Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample.

Bayesian decision theory (BDT) is frequently used to model normative performance in perceptual, motor, and cognitive decision tasks where the possible outcomes of actions are associated with rewards or penalties. The resulting normative models specify how decision makers should encode and combine information about uncertainty and value-step by step-in order to maximize their expected reward. When prior, likelihood, and posterior are probabilities, the Bayesian computation requires only simple arithmetic operations: addition, etc. We focus on visual cognitive tasks where Bayesian computations are carried out not on probabilities but on (1) probability density functions and (2) these probability density functions are derived from samples. We break the BDT model into a series of computations and test human ability to carry out each of these computations in isolation. We test three necessary properties of normative use of pdf information derived from a sample-accuracy, additivity and influence. Influence measures allow us to assess how much weight each point in the sample is assigned in making decisions and allow us to compare normative use (weighting) of samples to actual, point by point. We find that human decision makers violate accuracy and additivity systematically but that the cost of failure in accuracy or additivity would be minor in common decision tasks. However, a comparison of measured influence for each sample point with normative influence measures demonstrates that the individual's use of sample information is markedly different from the predictions of BDT. We will show that the normative BDT model takes into account the geometric symmetries of the pdf while the human decision maker does not. An alternative model basing decisions on a single extreme sample point provided a better account for participants' data than the normative BDT model.

Autonomous behaviour and the limits of human volition.

Humans and some other animals can autonomously generate action choices that contribute to solving complex problems. However, experimental investigations of the cognitive bases of human autonomy are challenging, because experimental paradigms typically constrain behaviour using controlled contexts, and elicit behaviour by external triggers. In contrast, autonomy and freedom imply unconstrained behaviour initiated by endogenous triggers. Here we propose a new theoretical construct of adaptive autonomy, meaning the capacity to make behavioural choices that are free from constraints of both immediate external triggers and of routine response patterns, but nevertheless show appropriate coordination with the environment. Participants (N = 152) played a competitive game in which they had to choose the right time to act, in the face of an opponent who punished (in separate blocks) either choice biases (such as always responding early), sequential patterns of action timing across trials (such as early, late, early, late…), or predictable action-outcome dependence (such as win-stay, lose-shift). Adaptive autonomy was quantified as the ability to maintain performance when each of these influences on action selection was punished. We found that participants could become free from habitual choices regarding when to act and could also become free from sequential action patterns. However, they were not able to free themselves from influences of action-outcome dependence, even when these resulted in poor performance. These results point to a new concept of autonomous behaviour as flexible adaptation of voluntary action choices in a way that avoids stereotypy. In a sequential analysis, we also demonstrated that participants increased their reliance on belief learning in which they attempt to understand the competitor's beliefs and intentions, when transition bias and reinforcement bias were punished. Taken together, our study points to a cognitive mechanism of adaptive autonomy in which competitive interactions with other agents could promote both social cognition and volition in the form of non-stereotyped action choices.

Detecting visual texture patterns in binary sequences through pattern features.

We measured human ability to detect texture patterns in a signal detection task. Observers viewed sequences of 20 blue or yellow tokens placed horizontally in a row. They attempted to discriminate sequences generated by a random generator ("a fair coin") from sequences produced by a disrupted Markov sequence (DMS) generator. The DMSs were generated in two stages: first a sequence was generated using a Markov chain with probability, pr = 0.9, that a token would be the same color as the token to its left. The Markov sequence was then disrupted by flipping each token from blue to yellow or vice versa with probability, pd-the probability of disruption. Disruption played the role of noise in signal detection terms. We can frame what observers are asked to do as detecting Markov texture patterns disrupted by noise. The experiment included three conditions differing in pd (0.1, 0.2, 0.3). Ninety-two observers participated, each in only one condition. Overall, human observers' sensitivities to texture patterns (d' values) were markedly less than those of an optimal Bayesian observer. We considered the possibility that observers based their judgments not on the entire texture sequence but on specific features of the sequences such as the length of the longest repeating subsequence. We compared human performance with that of multiple optimal Bayesian classifiers based on such features. We identify the single- and multiple-feature models that best match the performance of observers across conditions and develop a pattern feature pool model for the signal detection task considered.

Competition Rather Than Observation and Cooperation Facilitates Optimal Motor Planning.

