Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that it is the improper use and errors in interpretation, rather than the p-values themselves that are to blame. Similar exchanges about the role of p-values have occurred with some regularity every 10 to 15 years since their formal introduction in statistical practice. The apparent contradiction between the repeated failures in interpretation and continuous use of p-values suggest that there is an inferential value in the computation of these values. In this work we propose to attach a radical Bayesian interpretation to the number computed and reported as a p-value for the Generalized Linear Model, which has been the workhorse of applied statistical work. We introduce a decision analytic framework for thresholding posterior tail areas (pi-values) which for any given Bayesian analysis will have a direct correspondence to p-values in non-Bayesian approaches. Pi-values are non-controversial, posterior probability summaries of treatment effects. A predictive probability argument is made to justify the exploration of the stochastic variation (replication probability) of p and pi-values and culminates into a concrete proposal for the synthesis of Likelihood and Bayesian approaches to data analyses that aim for reproducibility. We illustrate these concepts using the results of recent randomized controlled trials in cardiometabolic and kidney diseases and provide R code for the implementation of the proposed methodology.
相關內容
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current approach toward Bayesian clinical trials is, however, a hybrid Bayesian-frequentist approach where the design and decision criteria are assessed with respect to frequentist operating characteristics such as power and type I error rate. These operating characteristics are commonly obtained via simulation studies. In this article we propose methodology to utilize large sample theory of the posterior distribution to define simple parametric models for the sampling distribution of the Bayesian test statistics, i.e., posterior tail probabilities. The parameters of these models are then estimated using a small number of simulation scenarios, thereby refining these models to capture the sampling distribution for small to moderate sample size. The proposed approach toward assessment of operating characteristics and sample size determination can be considered as simulation-assisted rather than simulation-based and significantly reduces the computational burden for design of Bayesian trials.
Multivariate sequential data collected in practice often exhibit temporal irregularities, including nonuniform time intervals and component misalignment. However, if uneven spacing and asynchrony are endogenous characteristics of the data rather than a result of insufficient observation, the information content of these irregularities plays a defining role in characterizing the multivariate dependence structure. Existing approaches for probabilistic forecasting either overlook the resulting statistical heterogeneities, are susceptible to imputation biases, or impose parametric assumptions on the data distribution. This paper proposes an end-to-end solution that overcomes these limitations by allowing the observation arrival times to play the central role of model construction, which is at the core of temporal irregularities. To acknowledge temporal irregularities, we first enable unique hidden states for components so that the arrival times can dictate when, how, and which hidden states to update. We then develop a conditional flow representation to non-parametrically represent the data distribution, which is typically non-Gaussian, and supervise this representation by carefully factorizing the log-likelihood objective to select conditional information that facilitates capturing time variation and path dependency. The broad applicability and superiority of the proposed solution are confirmed by comparing it with existing approaches through ablation studies and testing on real-world datasets.
State-of-the-art deep Q-learning methods update Q-values using state transition tuples sampled from the experience replay buffer. This strategy often uniformly and randomly samples or prioritizes data sampling based on measures such as the temporal difference (TD) error. Such sampling strategies can be inefficient at learning Q-function because a state's Q-value depends on the Q-value of successor states. If the data sampling strategy ignores the precision of the Q-value estimate of the next state, it can lead to useless and often incorrect updates to the Q-values. To mitigate this issue, we organize the agent's experience into a graph that explicitly tracks the dependency between Q-values of states. Each edge in the graph represents a transition between two states by executing a single action. We perform value backups via a breadth-first search starting from that expands vertices in the graph starting from the set of terminal states and successively moving backward. We empirically show that our method is substantially more data-efficient than several baselines on a diverse range of goal-reaching tasks. Notably, the proposed method also outperforms baselines that consume more batches of training experience and operates from high-dimensional observational data such as images.
