Motivations to reciprocate cooperation and punish defection are calibrated by estimates of how easily others can switch partners

Evolutionary models of dyadic cooperation demonstrate that selection favors different strategies for reciprocity depending on opportunities to choose alternative partners. We propose that selection has favored mechanisms that estimate the extent to which others can switch partners and calibrate motivations to reciprocate and punish accordingly. These estimates should reflect default assumptions about relational mobility: the probability that individuals in one’s social world will have the opportunity to form relationships with new partners. This prior probability can be updated by cues present in the immediate situation one is facing. The resulting estimate of a partner’s outside options should serve as input to motivational systems regulating reciprocity: Higher estimates should down-regulate the use of sanctions to prevent defection by a current partner, and up-regulate efforts to attract better cooperative partners by curating one’s own reputation and monitoring that of others. We tested this hypothesis using a Trust Game with Punishment (TGP), which provides continuous measures of reciprocity, defection, and punishment in response to defection. We measured each participant’s perception of relational mobility in their real-world social ecology and experimentally varied a cue to partner switching. Moreover, the study was conducted in the US (n = 519) and Japan (n = 520): societies that are high versus low in relational mobility. Across conditions and societies, higher perceptions of relational mobility were associated with increased reciprocity and decreased punishment: i.e., those who thought that others have many opportunities to find new partners reciprocated more and punished less. The situational cue to partner switching was detected, but relational mobility in one’s real social world regulated motivations to reciprocate and punish, even in the experimental setting. The current research provides evidence that motivational systems are designed to estimate varying degrees of partner choice in one’s social ecology and regulate reciprocal behaviors accordingly.

Evaluation of an integrative Bayesian peptide detection approach on a combinatorial peptide library

Detection of peptides lies at the core of bottom-up proteomics analyses. We examined a Bayesian approach to peptide detection, integrating match-based models (fragments, retention time, isotopic distribution, and precursor mass) and peptide prior probability models under a unified probabilistic framework. To assess the relevance of these models and their various combinations, we employed a complete- and a tail-complete search of a low-precursor-mass synthetic peptide library based on oncogenic KRAS peptides. The fragment match was by far the most informative match-based model, while the retention time match was the only remaining such model with an appreciable impact––increasing correct detections by around 8 %. A peptide prior probability model built from a reference proteome greatly improved the detection over a uniform prior, essentially transforming de novo sequencing into a reference-guided search. The knowledge of a correct sequence tag in advance to peptide-spectrum matching had only a moderate impact on peptide detection unless the tag was long and of high certainty. The approach also derived more precise error rates on the analyzed combinatorial peptide library than those estimated using PeptideProphet and Percolator, showing its potential applicability for the detection of homologous peptides. Although the approach requires further computational developments for routine data analysis, it illustrates the value of peptide prior probabilities and presents a Bayesian approach for their incorporation into peptide detection.

On Two Measure-Theoretic Aspects of the Full Bayesian Significance Test for Precise Bayesian Hypothesis Testing †

The Full Bayesian Significance Test (FBST) has been proposed as a convenient method to replace frequentist p-values for testing a precise hypothesis. Although the FBST enjoys various appealing properties, the purpose of this paper is to investigate two aspects of the FBST which are sometimes observed as measure-theoretic inconsistencies of the procedure and have not been discussed rigorously in the literature. First, the FBST uses the posterior density as a reference for judging the Bayesian statistical evidence against a precise hypothesis. However, under absolutely continuous prior distributions, the posterior density is defined only up to Lebesgue null sets which renders the reference criterion arbitrary. Second, the FBST statistical evidence seems to have no valid prior probability. It is shown that the former aspect can be circumvented by fixing a version of the posterior density before using the FBST, and the latter aspect is based on its measure-theoretic premises. An illustrative example demonstrates the two aspects and their solution. Together, the results in this paper show that both of the two aspects which are sometimes observed as measure-theoretic inconsistencies of the FBST are not tenable. The FBST thus provides a measure-theoretically coherent Bayesian alternative for testing a precise hypothesis.

Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers

Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple case study design was operated in which a purposive sample of PSMTs was selected to justify their reasoning in two probabilistic contexts while their responses were coded by NVivo, and corresponding categories were developed. As a result, PSMTs’ probabilistic reasoning was classified into mathematical (M), subjective (S), and outcome-oriented (O). Besides, several biases emerged along with these modes of reasoning. While M thinkers shared equiprobability and insensitivity to prior probability, the prediction bias and the belief of Allah’s willingness were yielded among S thinkers. Also, the causal conception spread among O thinkers.