Humans tend to select motor planning with a high reward and low success compared with motor planning, which has a small reward and high success rate. Previous studies have shown such a risk-seeking property in motor decision tasks. However, it is unclear how to facilitate a shift from risk-seeking to optimal motor planning that maximizes the expected reward. Here, we investigate the effect of interacting with virtual partners/opponents on motor plans since interpersonal interaction has a powerful influence on human perception, action, and cognition. This study compared three types of interactions (competition, cooperation, and observation) and two types of virtual partners/opponents (those engaged in optimal motor planning and those engaged in risk-averse motor planning). As reported in previous studies, the participants took a risky aim point when they performed a motor decision task alone. However, we found that the participant's aim point was significantly modulated when they performed the same task while competing with a risk-averse opponent (p = 0.018) and that there was no significant difference from the optimal aim point (p = 0.63). No significant modulation in the aim points was observed during the cooperation and observation tasks. These results highlight the importance of competition for modulating suboptimal decision-making and optimizing motor performance.

Optimizing motor decision-making through competition with opponents.

Although optimal decision-making is essential for sports performance and fine motor control, it has been repeatedly confirmed that humans show a strong risk-seeking bias, selecting a risky strategy over an optimal solution. Despite such evidence, the ideal method to promote optimal decision-making remains unclear. Here, we propose that interactions with other people can influence motor decision-making and improve risk-seeking bias. We developed a competitive reaching game (a variant of the "chicken game") in which aiming for greater rewards increased the risk of no reward and subjects competed for the total reward with their opponent. The game resembles situations in sports, such as a penalty kick in soccer, service in tennis, the strike zone in baseball, or take-off in ski jumping. In five different experiments, we demonstrated that, at the beginning of the competitive game, the subjects robustly switched their risk-seeking strategy to a risk-averse strategy. Following the reversal of the strategy, the subjects achieved optimal decision-making when competing with risk-averse opponents. This optimality was achieved by a non-linear influence of an opponent's decisions on a subject's decisions. These results suggest that interactions with others can alter human motor decision strategies and that competition with a risk-averse opponent is key for optimizing motor decision-making.

Sub-optimality in motor planning is not improved by explicit observation of motor uncertainty.

To make optimal decisions under risk, one must correctly weight potential rewards and penalties by the probabilities of receiving them. In motor decision tasks, the uncertainty in outcome is a consequence of motor uncertainty. When participants perform suboptimally as they often do in such tasks, it could be because they have insufficient information about their motor uncertainty: with more information, their performance could converge to optimal as they learn their own motor uncertainty. Alternatively, their suboptimal performance may reflect an inability to make use of the information they have or even to perform the correct computations. To discriminate between these two possibilities, we performed an experiment spanning two days. On the first day, all participants performed a reaching task with trial-by-trial feedback of motor error. At the end of the day, their aim points were still typically suboptimal. On the second day participants were divided into two groups one of which repeated the task of the first day and the other of which repeated the task but were intermittently given additional information summarizing their motor errors. Participants receiving additional information did not perform significantly better than those who did not.

[A Case of Large-Cell Neuroendocrine Carcinoma of the Stomach with Multiple Liver Metastases That Show Complete Response to Multidisciplinary Therapy].

A 64-year-old man was diagnosed with advanced gastric cancer based on an endoscopic examination in June 2009; histological findings indicated poorly differentiated adenocarcinoma.Computed tomography revealed multiple liver metastases and bulky lymph node metastases of LN#7.The multiple liver metastases of the gastric cancer were not considered to be candidates for surgical resection, and S-1/CDDP chemotherapy was initiated in July 2009. After 6 courses of this regimen, liver and lymph node metastases showed partial response(PR), but the gastric tumor showed progressive disease(PD).Therefore, we switched this regimen to bi-weekly CPT-11/CDDP in March 2010. However, because the gastric tumor had increased in size and presented with bleeding, we performed distal gastrectomy.The pathological diagnosis based on the resected speci- men was large-cell neuroendocrine carcinoma.After surgery, CPT-11/CDDP was continued but was switched to CPT-11 in June 2011 because of induced renal dysfunction.In November 2011, the regimen was switched to weekly paclitaxel because of a progressive increase in size of a solitary liver metastatic lesion located in S4-5.Two courses of this regimen were administered, but they were ineffective; therefore, we performed partial hepatectomy.No other recurrent lesions were observed during the surgery, and the patient was estimated to have achieved complete response(CR).After the surgery, no further adjuvant chemotherapy was administered.Four years after hepatectomy, the patient was diagnosed with esophageal cancer but exhibited no recurrence of the gastric cancer.We performed esophagectomy for the esophageal cancer in May 2016.T he patient is currently well without any relapse.

