Approximate leave-future-out cross-validation for Bayesian time series models

Seasonal-Spatial Distribution Variations and Predictions of Loliolus beka and Loliolus uyii in the East China Sea Region: Implications from Climate Change Scenarios

Global climate change profoundly impacts the East China Sea ecosystem and poses a major challenge to fishery management in this region. In addition, closely related species with low catches are often not distinguished in fishery production and relevant data are commonly merged in statistics and fishing logbooks, making it challenging to accurately predict their habitat distribution range. Here, merged fisheries-independent data of the closely related squid Loliolus beka (Sasaki, 1929) and Loliolus uyii (Wakiya and Ishikawa, 1921) were used to explore the construction and prediction performance of species distribution models. Data in 2018 to 2019 from the southern Yellow and East China Seas were used to identify the seasonal-spatial distribution characteristics of both species, revealing a boundary line at 29.00° N for L. uyii during the autumn, with the highest average individual weight occurring during the summer, with both larvae and juveniles occurring during the autumn. Thus, the life history of L. uyii can be divided into winter-spring nursery and summer-autumn spawning periods. L. beka showed a preference for inshore areas (15-60 m) during the summer and offshore areas (32.00-78.00 m) during the winter. High-value areas of both species included inshore areas of the southern Yellow and mid-East China Seas during the autumn, enlarging during the spring to include central areas of the survey region, before significantly decreasing during the summer. Therefore, this study provides both a novel perspective for modeling biological habitat distribution with limited data and a scientific basis for the adjustment of fishery resource management and conservation measures in the context of climate change.

Estimating causal effects from panel data with dynamic multivariate panel models

Panel data are ubiquitous in scientific fields such as social sciences. Various modeling approaches have been presented for observational causal inference based on such data. Existing approaches typically impose restrictive assumptions on the data-generating process such as Gaussian responses or time-invariant effects, or they can only consider short-term causal effects. To surmount these restrictions, we present the dynamic multivariate panel model (DMPM) that supports time-varying, time-invariant, and individual-specific effects, multiple responses across a wide variety of distributions, and arbitrary dependency structures of lagged responses of any order. We formally demonstrate how DMPM facilitates causal inference within the structural causal modeling framework and we take a Bayesian approach for the estimation of the posterior distributions of the model parameters and causal effects of interest. We demonstrate the use of DMPM by applying the approach to both real and synthetic data.

Modeling the spatiotemporal patterns and drivers of Dungeness crab fishing effort to inform whale entanglement risk mitigation on the U.S. West Coast

Understanding and characterizing the spatiotemporal dynamics of fishing fleets is crucial for ecosystem-based fisheries management (EBFM). EBFM must not only account for the sustainability of target species catches, but also for the collateral impacts of fishing operations on habitats and non-target species. Increased rates of large whale entanglements in commercial Dungeness crab fishing gear have made reducing whale-fishery interactions a current and pressing challenge on the U.S. West Coast. While several habitat models exist for different large whale species along the West Coast, less is known about the crab fishery and the degree to which different factors influence the intensity and distribution of aggregate fishing effort. Here, we modeled the spatiotemporal patterns of Dungeness crab fishing effort in Oregon and Washington as a function of environmental, economic, temporal, social, and management related predictor variables using generalized linear mixed effects models. We then assessed the predictive performance of such models and discussed their usefulness in informing fishery management. Our models revealed low between-year variability and consistent spatial and temporal patterns in commercial Dungeness crab fishing effort. However, fishing effort was also responsive to multiple environmental, economic and management cues, which influenced the baseline effort distribution pattern. The best predictive model, chosen through out-of-sample cross-validation, showed moderate predictive performance and relied upon environmental, economic, and social covariates. Our results help fill the current knowledge gap around Dungeness crab fleet dynamics, and support growing calls to integrate fisheries behavioral data into fisheries management and marine spatial planning.

