQED). Measuring deviations from the results of Furry-picture perturbation theory in SFQED at high $\chi$ can be valuable for testing existing predictions, as well as for guiding further theoretical developments. Nevertheless, such experimental measurements are challenging due to the probabilistic nature of the interaction processes, dominating signals of low-$\chi$ interactions and limited capabilities to control and measure the alignment and synchronization in such collision experiments. Here we elaborate a methodology of using approximate Bayesian computations for drawing statistical inferences based on the results of many repeated experiments despite partially unknown collision parameters that vary between experiments. As a proof-of-principle, we consider the problem of inferring the effective mass change due to coupling with the strong-field environment.

We use a Bayesian approach to estimate elasticities of former Conservation Reserve Program (CRP) land allocation and the impact of the US–China trade conflict on post-CRP land transitions. Economically acceptable elasticities of land exiting CRP are important for applied analysis, including market shocks and environmental policy. Taking as given the total area exiting the CRP, the Phase 1 deal raised the posterior mean of national post-CRP soybean area by 155 thousand acres and the market facilitation program by 89 thousand acres. Cross-commodity effects are important, and elasticities vary depending on the direction and magnitude of changes in net returns and payments.

We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson (Statist. Comput. 8, 1998). The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed the Haar mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the $\Delta$-guided Metropolis–Haar kernel, is constructed by using the Haar mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.

Robots and inertial measurement units (IMUs) are typically calibrated independently. IMUs are placed in purpose-built, expensive automated test rigs. Robot poses are typically measured using highly accurate (and thus expensive) tracking systems. In this paper, we present a quick, easy, and inexpensive new approach to calibrate both simultaneously, simply by attaching the IMU anywhere on the robot’s end-effector and moving the robot continuously through space. Our approach provides a fast and inexpensive alternative to both robot and IMU calibration, without any external measurement systems. We accomplish this using continuous-time batch estimation, providing statistically optimal solutions. Under Gaussian assumptions, we show that this becomes a nonlinear least-squares problem and analyze the structure of the associated Jacobian. Our methods are validated both numerically and experimentally and compared to standard individual robot and IMU calibration methods.

Judgment and decision making research overwhelmingly uses null hypothesis significance testing as the basis for statistical inference. This article examines an alternative, Bayesian approach which emphasizes the choice between two competing hypotheses and quantifies the balance of evidence provided by the data—one consequence of which is that experimental results may be taken to strongly favour the null hypothesis. We apply a recently-developed “Bayesian t-test” to existing studies of the anchoring effect in judgment, and examine how the change in approach affects both the tone of hypothesis testing and the substantive conclusions that one draws. We compare the Bayesian approach with Fisherian and Neyman-Pearson testing, examining its relationship to conventional p-values, the influence of effect size, and the importance of prior beliefs about the likely state of nature. The results give a sense of how Bayesian hypothesis testing might be applied to judgment and decision making research, and of both the advantages and challenges that a shift to this approach would entail.