Reflective equilibrium in practice and model selection: a methodological proposal from a survey experiment on the theories of distributive justice

As the increasing loss of ecosystem services severely affects life perspectives of today's poor and future populations, governing access to, and use of, ecosystem services in an intragenerational and intergenerational just way is an urgent issue. The author argues that theories of distributive justice should consider the distribution of access rights to ecosystem services. Three specific demands that a theory of distributive justice should fulfill to adequately cope with the distribution of access rights to ecosystem services, and show that Rawls’ “A Theory of Justice” (1971) can be consistently extended to meet the identified demands.

Consider the simple normal linear regression model for estimation/prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and information criteria can be used for identifying the right model. We compare the performances of such methods both theoretically and empirically from different perspectives for more insight. The testing approach at the conventional size of 0.05, in spite of being the “standard approach,” performs poorly in estimation. We also found that the frequently told story “the Bayesian information criterion (BIC) is good when the true model is finite-dimensional, and the Akaike information criterion (AIC) is good when the true model is infinite-dimensional” is far from being accurate. In addition, despite some successes in the effort to go beyond the debate between AIC and BIC by adaptive model selection, it turns out that it is not possible to share the pointwise adaptation property of BIC and the minimax-rate adaptation property of AIC by any model selection method. When model selection methods have difficulty in selection, model combining is a better alternative in terms of estimation accuracy.This work was completed when the author was on leave from Iowa State University and was a New Direction Visiting Professor at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. The fundings from both IMA and ISU are greatly appreciated. The work was also partly supported by NSF CAREER grant DMS0094323. The author thanks Xiaotong Shen and Hannes Leeb for very helpful discussions. The paper also benefited from the questions and comments from the participants at the statistics seminars the author gave at the University of Minnesota and Duke University. The author is very grateful to the anonymous reviewers and the co-editor Benedikt Potscher for carefully reading earlier versions of the paper, bringing my attention to several closely related previous and current results, and making many very valuable suggestions, which significantly improved the paper in both content and presentation.

Towards Accountability: The Articulation and Formalization of Fairness in Machine Learning

In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.

Rawls’ theory of distributive justice may serve as a useful model in conceptualizing a model of the ideal political economy – one that seeks to keep inequalities that have come about as a result of natural accident to a minimum. Moreover, his principles of justice can be used correctively, to address institutional inequalities that have the effect of entrenching social dislocation. Kenya has, over the decades up until now, been riven by injustices relating to land. This has led to the development of a small cluster of landed elites while the majority of citizens are effectively denied land access rights. This is regardless of the fact that most of the land so acquired by the former was acquired irregularly and with disregard of bona fide title of the original occupants. The concept and process of transitional justice may be viewed as the vehicle toward attaining corrective justice and accountability for offences committed in times of national crisis as a restorative measure.

In order to have confidence in model-based phylogenetic analysis, the model of nucleotide substitution adopted must be selected in a statistically rigorous manner. Several model-selection methods are applicable to maximum likelihood (ML) analysis, including the hierarchical likelihood-ratio test (hLRT), Akaike information criterion (AIC), Bayesian information criterion (BIC), and decision theory (DT), but their performance relative to empirical data has not been investigated thoroughly. In this study, we use 250 phylogenetic data sets obtained from TreeBASE to examine the effects that choice in model selection has on ML estimation of phylogeny, with an emphasis on optimal topology, bootstrap support, and hypothesis testing. We show that the use of different methods leads to the selection of two or more models for approximately 80% of the data sets and that the AIC typically selects more complex models than alternative approaches. Although ML estimation with different best-fit models results in incongruent tree topologies approximately 50% of the time, these differences are primarily attributable to alternative resolutions of poorly supported nodes. Furthermore, topologies and bootstrap values estimated with ML using alternative statistically supported models are more similar to each other than to topologies and bootstrap values estimated with ML under the Kimura two-parameter (K2P) model or maximum parsimony (MP). In addition, Swofford-Olsen-Waddell-Hillis (SOWH) tests indicate that ML trees estimated with alternative best-fit models are usually not significantly different from each other when evaluated with the same model. However, ML trees estimated with statistically supported models are often significantly suboptimal to ML trees made with the K2P model when both are evaluated with K2P, indicating that not all models perform in an equivalent manner. Nevertheless, the use of alternative statistically supported models generally does not affect tests of monophyletic relationships under either the Shimodaira-Hasegawa (S-H) or SOWH methods. Our results suggest that although choice in model selection has a strong impact on optimal tree topology, it rarely affects evolutionary inferences drawn from the data because differences are mainly confined to poorly supported nodes. Moreover, since ML with alternative best-fit models tends to produce more similar estimates of phylogeny than ML under the K2P model or MP, the use of any statistically based model-selection method is vastly preferable to forgoing the model-selection process altogether.