Comparison of statistical models to predict age-standardized cancer incidence in Switzerland

This study compares the performance of statistical methods for predicting age-standardized cancer incidence, including Poisson generalized linear models, age-period-cohort (APC) and Bayesian age-period-cohort (BAPC) models, autoregressive integrated moving average (ARIMA) time series, and simple linear models. The methods are evaluated via leave-future-out cross-validation, and performance is assessed using the normalized root mean square error, interval score, and coverage of prediction intervals. Methods were applied to cancer incidence from the three Swiss cancer registries of Geneva, Neuchatel, and Vaud combined, considering the five most frequent cancer sites: breast, colorectal, lung, prostate, and skin melanoma and bringing all other sites together in a final group. Best overall performance was achieved by ARIMA models, followed by linear regression models. Prediction methods based on model selection using the Akaike information criterion resulted in overfitting. The widely used APC and BAPC models were found to be suboptimal for prediction, particularly in the case of a trend reversal in incidence, as it was observed for prostate cancer. In general, we do not recommend predicting cancer incidence for periods far into the future but rather updating predictions regularly.

Neural superstatistics for Bayesian estimation of dynamic cognitive models

Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension and estimate the resulting dynamics from a superstatistics perspective. Such a model entails a hierarchy between a low-level observation model and a high-level transition model. The observation model describes the local behavior of a system, and the transition model specifies how the parameters of the observation model evolve over time. To overcome the estimation challenges resulting from the complexity of superstatistical models, we develop and validate a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. We first benchmark our method against two existing frameworks capable of estimating time-varying parameters. We then apply our method to fit a dynamic version of the diffusion decision model to long time series of human response times data. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model. Furthermore, we show that the erroneous assumption of static or homogeneous parameters will hide important temporal information.

Mathematical theory of Bayesian statistics for unknown information source

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases, statistical measures have been constructed, such as cross validation, information criteria and marginal likelihood; however, their mathematical properties have not yet been completely clarified when statistical models are under- or over-parametrized. We introduce a place of mathematical theory of Bayesian statistics for unknown uncertainty, which clarifies general properties of cross validation, information criteria and marginal likelihood, even if an unknown data-generating process is unrealizable by a model or even if the posterior distribution cannot be approximated by any normal distribution. Hence it gives a helpful standpoint for a person who cannot believe in any specific model and prior. This paper consists of three parts. The first is a new result, whereas the second and third are well-known previous results with new experiments. We show there exists a more precise estimator of the generalization loss than leave-one-out cross validation, there exists a more accurate approximation of marginal likelihood than Bayesian information criterion, and the optimal hyperparameters for generalization loss and marginal likelihood are different. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

On predictive inference for intractable models via approximate Bayesian computation

Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based statistical models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility of ABC as a generic approximate method for predictive inference, in particular, for computing the posterior predictive distribution of future observations or missing data of interest. We consider three complementary ABC approaches for this goal, each based on different assumptions regarding which predictive density of the intractable model can be sampled from. The case where only simulation from the joint density of the observed and future data given the model parameters can be used for inference is given particular attention and it is shown that the ideal summary statistic in this setting is minimal predictive sufficient instead of merely minimal sufficient (in the ordinary sense). An ABC prediction approach that takes advantage of a certain latent variable representation is also investigated. We additionally show how common ABC sampling algorithms can be used in the predictive settings considered. Our main results are first illustrated by using simple time-series models that facilitate analytical treatment, and later by using two common intractable dynamic models.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11222-022-10163-6.

