Doubly Robust Crowdsourcing

Large-scale labeled dataset is the indispensable fuel that ignites the AI revolution as we see today. Most such datasets are constructed using crowdsourcing services such as Amazon Mechanical Turk which provides noisy labels from non-experts at a fair price. The sheer size of such datasets mandates that it is only feasible to collect a few labels per data point. We formulate the problem of test-time label aggregation as a statistical estimation problem of inferring the expected voting score. By imitating workers with supervised learners and using them in a doubly robust estimation framework, we prove that the variance of estimation can be substantially reduced, even if the learner is a poor approximation. Synthetic and real-world experiments show that by combining the doubly robust approach with adaptive worker/item selection rules, we often need much lower label cost to achieve nearly the same accuracy as in the ideal world where all workers label all data points.

Modeling non-normality using multivariate t: implications for asset pricing

Purpose The purpose of this paper is to show that multivariate t-distribution assumption provides a better description of stock return data than multivariate normality assumption. Design/methodology/approach The EM algorithm is applied to solve the statistical estimation problem almost analytically, and the asymptotic theory is provided for inference. Findings The authors find that the multivariate normality assumption is almost always rejected by real stock return data, while the multivariate t-distribution assumption can often be adequate. Conclusions under normality vs under t can be drastically different for estimating expected returns and Jensen’s αs, and for testing asset pricing models. Practical implications The results provide improved estimates of cost of capital and asset moment parameters that are useful for corporate project evaluation and portfolio management. Originality/value The authors proposed new procedures that makes it easy to use a multivariate t-distribution, which models well the data, as a simple and viable alternative in practice to examine the robustness of many existing results.

Statistical mechanics of multistable perception

The stochastic dynamics of multistable perception poses an enduring challenge to our understanding of neural signal processing in the brain. We show that the emergence of perception switching and stability can be understood using principles of probabilistic Bayesian inference where the prior temporal expectations are matched to a scale-free power spectrum, characteristic of fluctuations in the natural environment. The optimal percept dynamics are inferred by an exact mapping of the statistical estimation problem to the motion of a dissipative quantum particle in a multi-well potential. In the bistable case the problem is further mapped to a long-ranged Ising model. Optimal inference in the presence of a 1/f noise prior leads to critical dynamics, exhibiting a dynamical phase transition from unstable perception to stable perception, as demonstrated in recent experiments. The effect of stimulus fluctuations and perception bias is also discussed.

Discussion of Identification, Estimation and Approximation of Risk under Interventions that Depend on the Natural Value of Treatment Using Observational Data, by Jessica Young, Miguel Hernán, and James Robins

Young, Hernán, and Robins consider the mean outcome under a dynamic intervention that may rely on the natural value of treatment. They first identify this value with a statistical target parameter, and then show that this statistical target parameter can also be identified with a causal parameter which gives the mean outcome under a stochastic intervention. The authors then describe estimation strategies for these quantities. Here we augment the authors’ insightful discussion by sharing our experiences in situations where two causal questions lead to the same statistical estimand, or the newer problem that arises in the study of data adaptive parameters, where two statistical estimands can lead to the same estimation problem. Given a statistical estimation problem, we encourage others to always use a robust estimation framework where the data generating distribution truly belongs to the statistical model. We close with a discussion of a framework which has these properties.

Why Uninformed Agents (Pretend to) Know More

Many social interactions (examples are market overreactions, high rates of acquisitions, strikes, wars) are the result of agents' overconfidence. Agents are in particular overconfident for difficult tasks. This paper analyzes overconfidence in the context of a statistical estimation problem. The authors find that it is rational to (i) be overconfident and (ii) to be notably overconfident if the task is difficult. The counterintuitive finding that uninformed agents which should be the least confident ones show the highest degree of overconfidence can be explained as a rational behavior.

Application of Bayesian Method in Stochastic Analysis of Rock Slope Stability

The analysis of structural plane in rock slope is of vital importance to stability analysis of rock slope. In this paper, Bayesian method was adopted in the analysis of shear strength parameters along the fault in the West Slope of Upper Reservoir, Shisanling Pumped Storage Power Station. Full advantage was taken of the geological information outside the structural plane along with the practical experience of on-site engineers. The statistical estimation problem of small samples thus was successfully solved. The determination of sliding plane in rock slope is another key issue in the stability analysis of rock slope. The cracking process was utilized to track the most possible sliding plane in the slope. In consideration of the randomicity of both mechanical parameters of rock and structural plane and resistance of slide resistant piles, reliability index of slope stability was established with the aid of discretized dimensional reduction method of reliability and conditional probability.

Locally asymptotic normality of Gibbs models on a lattice

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.