Assessing probabilistic inference by comparing the generalized mean of the model and source probabilities

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy”. Upper and lower error bars on the accuracy are provided by the arithmetic mean and the −2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the −2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and −2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the −2/3 mean decreases/increases, respectively.https://doi.org/10.3390/e19060286Published versio

Spatial confounding in Bayesian species distribution modeling

1) Species distribution models (SDMs) are currently the main tools to derive species niche estimates and spatially explicit predictions for species geographical distribution. However, unobserved environmental conditions and ecological processes may confound the model estimates if they have direct impact on the species and, at the same time, they are correlated with the observed environmental covariates. This, so-called spatial confounding, is a general property of spatial models and it has not been studied in the context of SDMs before. 2) We examine how the estimation accuracy of SDMs depends on the type of spatial confounding. We construct two simulation studies where we alter spatial structures of the observed and unobserved covariates and the level of dependence between them. We fit generalized linear models with and without spatial random effects applying Bayesian inference and recording the bias induced to model estimates by spatial confounding. After this we examine spatial confounding also with real vegetation data from northern Norway. 3) Our results show that model estimates for coarse scale covariates, such as climate covariates, are likely to be biased if a species distribution depends also on an unobserved covariate operating on a finer spatial scale. Pushing higher probability for a relatively weak and smoothly varying spatial random effect compared to the observed covariates improved the model's estimation accuracy. The improvement was independent of the actual spatial structure of the unobserved covariate. 4) Our study addresses the major factors of spatial confounding in SDMs and provides a list of recommendations for pre-inference assessment of spatial confounding and for inference-based methods to decrease the chance of biased model estimates.Peer reviewe

A Posterior Probability Approach for Gene Regulatory Network Inference in Genetic Perturbation Data

Inferring gene regulatory networks is an important problem in systems biology. However, these networks can be hard to infer from experimental data because of the inherent variability in biological data as well as the large number of genes involved. We propose a fast, simple method for inferring regulatory relationships between genes from knockdown experiments in the NIH LINCS dataset by calculating posterior probabilities, incorporating prior information. We show that the method is able to find previously identified edges from TRANSFAC and JASPAR and discuss the merits and limitations of this approach

Convex mixture regression for quantitative risk assessment

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. In addressing this goal, popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose-response relationships. We instead propose a Bayesian convex mixture regression model that allows the entire distribution of the health outcome to be unknown and changing with the dose. To balance flexibility and parsimony, we rely on a mixture model for the density at the extreme doses, and express the conditional density at each intermediate dose via a convex combination of these extremal densities. This representation generalizes classical dose-response models for quantitative outcomes, and provides a more parsimonious, but still powerful, formulation compared to nonparametric methods, thereby improving interpretability and efficiency in inference on risk functions. A Markov chain Monte Carlo algorithm for posterior inference is developed, and the benefits of our methods are outlined in simulations, along with a study on the impact of dde exposure on gestational age

A Dilated Inception Network for Visual Saliency Prediction

Recently, with the advent of deep convolutional neural networks (DCNN), the improvements in visual saliency prediction research are impressive. One possible direction to approach the next improvement is to fully characterize the multi-scale saliency-influential factors with a computationally-friendly module in DCNN architectures. In this work, we proposed an end-to-end dilated inception network (DINet) for visual saliency prediction. It captures multi-scale contextual features effectively with very limited extra parameters. Instead of utilizing parallel standard convolutions with different kernel sizes as the existing inception module, our proposed dilated inception module (DIM) uses parallel dilated convolutions with different dilation rates which can significantly reduce the computation load while enriching the diversity of receptive fields in feature maps. Moreover, the performance of our saliency model is further improved by using a set of linear normalization-based probability distribution distance metrics as loss functions. As such, we can formulate saliency prediction as a probability distribution prediction task for global saliency inference instead of a typical pixel-wise regression problem. Experimental results on several challenging saliency benchmark datasets demonstrate that our DINet with proposed loss functions can achieve state-of-the-art performance with shorter inference time.Comment: Accepted by IEEE Transactions on Multimedia. The source codes are available at https://github.com/ysyscool/DINe