BackgroundPre-clinical models are commonly used to determine human antibiotic dosage regimens using pharmacokinetic/pharmacodynamic (PKPD) indices. The murine thigh infection model (MTIM) is most commonly used for PKPD index determination, while the hollow fibre infection model (HFIM) may be a viable alternative. However, there is no standardized method for determining the PKPD index and R2 may not be the ideal metric to determine goodness of fit for nonlinear models. This study aimed to reanalyse PKPD indices published in MTIM and HFIM, using a standardized modelling approach.MethodsSystematic literature review was conducted to identify MTIM and HFIM dose fractionation studies. Searches covered databases including PubMed, MEDLINE, BIOSIS, SCOPUS and EMBASE. Data were extracted and modelled using eight variations of Emax model, with model selection based on the lowest Akaike information criterion (AIC) and parameter plausibility in terms of precision and interpretability.ResultsA total of 53 studies were included: 50 MTIM (of 1138) and 3 HFIM (of 316). Among the 53 studies, reporting issues included an infrequent use of AIC for model selection as applied in only one paper, and a lack of methodological transparency in 29 papers. Remodelling revealed some disagreement in optimal PKPD indices in six studies.ConclusionsThis study suggests a standard method for PKPD index model selection and provides a database on PKPD index analysis. Building the Emax model from one to four estimated parameters and assessing them with AIC is recommended to avoid over fitting. Too few HFIM dose fractionation studies were found to allow comparison of PKPD index with MTIM.

This chapter explicates many of the words of Plato’s Socrates on the problem of distributive justice. One of the main points of this chapter is to demonstrate how the Socratic Anti-Mouthpiece Interpretation can and ought to function when it interprets the words placed in Socrates’ mouth by Plato. One of the leading contemporary philosophers of Plato, Richard Kraut , argues that Plato has a theory of distributive justice. However, while this chapter will argue that there is no theory of distributive justice found in the words of Plato’s Socrates, there are philosophically interesting concepts and arguments which are articulated and may be useful to contemporary moral, legal, social and political philosophers.

The theory of distributive justice is concerned with the way in which socially valued rewards, such as salaries, promotions, or special privileges, get allocated to members of a social system. The two basic notions are: (1) individuals have what they regard as legitimate expectations about how rewards shiould be allocated, and (2) if such expectations are violated there is both strain and pressures for social change. In considering injustice or inequity, the idea of relative deprivation has played a key role. That is, feelings of dissatisfaction and associated pressures for change depend not on the absolute level of reward received but on the relationship between rewards received and rewards expected. The idea of relative deprivation was already prominent in studies of military personnel in World War H. It was found, for instance, that the Air Force, despite objectively greater opportunities for promotion than the Military Police, showed more dissatisfaction with its promotion opportunities because of its greater expe tations for promotion.' In general, relative deprivation occurs where similar individuals are not given similar rewards. For example, whatever their absolute wage, airline mechanics will be upset if they are paid less than automobile mechanics if they believe that they are as skiUled as automobile mechanics. Thus, inequity in the reward-allocation process is found whenever similar actors are given dissimilar rewards, or dissimilar actors are given similar rewards. For example: Homans describes the billing office of a public utility in which one status, the ledger clerks, is rewarded as more skilled than a second status, the cash posters, but the two are paid the same wage. The wage policy is regarded by girls in both statuses as -unjust and they agitate in their union for a wage differential.2 Investigators have found numerous responses to injustice or inequity, ranging from status protest to some psychosomatic symptoms, but the response is always some form of socially or psychologically disruptive condition. There are basically two formulations of the theory of distributive justice: an exchange formulation most prominently represented by the works of Homans3 and Adams 4, and a status-value formulation developed recently by ourselves. Elsewhere we have stated in some detail why we prefer a status-value to the exchange formulation.5 We shall not repeat the arguments here. We are currently engaged in experimental work that contrasts predictions made using the status-value formulation with predictions from the exchange theory of distributive justice.

A central question in international climate policy making is how to distribute the burdens of keeping global average temperature increase to well below 2 °C above pre-industrial levels. In particular, there are four distributional issues: how to allocate the total amount of greenhouse gases that can still be emitted, who should bear the costs of mitigation, who should bear the costs of adaptation to unavoidable climate change, and who should bear the costs of residual climate damage. Regarding these distributional issues the academic literature offers a plethora of fairness principles, such as ‘polluter pays’, ‘beneficiary pays’, ‘equal per capita rights’, ‘grandfathering’, ‘ability to pay’, ‘historical responsibility’ and ‘cost effectiveness’. Remarkably, there is a theoretical gap between these principles and the central theories of distributive justice in moral and political philosophy. As a consequence, it is unclear how these principles are related, whether they can be combined or are mutually exclusive, and what the fundamental underlying values are. This paper aims to elucidate that debate. Understanding the different underlying values may facilitate bridge-building and movement in negotiation positions.

