Processing Data from Social Dilemma Experiments: A Bayesian Comparison of Parametric Estimators

Observed choices in Social Dilemma Games usually take the form of bounded integers. We propose a doubly-truncated count data framework to process such data. We compare this framework to past approaches based on ordered outcomes and truncated continuous densities using Bayesian estimation and model selection techniques. We find that all three frameworks (i) support the presence of unobserved heterogeneity in individual decision-making, and (ii) agree on the ranking of regulatory treatment effects. The count data framework exhibits superior efficiency and produces more informative predictive distributions for outcomes of interest. The continuous framework fails to allocate adequate probability mass to boundary outcomes, which are often of pivotal importance in these games.Social dilemma games; Hierarchical modeling; Bayesian simulation; Common property resource

Collective Animal Behavior from Bayesian Estimation and Probability Matching

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is based on empirical fits to observations and we lack first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching.
In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability given by the Bayesian estimation that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior

Climate change adaptation in Africa : a microeconomic analysis of livestock choice

This paper uses quantitative methods to examine the way African farmers have adapted livestock management to the range of climates found across the African continent. The authors use logit analysis to estimate whether farmers adopt livestock. They then use three econometric models to examine which species farmers choose: a primary choice multinomial logit, an optimal portfolio multinomial logit, and a demand system multivariate probit. Comparing the results of the three methods of estimating species selection reveals that the three approaches yield similar results. Using data from over 9,000 African livestock farmers in 10 countries, the analysis finds that farmers are more likely to choose to have livestock as temperatures increase and as precipitation decreases. Across all methods of estimating choice, livestock farmers in warmer locations are less likely to choose beef cattle and chickens and more likely to choose goats and sheep. As precipitation increases, cattle and sheep decrease but goats and chickens increase. The authors simulate the way farmers'choices might change with a set of uniform climate changes and a set of climate model scenarios. The uniform scenarios predict that warming and drying would increase livestock ownership but that increases in precipitation would decrease it. The climate scenarios predict a decrease in the probability of beef cattle and an increase in the probability of sheep and goats, and they predict that more heat-tolerant animals will dominate the future African landscape.Livestock&Animal Husbandry,Wildlife Resources,Peri-Urban Communities,Rural Urban Linkages,Climate Change

A robust dynamic classifier selection approach for hyperspectral images with imprecise label information

Supervised hyperspectral image (HSI) classification relies on accurate label information. However, it is not always possible to collect perfectly accurate labels for training samples. This motivates the development of classifiers that are sufficiently robust to some reasonable amounts of errors in data labels. Despite the growing importance of this aspect, it has not been sufficiently studied in the literature yet. In this paper, we analyze the effect of erroneous sample labels on probability distributions of the principal components of HSIs, and provide in this way a statistical analysis of the resulting uncertainty in classifiers. Building on the theory of imprecise probabilities, we develop a novel robust dynamic classifier selection (R-DCS) model for data classification with erroneous labels. Particularly, spectral and spatial features are extracted from HSIs to construct two individual classifiers for the dynamic selection, respectively. The proposed R-DCS model is based on the robustness of the classifiers’ predictions: the extent to which a classifier can be altered without changing its prediction. We provide three possible selection strategies for the proposed model with different computational complexities and apply them on three benchmark data sets. Experimental results demonstrate that the proposed model outperforms the individual classifiers it selects from and is more robust to errors in labels compared to widely adopted approaches

Analyzing Extreme Cases: How Quantile Regression can Enhance Our Ability to Identify Productivity Stars

Recent research suggests that individual productivity may not be normally distributed and is best modeled by a power law, a form of a heavy-tailed distribution where extreme cases on the right side of the distribution affect the mean and skew the probability distribution. These extreme cases, commonly referred to as “star performers” or “productivity stars,” provide a disproportionately positive impact on organizations. Yet, the field of industrial-organizational psychology has failed to uncover effective techniques to identify them during selection accurately. Limiting factors in the identification of star performers are the traditional methods (e.g., Pearson correlation, ordinary least squares regression) used to establish criterion-related validity and inform selection battery design (i.e., determine which assessments should be retained and how those assessments should be weighted). Pearson correlation and ordinary least squares regression do not perform well (i.e., do not provide accurate estimates) when data are highly skewed and contain outliers. Thus, the purpose of this dissertation was to investigate whether an alternative method, specifically the quantile regression model (QRM), outperforms traditional approaches during criterion-related validation and selection battery design. Across three unique samples, results suggest that although the QRM provides a much more detailed understanding of predictor-criterion relationships, the practical usefulness of the QRM in selection assessment battery design is similar to the OLS regression