Deep Neural Networks Applied to Stock Market Sentiment Analysis

The volume of data is growing exponentially and becoming more valuable to organizations that collect it, from e-commerce data, shipping, audio and video logs, text messages, internet search queries, stock market activity, financial transactions, the Internet of Things, and various other sources. The major challenges are related with the way to extract insights from such a rich data environment and whether Deep Learning can be successful with Big Data. To get some insight on these topics, social network data are employed as a case study on how sentiments can affect decisions in stock market environments. In this paper, we propose a generalized Deep Learning-based classification framework for Stock Market Sentiment Analysis. This work comprises the study, the development, and implementation of an automatic classification system based on Deep Learning and the validation of its adequacy and efficiency in any scenario, particularly Stock Market Sentiment Analysis. Distinct datasets and several Deep Learning approaches with different layers and embedded techniques are used, and their performances are evaluated. These developments show how Deep Learning reacts to distinct contexts. The results also give context on how different techniques with different parameter combinations react to certain types of data. Convolution obtained the best results when dealing with complex data inputs, and long short-term layers kept a memory of data, allowing inputs which are not as common to still be considered for decisions. The models that resulted from Stock Market Sentiment Analysis datasets were applied with some success to real-life problems. The best models reached accuracies of 73% in training and 69% in certain test datasets. In a simulation, a model was able to provide a Return on Investment of 4.4%. The results contribute to understanding how to process Big Data efficiently using Deep Learning and specialized hardware techniques.

Statistical Comparison and Assessment of Four Fire Emissions Inventories for 2013 and a Large Wildfire in the Western United States

Wildland fires produce smoke plumes that impact air quality and human health. To understand the effects of wildland fire smoke on humans, the amount and composition of the smoke plume must be quantified. Using a fire emissions inventory is one way to determine the emissions rate and composition of smoke plumes from individual fires. There are multiple fire emissions inventories, and each uses a different method to estimate emissions. This paper presents a comparison of four emissions inventories and their products: Fire INventory from NCAR (FINN version 1.5), Global Fire Emissions Database (GFED version 4s), Missoula Fire Labs Emissions Inventory (MFLEI (250 m) and MFLEI (10 km) products), and Wildland Fire Emissions Inventory System (WFEIS (MODIS) and WFEIS (MTBS) products). The outputs from these inventories are compared directly. Because there are no validation datasets for fire emissions, the outlying points from the Bayesian models developed for each inventory were compared with visible images and fire radiative power (FRP) data from satellite remote sensing. This comparison provides a framework to check fire emissions inventory data against additional data by providing a set of days to investigate closely. Results indicate that FINN and GFED likely underestimate emissions, while the MFLEI products likely overestimate emissions. No fire emissions inventory matched the temporal distribution of emissions from an external FRP dataset. A discussion of the differences impacting the emissions estimates from the four fire emissions inventories is provided, including a qualitative comparison of the methods and inputs used by each inventory and the associated strengths and limitations.

Bayesian workflow for disease transmission modeling in Stan

This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic and other infectious diseases in a Bayesian framework. Bayesian modeling provides a principled way to quantify uncertainty and incorporate both data and prior knowledge into the model estimates. Stan is an expressive probabilistic programming language that abstracts the inference and allows users to focus on the modeling. As a result, Stan code is readable and easily extensible, which makes the modeler's work more transparent. Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is amiable to diagnostics, which means the user can verify whether the obtained inference is reliable. In this tutorial, we demonstrate how to formulate, fit, and diagnose a compartmental transmission model in Stan, first with a simple susceptible-infected-recovered model, then with a more elaborate transmission model used during the SARS-CoV-2 pandemic. We also cover advanced topics which can further help practitioners fit sophisticated models; notably, how to use simulations to probe the model and priors, and computational techniques to scale-up models based on ordinary differential equations.

A comparison of five epidemiological models for transmission of SARS-CoV-2 in India

BACKGROUND

Many popular disease transmission models have helped nations respond to the COVID-19 pandemic by informing decisions about pandemic planning, resource allocation, implementation of social distancing measures, lockdowns, and other non-pharmaceutical interventions. We study how five epidemiological models forecast and assess the course of the pandemic in India: a baseline curve-fitting model, an extended SIR (eSIR) model, two extended SEIR (SAPHIRE and SEIR-fansy) models, and a semi-mechanistic Bayesian hierarchical model (ICM).