Statistical model selection and evaluation methods like Akaike information criteria (AIC) and Monte Carlo simulation (MCS) have often established efficient output for reliability analysis with large sample size. Information criterion can provide better model selection and evaluation in small sample sizes setup by considering the well-known measure of bootstrap resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion to check for uncertainty arising from model selection as well as statistics of interest for small sample size using reliability analysis. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection devised from efficient bootstrap simulation or variance reduced bootstrap information criterion to be combined with reliability analysis. It is beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest for uncertainty analysis. The proposed simulation scheme is verified using a number of sample size focused response functions under repetitions-centred approach with AIC-based reliability analysis for comparison and MCS for accuracy. The results show that the proposed simulation scheme aids the statistics of interest by reducing the spread and hence the uncertainty in sample size-based reliability analysis when compared with conventional methods.

We illustrate a recently proposed two-step bootstrap model averaging (bootstrap MA) approach to cope with model selection uncertainty. The predictive performance is investigated in an example and in a simulation study. Results are compared to those derived from other model selection methods. In the framework of the linear regression model we use the two-step bootstrap MA, which consists of a screening step to eliminate covariates thought to have no influence on the response, and a model-averaging step. We also apply the full model, variable selection using backward elimination based on Akaike's Information Criterion (AIC), the Bayes Information Criterion (BIC) and the bagging approach. The predictive performance is measured by the mean squared error (MSE) and the coverage of confidence intervals for the true response. We obtained similar results for all approaches in the example. In the simulation the MSE was reduced by all approaches in comparison to the full model. The smallest values are obtained for bootstrap MA. Only the bootstrap MA and the full model correctly estimated the nominal coverage. The backward elimination procedures led to substantial underestimation and bagging to an overestimation of the true coverage. The screening step of bootstrap MA eliminates most of the unimportant factors. The new bootstrap MA approach shows promising results for predictive performance. It increases practical usefulness by eliminating unimportant factors in the screening step.

In this research, the impact of total early-stage entrepreneurial activity and competitiveness of the economy on the real gross domestic product (GDP) per capita is analyzed in a cross-section of world economies using the methods of correlation and multiple regression analysis. In the attempt to select between the linear and the double-logarithmic model, the regression diagnostics and quality of the relationship between the dependent and the independent variables were analyzed. The functional form of the model was tested by the MacKinnon, White and Davidson test. Model selection methods regarding the comparison of coefficients of determination and the Akaike information criterion were used. The results of the analysis show that independent variables have a statistically significant impact on the real GDP per capita, and that the real GDP per capita is elastic to the changes of competitiveness but inelastic to the changes of total early-stage entrepreneurial activity.

This essay considers the role of impartiality in theories of distributive justice. Impartiality is modelled by Rawls in his famous thought experiment of a veil of ignorance, where individuals reason about principles of justice without knowing fundamental aspects of themselves — such as talent or family background. It is argued that the veil of ignorance delivers recommendations that are inconsistent with prioritarianism, that is, the view that priority should be given to ameliorating the disadvantage of the worst off. Hence, prioritarianism, which is after all far weaker than strict egalitarianism, cannot be justified by appeal to a veil of ignorance. The veil of ignorance achieves impartiality, but impartiality needs to be conjoined with a principle of solidarity in order to justify the redistribution of wealth. The resource allocation rules that jointly satisfy impartiality, priority, and solidarity are described.

BackgroundMixed graphical models (MGMs) are graphical models learned over a combination of continuous and discrete variables. Mixed variable types are common in biomedical datasets. MGMs consist of a parameterized joint probability density, which implies a network structure over these heterogeneous variables. The network structure reveals direct associations between the variables and the joint probability density allows one to ask arbitrary probabilistic questions on the data. This information can be used for feature selection, classification and other important tasks.ResultsWe studied the properties of MGM learning and applications of MGMs to high-dimensional data (biological and simulated). Our results show that MGMs reliably uncover the underlying graph structure, and when used for classification, their performance is comparable to popular discriminative methods (lasso regression and support vector machines). We also show that imposing separate sparsity penalties for edges connecting different types of variables significantly improves edge recovery performance. To choose these sparsity parameters, we propose a new efficient model selection method, named Stable Edge-specific Penalty Selection (StEPS). StEPS is an expansion of an earlier method, StARS, to mixed variable types. In terms of edge recovery, StEPS selected MGMs outperform those models selected using standard techniques, including AIC, BIC and cross-validation. In addition, we use a heuristic search that is linear in size of the sparsity value search space as opposed to the cubic grid search required by other model selection methods. We applied our method to clinical and mRNA expression data from the Lung Genomics Research Consortium (LGRC) and the learned MGM correctly recovered connections between the diagnosis of obstructive or interstitial lung disease, two diagnostic breathing tests, and cigarette smoking history. Our model also suggested biologically relevant mRNA markers that are linked to these three clinical variables.ConclusionsMGMs are able to accurately recover dependencies between sets of continuous and discrete variables in both simulated and biomedical datasets. Separation of sparsity penalties by edge type is essential for accurate network edge recovery. Furthermore, our stability based method for model selection determines sparsity parameters faster and more accurately (in terms of edge recovery) than other model selection methods. With the ongoing availability of comprehensive clinical and biomedical datasets, MGMs are expected to become a valuable tool for investigating disease mechanisms and answering an array of critical healthcare questions.