A Spreadsheet Simulation Of The Monty Hall Problem

The “Monty Hall” problem or “Three Door” problem—where a person chooses one of three doors in hope of winning a valuable prize but is subsequently offered the choice of changing his or her selection—is a well known and often discussed probability problem.  In this paper, the structure, history, and ultimate solution of the Monty Hall problem are discussed. The problem solution is modeled with a spreadsheet simulation that evaluates the frequencies of the possible outcomes (win or lose) under the two choices or strategies available:  switch to the unopened door or do not switch. A Law of Large Numbers approach is also used to graphically demonstrate the long run outcome of adopting one the two available strategies. As is known, the optimal strategy is to switch to the unopened door; the spreadsheet model illustrates why this strategy is optimal. A complete discussion of the spreadsheet logic is included. Pedagogical approaches and applications of the spreadsheet simulation approach are also discussed

Epidemiologic Considerations Related to the Use of the Prognostic Score in Selection Bias and Confounding.

Background: The propensity score is often used to obtain unbiased effect estimates in the presence of confounding. The prognostic score is a method similar to the propensity score that estimates the conditional probability of the outcome. While the prognostic score has been applied to address confounding, an application to selection bias has not been explored. The existing methods to correct for selection bias are limited when dealing with non-participation in forming the study population. The prognostic score could be potentially applied to obtain unbiased effect estimates in the presence of selection bias. Objective: This thesis explores the use of the prognostic score as a method to address confounding and selection bias in epidemiologic research. The first investigation of the prognostic score will employ multiple forms of the prognostic score to estimate the unbiased effect in the presence of confounding. We will show that the propensity score and a modified version of the prognostic score yield equivalent effect estimates for a logistic model. The second investigation compares the use of the prognostic score in the presence of selection bias to existing methods including inverse probability of selection weights (IPSW) and direct adjustment with and without the presence of confounding. Design: Based on several directed acyclic graphs, Monte Carlo simulations compared several approaches to isolating the effect estimate. In the presence of confounding, weighting using three variations of the prognostic score were compared to weighting using the propensity score. Approaches to combining the prognostic and propensity score were also investigated. In the presence of selection bias, weighting using the three prognostic score approaches, IPSW, and direct adjustment were compared. Main Outcomes: Percent relative bias, robust variance estimates, Monte Carlo variance estimates, and mean squared error with respect to the marginal and conditional odds ratios were compared between all of the methods. Results: In the presence of confounding, the stabilized modified prognostic score weights and stabilized inverse probability of exposure weights yielded the marginal odds ratio, while the combination prognostic and propensity score approaches, the unexposed prognostic score weights, and the full population prognostic score weights resulted in the conditional odds ratio. For the selection bias simulations, the unexposed and full population prognostic score weights estimated the conditional odds ratio and were comparable to direct adjustment methods. The modified prognostic score yielded a result that appeared to be a mix of the marginal and conditional odds ratio. In the presence of unmeasured selection variables, the prognostic score approaches and direct adjustment were biased. Conclusions and Relevance: The prognostic score is an acceptable alternative method to adjust for confounding and for selection bias except for when the selection variable acts as a collider in the presence of unmeasured variables

Risk Modelling Framework for Emergency Hospital Readmission, Using Hospital Episode Statistics Inpatient Data

The objective of this study was to develop, test and benchmark a framework and a predictive risk model for hospital emergency readmission within 12 months. We performed the development using routinely collected Hospital Episode Statistics data covering inpatient hospital admissions in England. Three different timeframes were used for training, testing and benchmarking: 1999 to 2004, 2000 to 2005 and 2004 to 2009 financial years. Each timeframe includes 20% of all inpatients admitted within the trigger year. The comparisons were made using positive predictive value, sensitivity and specificity for different risk cut-offs, risk bands and top risk segments, together with the receiver operating characteristic curve. The constructed Bayes Point Machine using this feature selection framework produces a risk probability for each admitted patient, and it was validated for different timeframes, sub-populations and cut-off points. At risk cut-off of 50%, the positive predictive value was 69.3% to 73.7%, the specificity was 88.0% to 88.9% and sensitivity was 44.5% to 46.3% across different timeframes. Also, the area under the receiver operating characteristic curve was 73.0% to 74.3%. The developed framework and model performed considerably better than existing modelling approaches with high precision and moderate sensitivity

Exploring dependence between categorical variables: benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms

This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing log-linear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the log-linear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize log-linear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.Comment: Preprin