Reverse Bayesian Implications of p-Values Reported in Critical Care Randomized Trials

Background Misinterpretations of the p-value in null-hypothesis statistical testing are common. We aimed to determine the implications of observed p-values in critical care randomized controlled trials (RCTs). Methods We included three cohorts of published RCTs: Adult-RCTs reporting a mortality outcome, Pediatric-RCTs reporting a mortality outcome, and recent Consecutive-RCTs reporting p-value ≤.10 in six higher-impact journals. We recorded descriptive information from RCTs. Reverse Bayesian implications of obtained p-values were calculated, reported as percentages with inter-quartile ranges. Results Obtained p-value was ≤.005 in 11/216 (5.1%) Adult-RCTs, 2/120 (1.7%) Pediatric-RCTs, and 37/90 (41.1%) Consecutive-RCTs. An obtained p-value .05–.0051 had high False Positive Rates; in Adult-RCTs, minimum (assuming prior probability of the alternative hypothesis was 50%) and realistic (assuming prior probability of the alternative hypothesis was 10%) False Positive Rates were 16.7% [11.2, 21.8] and 64.3% [53.2, 71.4]. An obtained p-value ≤.005 had lower False Positive Rates; in Adult-RCTs the realistic False Positive Rate was 7.7% [7.7, 16.0]. The realistic probability of the alternative hypothesis for obtained p-value .05–.0051 (ie, Positive Predictive Value) was 28.0% [24.1, 34.8], 30.6% [27.7, 48.5], 29.3% [24.3, 41.0], and 32.7% [24.1, 43.5] for Adult-RCTs, Pediatric-RCTs, Consecutive-RCTs primary and secondary outcome, respectively. The maximum Positive Predictive Value for p-value category .05–.0051 was median 77.8%, 79.8%, 78.8%, and 81.4% respectively. To have maximum or realistic Positive Predictive Value >90% or >80%, RCTs needed to have obtained p-value ≤.005. The credibility of p-value .05–.0051 findings were easy to challenge, and the credibility to rule-out an effect with p-value >.05 to .10 was low. The probability that a replication study would obtain p-value ≤.05 did not approach 90% unless the obtained p-value was ≤.005. Conclusions Unless the obtained p-value was ≤.005, the False Positive Rate was high, and the Positive Predictive Value and probability of replication of “statistically significant” findings were low.

Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal pure states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two mixed states.

Word Sense Disambiguation Using Prior Probability Estimation Based on the Korean WordNet

Supervised disambiguation using a large amount of corpus data delivers better performance than other word sense disambiguation methods. However, it is not easy to construct large-scale, sense-tagged corpora since this requires high cost and time. On the other hand, implementing unsupervised disambiguation is relatively easy, although most of the efforts have not been satisfactory. A primary reason for the performance degradation of unsupervised disambiguation is that the semantic occurrence probability of ambiguous words is not available. Hence, a data deficiency problem occurs while determining the dependency between words. This paper proposes an unsupervised disambiguation method using a prior probability estimation based on the Korean WordNet. This performs better than supervised disambiguation. In the Korean WordNet, all the words have similar semantic characteristics to their related words. Thus, it is assumed that the dependency between words is the same as the dependency between their related words. This resolves the data deficiency problem by determining the dependency between words by calculating the χ2 statistic between related words. Moreover, in order to have the same effect as using the semantic occurrence probability as prior probability, which is used in supervised disambiguation, semantically related words of ambiguous vocabulary are obtained and utilized as prior probability data. An experiment was conducted with Korean, English, and Chinese to evaluate the performance of our proposed lexical disambiguation method. We found that our proposed method had better performance than supervised disambiguation methods even though our method is based on unsupervised disambiguation (using a knowledge-based approach).

Assessment of Dynamic Bayesian Models for Gas Turbine Diagnostics, Part 1: Prior Probability Analysis

The reliability and cost-effectiveness of energy conversion in gas turbine systems are strongly dependent on an accurate diagnosis of possible process and sensor anomalies. Because data collected from a gas turbine system for diagnosis are inherently uncertain due to measurement noise and errors, probabilistic methods offer a promising tool for this problem. In particular, dynamic Bayesian networks present numerous advantages. In this work, two Bayesian networks were developed for compressor fouling and turbine erosion diagnostics. Different prior probability distributions were compared to determine the benefits of a dynamic, first-order hierarchical Markov model over a static prior probability and one dependent only on time. The influence of data uncertainty and scatter was analyzed by testing the diagnostics models on simulated fleet data. It was shown that the condition-based hierarchical model resulted in the best accuracy, and the benefit was more significant for data with higher overlap between states (i.e., for compressor fouling). The improvement with the proposed dynamic Bayesian network was 8 percentage points (in classification accuracy) for compressor fouling and 5 points for turbine erosion compared with the static network.

Regularization, Bayesian Inference and Machine Learning methods for Inverse Problems†

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Implementation of Tactical Decision Aids Based on Event Knowledge Graph

This paper proposes a new tactical decision aids method based on event knowledge graph (EventKG). In the warfare domain, EventKG can be constructed through event types design, event network construction and transition probability computation between events. Initially, four event classes are introduced in accordance with the OODA loop, and eighteen subclasses are further decomposed. With the aids of a common event template, all the events taking place in the battle field can be described. Event networks are built by adopting the hierarchical task network (HTN) and described through Bayesian network, to exhibit various relations between battle events. Transition probability, namely the occurrence probability of next possible event, is computed by using the prior probability and conditional probability of event occurring. On the basis of structured EventKG, entity knowledge graph (EKG) and entity relation knowledge graph (ERKG), tactical decision aid instructions can be generated by combining with the battlefield situation information.