Inferring an unobservable population size from observable samples.

Success in the physical and social worlds often requires knowledge of population size. However, many populations cannot be observed in their entirety, making direct assessment of their size difficult, if not impossible. Nevertheless, an unobservable population size can be inferred from observable samples. We measured people's ability to make such inferences and their confidence in these inferences. Contrary to past work suggesting insensitivity to sample size and failures in statistical reasoning, inferences of populations size were accurate-but only when observable samples indicated a large underlying population. When observable samples indicated a small underlying population, inferences were systematically biased. This error, which cannot be attributed to a heuristics account, was compounded by a metacognitive failure: Confidence was highest when accuracy was at its worst. This dissociation between accuracy and confidence was confirmed by a manipulation that shifted the magnitude and variability of people's inferences without impacting their confidence. Together, these results (a) highlight the mental acuity and limits of a fundamental human judgment and (b) demonstrate an inverse relationship between cognition and metacognition.

People Make the Same Bayesian Judgment They Criticize in Others.

When two individuals from different social groups exhibit identical behavior, egalitarian codes of conduct call for equal judgments of both individuals. However, this moral imperative is at odds with the statistical imperative to consider priors based on group membership. Insofar as these priors differ, Bayesian rationality calls for unequal judgments of both individuals. We show that participants criticized the morality and intellect of someone else who made a Bayesian judgment, shared less money with this person, and incurred financial costs to punish this person. However, participants made unequal judgments as a Bayesian statistician would, thereby rendering the same judgment that they found repugnant when offered by someone else. This inconsistency, which can be reconciled by differences in which base rate is attended to, suggests that participants use group membership in a way that reflects the savvy of a Bayesian and the disrepute of someone they consider to be a bigot.

Statistically inaccurate and morally unfair judgements via base rate intrusion.

From a statistical standpoint, judgements about an individual are more accurate if base rates about the individual's social group are taken into account 1-4 . But from a moral standpoint, using these base rates is considered unfair and can even be illegal 5-9 . Thus, the imperative to be statistically accurate is directly at odds with the imperative to be morally fair. This conflict was resolved by creating tasks in which Bayesian rationality and moral fairness were aligned, thereby allowing social judgements to be both accurate and fair. Despite this alignment, we show that social judgements were inaccurate and unfair. Instead of appropriately setting aside social group differences, participants erroneously relied on them when making judgements about specific individuals. This bias-which we call base rate intrusion-was robust, generalized across various social groups (gender, race, nationality and age), and differed from analogous non-social judgements. Results also demonstrate how social judgements can be corrected to achieve both statistical accuracy and moral fairness. Overall, these data (total N = 5,138) highlight the pernicious effects of social base rates: under conditions that closely approximate those of everyday life 10-12 , these base rates can undermine the rationality and fairness of human judgements.

The base rate principle and the fairness principle in social judgment.

Meet Jonathan and Elizabeth. One person is a doctor and the other is a nurse. Who is the doctor? When nothing else is known, the base rate principle favors Jonathan to be the doctor and the fairness principle favors both individuals equally. However, when individuating facts reveal who is actually the doctor, base rates and fairness become irrelevant, as the facts make the correct answer clear. In three experiments, explicit and implicit beliefs were measured before and after individuating facts were learned. These facts were either stereotypic (e.g., Jonathan is the doctor, Elizabeth is the nurse) or counterstereotypic (e.g., Elizabeth is the doctor, Jonathan is the nurse). Results showed that before individuating facts were learned, explicit beliefs followed the fairness principle, whereas implicit beliefs followed the base rate principle. After individuating facts were learned, explicit beliefs correctly aligned with stereotypic and counterstereotypic facts. Implicit beliefs, however, were immune to counterstereotypic facts and continued to follow the base rate principle. Having established the robustness and generality of these results, a fourth experiment verified that gender stereotypes played a causal role: when both individuals were male, explicit and implicit beliefs alike correctly converged with individuating facts. Taken together, these experiments demonstrate that explicit beliefs uphold fairness and incorporate obvious and relevant facts, but implicit beliefs uphold base rates and appear relatively impervious to counterstereotypic facts.

A naive Bayes model to predict coupling between seven transmembrane domain receptors and G-proteins.

MOTIVATION: An understanding of the coupling between a G-protein coupled receptor (GPCR) and a specific class of heterotrimeric GTP-binding proteins (G-proteins) is vital for further comprehending the function of the receptor within a cell. However, predicting G-protein coupling based on the amino acid sequence of a receptor has been a daunting task. While experimental data for G-protein coupling exist, published models that rely on sequence based prediction are few. In this study, we have developed a Naive Bayes model to successfully predict G-protein coupling specificity by training over 80 GPCRs with known coupling. Each intracellular domain of GPCRs was treated as a discrete random variable, conditionally independent of one another. In order to determine the conditional probability distributions of these variables, ClustalW-generated phylogenetic trees were used as an approximation for the clustering of the intracellular domain sequences. The sampling of an intracellular domain sequence was achieved by identifying the cluster containing the homologue with the highest sequence similarity. RESULTS: Out of 55 GPCRs validated, the model yielded a correct classification rate of 72%. Our model also predicted multiple G-protein coupling for most of the GPCRs in the validation set. The Bayesian approach in this work offers an alternative to the experimental approach in order to answer the biological problem of GPCR/G-protein coupling selectivity. AVAILABILITY: Academic users should send their request for the perl program for calculating likelihood probabilities at jack.cao@astrazeneca.com. SUPPLEMENTARY INFORMATION: The materials can be viewed at http://www.astrazeneca-montreal.com/AZRDM_info/supporting_info.pdf.

Proenkephalin A gene products activate a new family of sensory neuron--specific GPCRs.

Several peptide fragments are produced by proteolytic cleavage of the opioid peptide precursor proenkephalin A, and among these are a number of enkephalin fragments, in particular bovine adrenal medulla peptide 22 (BAM22). These peptide products have been implicated in diverse biological functions, including analgesia. We have cloned a newly identified family of 'orphan' G protein--coupled receptors (GPCRs) and demonstrate that BAM22 and a number of its fragments bind to and activate these receptors with nanomolar affinities. This family of GPCRs is uniquely localized in the human and rat small sensory neuron, and we called this family the sensory neuron--specific G protein--coupled receptors (SNSRs). Receptors of the SNSR family are distinct from the traditional opioid receptors in their insensitivity to the classical opioid antagonist naloxone and poor activation by opioid ligands. The unique localization of SNSRs and their activation by proenkephalin A peptide fragments indicate a possible function for SNSRs in sensory neuron regulation and in the modulation of nociception.