Transcranial Direct Current Stimulation Over Dorsolateral Prefrontal Cortex Modulates Risk-Attitude in Motor Decision-Making.

Humans often face situations requiring a decision about where to throw an object or when to respond to a stimulus under risk. Several behavioral studies have shown that such motor decisions can be suboptimal, which results from a cognitive bias toward risk-seeking behavior. However, brain regions involved in risk-attitude of motor decision-making remain unclear. Here, we investigated the role of the dorsolateral prefrontal cortex (DLPFC) in risky motor decisions using transcranial direct current stimulation (tDCS). The experiment comprised a selective timing task requiring participants to make a continuous decision about the timing of their response under the risk of no rewards. The participants performed this task twice in a day: before and while receiving either anodal stimulation over the right DLPFC with cathodal stimulation over the left DLPFC (20 min, 2 mA), cathodal stimulation over the right DLPFC with anodal stimulation over the left DLPFC, or sham stimulation. In line with previous studies, their strategies before the stimulation were biased toward risk-seeking. During anodal stimulation over right DLPFC with cathodal stimulation over left DLPFC, participants showed a more conservative strategy to avoid the risk of no rewards. The additional experiment confirmed that tDCS did not affect the ability of timing control regarding the time intervals at which they aimed to respond. These results suggest a potential role for the DLPFC in modulating action selection in motor decision-making under risk.

Risk aversion in the adjustment of speed-accuracy tradeoff depending on time constraints.

Humans are often required to make decisions under time constraints and to adjust speed-accuracy tradeoff (SAT) based on time constraints. Previous studies have investigated how humans adjust SAT depending on the time discount rate of expected gain. Although the expected gain of actions can be determined by both gain and probability, only situations where gain decreases over time have been tested. Considering the effect of risk on decision-making, the difference in time discount factors may modulate the response strategies for SAT, since temporal changes in variance of possible outcomes differ when gain or probability decreases over time. Here, we investigated the response strategies for SAT under different time discount factors. Participants were required to select one of the two options with different initial values in situations where the expected gain of options declined over time by a linear decrease in gain or probability. Comparison of response strategies between conditions revealed that response times in the gain condition were longer than those in the probability condition, possibly due to risk-aversion. These findings indicate the existence of common rules underpinning sensorimotor and economic decision-making.

Sub-optimality in motor planning is retained throughout 9 days practice of 2250 trials.

Optimality in motor planning, as well as accuracy in motor execution, is required to maximize expected gain under risk. In this study, we tested whether humans are able to update their motor planning. Participants performed a coincident timing task with an asymmetric gain function, in which optimal response timing to gain the highest total score depends on response variability. Their behaviours were then compared using a Bayesian optimal decision model. After 9 days of practicing 2250 trials, the total score increased, and temporal variance decreased. On the other hand, the participants showed consistent risk-seeking or risk-averse behaviour, preserving suboptimal motor planning. These results suggest that a human's computational ability to calculate an optimal motor plan is limited, and it is difficult to improve it through repeated practice with a score feedback.

Motor planning under temporal uncertainty is suboptimal when the gain function is asymmetric.

For optimal action planning, the gain/loss associated with actions and the variability in motor output should both be considered. A number of studies make conflicting claims about the optimality of human action planning but cannot be reconciled due to their use of different movements and gain/loss functions. The disagreement is possibly because of differences in the experimental design and differences in the energetic cost of participant motor effort. We used a coincident timing task, which requires decision making with constant energetic cost, to test the optimality of participant's timing strategies under four configurations of the gain function. We compared participant strategies to an optimal timing strategy calculated from a Bayesian model that maximizes the expected gain. We found suboptimal timing strategies under two configurations of the gain function characterized by asymmetry, in which higher gain is associated with higher risk of zero gain. Participants showed a risk-seeking strategy by responding closer than optimal to the time of onset/offset of zero gain. Meanwhile, there was good agreement of the model with actual performance under two configurations of the gain function characterized by symmetry. Our findings show that human ability to make decisions that must reflect uncertainty in one's own motor output has limits that depend on the configuration of the gain function.