Photon-Driven Neural Reconstruction for Path Guiding

Although Monte Carlo path tracing is a simple and effective algorithm to synthesize photo-realistic images, it is often very slow to converge to noise-free results when involving complex global illumination. One of the most successful variance-reduction techniques is path guiding, which can learn better distributions for importance sampling to reduce pixel noise. However, previous methods require a large number of path samples to achieve reliable path guiding. We present a novel neural path guiding approach that can reconstruct high-quality sampling distributions for path guiding from a sparse set of samples, using an offline trained neural network. We leverage photons traced from light sources as the primary input for sampling density reconstruction, which is effective for challenging scenes with strong global illumination. To fully make use of our deep neural network, we partition the scene space into an adaptive hierarchical grid, in which we apply our network to reconstruct high-quality sampling distributions for any local region in the scene. This allows for effective path guiding for arbitrary path bounce at any location in path tracing. We demonstrate that our photon-driven neural path guiding approach can generalize to diverse testing scenes, often achieving better rendering results than previous path guiding approaches and opening up interesting future directions.

Estimation of Domain Means from Business Surveys in the Presence of Stratum Jumpers and Nonresponse

Misclassified frame records (also called stratum jumpers) and low response rates are characteristic for business surveys. In the context of estimation of the domain parameters, jumpers may contribute to extreme variation in sample weights and skewed sampling distributions of the estimators, especially for domains with a small number of observations. There is limited literature about the extent to which these problems may affect the performance of the ratio estimators with nonresponse-adjusted weights. To address this gap, we designed a simulation study to explore the properties of the Horvitz-Thompson type ratio estimators, with and without smoothing of the weights, under different scenarios. The ratio estimator with propensity-adjusted weights showed satisfactory performance in all scenarios with a high response rate. For scenarios with a low response rate, the performance of this estimator improved with an increase in the proportion of jumpers in the domain. The smoothed estimators that we studied performed well in scenarios with non-informative weights, but can become markedly biased when the weights are informative, irrespective of response rate. We also studied the performance of the ’doubled half’ bootstrap method for variance estimation. We illustrated an application of the methods in a real business survey.

Introducing Statistical Inference: Design of a Theoretically and Empirically Based Learning Trajectory

This paper comprises the results of a design study that aims at developing a theoretically and empirically based learning trajectory on statistical inference for 9th-grade students. Based on theories of informal statistical inference, an 8-step learning trajectory was designed. The trajectory consisted of two similar four step sequences: (1) experimenting with a physical black box, (2) visualizing distributions, (3) examining sampling distributions using simulation software, and (4) interpreting sampling distributions to make inferences in real -life contexts. Sequence I included only categorical data and Sequence II regarded numerical data. The learning trajectory was implemented in an intervention among 267 students. To examine the effects of the trajectory on students’ understanding of statistical inference, we analyzed their posttest results after the intervention. To investigate how the stepwise trajectory fostered the learning process, students’ worksheets during each learning step were analyzed. The posttest results showed that students who followed the learning trajectory scored significantly higher on statistical inference and on concepts related to each step than students of a comparison group (n = 217) who followed the regular curriculum. Worksheet analysis demonstrated that the 8-step trajectory was beneficial to students’ learning processes. We conclude that ideas of repeated sampling with a black box and statistical modeling seem fruitful for introducing statistical inference. Both ideas invite more advanced follow-up activities, such as hypothesis testing and comparing groups. This suggests that statistics curricula with a descriptive focus can be transformed to a more inferential focus, to anticipate on subsequent steps in students’ statistics education.

The tenets of indirect inference in Bayesian models

This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips and implementation of these algorithms in Stan and R. We also extend the same method to propose the definition of an *indirect prior* and discuss the situations where it can be useful

Optimal Subsampling Methods in Bike Sharing Data Analysis

Bike sharing system are popular around the world. Traditional bike sharing system require the bikes to be returned to fixed stations, while morden system allows users to leave bikes wherever they like, ready for the next user to pick them up. Smartphone use GPS signal to keep track of its bikes and monitor where most bikes are used and where to place them. Smartphone simultaneously collect many other information such as weather condition, temperature and so on, these features have influence on the delivering amount of bikes. Due to the extensive number of smartphone users, big data technique is requried to handle this situation. We apply subsample method to this smartphone collected big data. In this paper, we derive non-uniform sampling distributions and propose optimal subsampling algorithm. We apply the proposed optimal subsampling algorithm to analyze the smartphone collected bike sharing data set, perfrom extensive computer experiments to evaluate the numerical performance of the proposed sampling algorithm. Our results indicated that the proposed optimal algorithm outperformed the uniform method and have faster running time than using the whole data set.

A Hierarchical Unequal-Variance Signal Detection Model for Binary Data

Gaussian signal detection models with equal variance are typically used for detection and discrimination data whereas models with unequal variance rely on data with multiple response categories or multiple conditions. Here a hier- archical signal detection model with unequal variance is suggested that requires only binary responses from a sample of participants. Introducing plausible constraints on the sampling distributions for sensitivity and response criterion makes it possible to estimate signal variance at the population level. This model was applied to existing data from memory and reasoning tasks and the results suggest that parameters can be reliably estimated, allowing a direct comparison of signal detection models with equal- and unequal-variance.