The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the data likelihood is Gaussian. Moreover, inference for GPLVMs has typically been restricted to obtaining maximum a posteriori point estimates, which can lead to overfitting, or variational approximations, which mischaracterize the posterior uncertainty. Here, we present a method to perform Markov chain Monte Carlo (MCMC) inference for generalized Bayesian nonlinear latent variable modeling. The crucial insight necessary to generalize GPLVMs to arbitrary observation models is that we approximate the kernel function in the Gaussian process mappings with random Fourier features; this allows us to compute the gradient of the posterior in closed form with respect to the latent variables. We show that we can generalize GPLVMs to non-Gaussian observations, such as Poisson, negative binomial, and multinomial distributions, using our random feature latent variable model (RFLVM). Our generalized RFLVMs perform on par with state-of-the-art latent variable models on a wide range of applications, including motion capture, images, and text data for the purpose of estimating the latent structure and imputing the missing data of these complex data sets.
This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter $\kappa(x)$ often referred to as $B/A$ in the acoustics literature and the wave speed $c_0(x)$. The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. For a reformulation of the problem in terms of the squared slowness $\mathfrak{s}=1/c_0^2$ and the combined coefficient $\eta=\frac{B/A+2}{\varrho_0 c_0^4}$ we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.
Traffic Signal Control (TSC) aims to reduce the average travel time of vehicles in a road network, which in turn enhances fuel utilization efficiency, air quality, and road safety, benefiting society as a whole. Due to the complexity of long-horizon control and coordination, most prior TSC methods leverage deep reinforcement learning (RL) to search for a control policy and have witnessed great success. However, TSC still faces two significant challenges. 1) The travel time of a vehicle is delayed feedback on the effectiveness of TSC policy at each traffic intersection since it is obtained after the vehicle has left the road network. Although several heuristic reward functions have been proposed as substitutes for travel time, they are usually biased and not leading the policy to improve in the correct direction. 2) The traffic condition of each intersection is influenced by the non-local intersections since vehicles traverse multiple intersections over time. Therefore, the TSC agent is required to leverage both the local observation and the non-local traffic conditions to predict the long-horizontal traffic conditions of each intersection comprehensively. To address these challenges, we propose DenseLight, a novel RL-based TSC method that employs an unbiased reward function to provide dense feedback on policy effectiveness and a non-local enhanced TSC agent to better predict future traffic conditions for more precise traffic control. Extensive experiments and ablation studies demonstrate that DenseLight can consistently outperform advanced baselines on various road networks with diverse traffic flows. The code is available at //github.com/junfanlin/DenseLight.
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a mixture of Gaussian distributions while satisfying all metric properties. These characteristics enable fast, stable, and efficient calculations, which are highly desirable in real-world signal processing applications. The application in mind is Gaussian Mixture Reduction (GMR), which is widely used in density estimation, recursive tracking, and belief propagation. To address this problem, we developed a novel algorithm dubbed the Optimization-based Greedy GMR (OGGMR), which employs our metric as a criterion to approximate a high-order Gaussian mixture with a lower order. Experimental results show that the OGGMR algorithm is significantly faster and more efficient than state-of-the-art GMR algorithms while retaining the geometric shape of the original mixture.
Data for pretraining machine learning models often consists of collections of heterogeneous datasets. Although training on their union is reasonable in agnostic settings, it might be suboptimal when the target domain -- where the model will ultimately be used -- is known in advance. In that case, one would ideally pretrain only on the dataset(s) most similar to the target one. Instead of limiting this choice to those datasets already present in the pretraining collection, here we explore extending this search to all datasets that can be synthesized as `combinations' of them. We define such combinations as multi-dataset interpolations, formalized through the notion of generalized geodesics from optimal transport (OT) theory. We compute these geodesics using a recent notion of distance between labeled datasets, and derive alternative interpolation schemes based on it: using either barycentric projections or optimal transport maps, the latter computed using recent neural OT methods. These methods are scalable, efficient, and -- notably -- can be used to interpolate even between datasets with distinct and unrelated label sets. Through various experiments in transfer learning in computer vision, we demonstrate this is a promising new approach for targeted on-demand dataset synthesis.
Future wireless systems are expected to support mission-critical services demanding higher and higher reliability. In this letter, we dimension the radio resources needed to achieve a given failure probability target for ultra-reliable wireless systems in high interference conditions, assuming a protocol with frequency hopping combined with packet repetitions. We resort to packet erasure channel models and derive the minimum amount of resource units in the case of receiver with and without collision resolution capability, as well as the number of packet repetitions needed for achieving the failure probability target. Analytical results are numerically validated and can be used as a benchmark for realistic system simulations
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