METHODS

Using COVID-19 case-recovery-death count data reported in India from March 15 to October 15 to train the models, we generate predictions from each of the five models from October 16 to December 31. To compare prediction accuracy with respect to reported cumulative and active case counts and reported cumulative death counts, we compute the symmetric mean absolute prediction error (SMAPE) for each of the five models. For reported cumulative cases and deaths, we compute Pearson's and Lin's correlation coefficients to investigate how well the projected and observed reported counts agree. We also present underreporting factors when available, and comment on uncertainty of projections from each model.

RESULTS

For active case counts, SMAPE values are 35.14% (SEIR-fansy) and 37.96% (eSIR). For cumulative case counts, SMAPE values are 6.89% (baseline), 6.59% (eSIR), 2.25% (SAPHIRE) and 2.29% (SEIR-fansy). For cumulative death counts, the SMAPE values are 4.74% (SEIR-fansy), 8.94% (eSIR) and 0.77% (ICM). Three models (SAPHIRE, SEIR-fansy and ICM) return total (sum of reported and unreported) cumulative case counts as well. We compute underreporting factors as of October 31 and note that for cumulative cases, the SEIR-fansy model yields an underreporting factor of 7.25 and ICM model yields 4.54 for the same quantity. For total (sum of reported and unreported) cumulative deaths the SEIR-fansy model reports an underreporting factor of 2.97. On October 31, we observe 8.18 million cumulative reported cases, while the projections (in millions) from the baseline model are 8.71 (95% credible interval: 8.63-8.80), while eSIR yields 8.35 (7.19-9.60), SAPHIRE returns 8.17 (7.90-8.52) and SEIR-fansy projects 8.51 (8.18-8.85) million cases. Cumulative case projections from the eSIR model have the highest uncertainty in terms of width of 95% credible intervals, followed by those from SAPHIRE, the baseline model and finally SEIR-fansy.

CONCLUSIONS

In this comparative paper, we describe five different models used to study the transmission dynamics of the SARS-Cov-2 virus in India. While simulation studies are the only gold standard way to compare the accuracy of the models, here we were uniquely poised to compare the projected case-counts against observed data on a test period. The largest variability across models is observed in predicting the "total" number of infections including reported and unreported cases (on which we have no validation data). The degree of under-reporting has been a major concern in India and is characterized in this report. Overall, the SEIR-fansy model appeared to be a good choice with publicly available R-package and desired flexibility plus accuracy.

Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19

Hawkes processes are a form of self-exciting process that has been used in numerous applications, including neuroscience, seismology, and terrorism. While these self-exciting processes have a simple formulation, they can model incredibly complex phenomena. Traditionally Hawkes processes are a continuous-time process, however we enable these models to be applied to a wider range of problems by considering a discrete-time variant of Hawkes processes. We illustrate this through the novel coronavirus disease (COVID-19) as a substantive case study. While alternative models, such as compartmental and growth curve models, have been widely applied to the COVID-19 epidemic, the use of discrete-time Hawkes processes allows us to gain alternative insights. This paper evaluates the capability of discrete-time Hawkes processes by modelling daily mortality counts as distinct phases in the COVID-19 outbreak. We first consider the initial stage of exponential growth and the subsequent decline as preventative measures become effective. We then explore subsequent phases with more recent data. Various countries that have been adversely affected by the epidemic are considered, namely, Brazil, China, France, Germany, India, Italy, Spain, Sweden, the United Kingdom and the United States. These countries are all unique concerning the spread of the virus and their corresponding response measures. However, we find that this simple model is useful in accurately capturing the dynamics of the process, despite hidden interactions that are not directly modelled due to their complexity, and differences both within and between countries. The utility of this model is not confined to the current COVID-19 epidemic, rather this model could explain many other complex phenomena. It is of interest to have simple models that adequately describe these complex processes with unknown dynamics. As models become more complex, a simpler representation of the process can be desirable for the sake of parsimony.