Optimal Tuning of Random Survival Forest Hyperparameter with an Application to Liver Disease.

Background: Random Forest (RF) is a technique that optimises predictive accuracy by fitting an ensemble of trees to stabilise model estimates. The RF techniques were adapted into survival analysis to model the survival of patients with liver disease in order to identify biomarkers that are highly influential in patient prognostics. Methods: The methodology of this study begins by applying the classical Cox proportional hazard (Cox-PH) model and three parametric survival models (exponential, Weibull and lognormal) to the published dataset. The study further applied the supervised learning methods of Tuning Random Survival Forest (TRSF) parameters and the conditional inference Forest (Cforest) to optimally predict patient survival probabilities. Results: The efficiency of these models was compared using the Akaike information criteria (AIC) and integrated Brier score (IBS). The results revealed that the Cox-PH model (AIC = 185.7233) outperforms the three classical models. We further analysed these data to observe the functional relationships that exist between the patient survival function and the covariates using TRSF. Conclusion: The IBS result of the TRFS demonstrated satisfactory performance over other methods. Ultimately, it was observed from the TRSF results that some of the covariates contributed positively and negatively to patient survival prognostics.

Weighting and aggregating expert ecological judgments.

Performance weighted aggregation of expert judgments, using calibration questions, has been advocated to improve pooled quantitative judgments for ecological questions. However, there is little discussion or practical advice in the ecological literature regarding the application, advantages or challenges of performance weighting. In this paper we (1) illustrate how the IDEA protocol with four-step question format can be extended to include performance weighted aggregation from the Classical Model, and (2) explore the extent to which this extension improves pooled judgments for a range of performance measures. Our case study demonstrates that performance weights can improve judgments derived from the IDEA protocol with four-step question format. However, there is no a-priori guarantee of improvement. We conclude that the merits of the method lie in demonstrating that the final aggregation of judgments provides the best representation of uncertainty (i.e., validation), whether that be via equally weighted or performance weighted aggregation. Whether the time and effort entailed in performance weights can be justified is a matter for decision-makers. Our case study outlines the rationale, challenges, and benefits of performance weighted aggregations. It will help to inform decisions about the deployment of performance weighting and avoid common pitfalls in its application.

Axiomatic Natural Philosophy and the Emergence of Biology as a Science.

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany-Caspar Friedrich Wolff and Gottfried Reinhold Treviranus-sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science.

Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory.

In this paper, we classify quantum statistical models based on their information geometric properties and the estimation error bound, known as the Holevo bound, into four different classes: classical, quasi-classical, D-invariant, and asymptotically classical models. We then characterize each model by several equivalent conditions and discuss their properties. This result enables us to explore the relationships among these four models as well as reveals the geometrical understanding of quantum statistical models. In particular, we show that each class of model can be identified by comparing quantum Fisher metrics and the properties of the tangent spaces of the quantum statistical model.

The aggregation of expert judgment: do good things come to those who weight?

This responds to an "evaluation" of the classical model for structured expert judgment by Bolger and Rowe in this issue. This response references extensive expert judgment performance data in the public domain which played no role in their evaluation.

A retrospective assessment of COVID-19 model performance in the USA.

Coronavirus disease 2019 (COVID-19) forecasts from over 100 models are readily available. However, little published information exists regarding the performance of their uncertainty estimates (i.e. probabilistic performance). To evaluate their probabilistic performance, we employ the classical model (CM), an established method typically used to validate expert opinion. In this analysis, we assess both the predictive and probabilistic performance of COVID-19 forecasting models during 2021. We also compare the performance of aggregated forecasts (i.e. ensembles) based on equal and CM performance-based weights to an established ensemble from the Centers for Disease Control and Prevention (CDC). Our analysis of forecasts of COVID-19 mortality from 22 individual models and three ensembles across 49 states indicates that-(i) good predictive performance does not imply good probabilistic performance, and vice versa; (ii) models often provide tight but inaccurate uncertainty estimates; (iii) most models perform worse than a naive baseline model; (iv) both the CDC and CM performance-weighted ensembles perform well; but (v) while the CDC ensemble was more informative, the CM ensemble was more statistically accurate across states. This study presents a worthwhile method for appropriately assessing the performance of probabilistic forecasts and can potentially improve both public health decision-making and COVID-19 modelling.

Out-of-sample validation for structured expert judgment of Asian carp establishment in Lake Erie.

Structured expert judgment (SEJ) is used to quantify the uncertainty of nonindigenous fish (bighead carp [Hypophthalmichthys nobilis] and silver carp [H. molitrix]) establishment in Lake Erie. The classical model for structured expert judgment model is applied. Forming a weighted combination (called a decision maker) of experts' distributions, with weights derived from performance on a set of calibration variables from the experts' field, exhibits greater statistical accuracy and greater informativeness than simple averaging with equal weights. New methods of cross validation are applied and suggest that performance characteristics relative to equal weighting could be predicted with a small number (1-2) of calibration variables. The performance-based decision maker is somewhat degraded on out-of-sample prediction, but remained superior to the equal weight decision maker in terms of statistical accuracy and informativeness.