ABSTRACT: Humans anticipate events signaled by sensory cues. It is commonly assumed that two uncertainty parameters modulate the brain's capacity to predict: the hazard rate (HR) of event probability and the uncertainty in time estimation which increases with elapsed time. We investigate both assumptions by presenting event probability density functions (PDFs) in each of three sensory modalities. We show that perceptual systems use the reciprocal PDF and not the HR to model event probability density. We also demonstrate that temporal uncertainty does not necessarily grow with elapsed time but can also diminish, depending on the event PDF. Previous research identified neuronal activity related to event probability in multiple levels of the cortical hierarchy (sensory (V4), association (LIP), motor and other areas) proposing the HR as an elementary neuronal computation. Our results-consistent across vision, audition, and somatosensation-suggest that the neurobiological implementation of event anticipation is based on a different, simpler and more stable computation than HR: the reciprocal PDF of events in time.
Project description:The environment is shaped by two sources of temporal uncertainty: the discrete probability of whether an event will occur and-if it does-the continuous probability of when it will happen. These two types of uncertainty are fundamental to every form of anticipatory behavior including learning, decision-making, and motor planning. It remains unknown how the brain models the two uncertainty parameters and how they interact in anticipation. It is commonly assumed that the discrete probability of whether an event will occur has a fixed effect on event expectancy over time. In contrast, we first demonstrate that this pattern is highly dynamic and monotonically increases across time. Intriguingly, this behavior is independent of the continuous probability of when an event will occur. The effect of this continuous probability on anticipation is commonly proposed to be driven by the hazard rate (HR) of events. We next show that the HR fails to account for behavior and propose a model of event expectancy based on the probability density function of events. Our results hold for both vision and audition, suggesting independence of the representation of the two uncertainties from sensory input modality. These findings enrich the understanding of fundamental anticipatory processes and have provocative implications for many aspects of behavior and its neural underpinnings.
Project description:To prepare for an impending event of unknown temporal distribution, humans internally increase the perceived probability of event onset as time elapses. This effect is termed the hazard rate of events. We tested how the neural encoding of hazard rate changes by providing human participants with prior information on temporal event probability. We recorded behavioral and electroencephalographic (EEG) data while participants listened to continuously repeating five-tone sequences, composed of four standard tones followed by a non-target deviant tone, delivered at slow (1.6 Hz) or fast (4 Hz) rates. The task was to detect a rare target tone, which equiprobably appeared at either position two, three or four of the repeating sequence. In this design, potential target position acts as a proxy for elapsed time. For participants uninformed about the target's distribution, elapsed time to uncertain target onset increased response speed, displaying a significant hazard rate effect at both slow and fast stimulus rates. However, only in fast sequences did prior information about the target's temporal distribution interact with elapsed time, suppressing the hazard rate. Importantly, in the fast, uninformed condition pre-stimulus power synchronization in the beta band (Beta 1, 15-19 Hz) predicted the hazard rate of response times. Prior information suppressed pre-stimulus power synchronization in the same band, while still significantly predicting response times. We conclude that Beta 1 power does not simply encode the hazard rate, but-more generally-internal estimates of temporal event probability based upon contextual information.
Project description:We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems from a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the "next-best" data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach uses Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds using the posterior distribution of the inferred map. The next-best design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process uses only information from the inferred map, it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size and for problems where each sample is very expensive to obtain. We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: an offshore platform subjected to 3D irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using a limited number of samples.
Project description:Perceptual organization is the process of grouping scene elements into whole entities. A classic example is contour integration, in which separate line segments are perceived as continuous contours. Uncertainty in such grouping arises from scene ambiguity and sensory noise. Some classic Gestalt principles of contour integration, and more broadly, of perceptual organization, have been re-framed in terms of Bayesian inference, whereby the observer computes the probability that the whole entity is present. Previous studies that proposed a Bayesian interpretation of perceptual organization, however, have ignored sensory uncertainty, despite the fact that accounting for the current level of perceptual uncertainty is one of the main signatures of Bayesian decision making. Crucially, trial-by-trial manipulation of sensory uncertainty is a key test to whether humans perform near-optimal Bayesian inference in contour integration, as opposed to using some manifestly non-Bayesian heuristic. We distinguish between these hypotheses in a simplified form of contour integration, namely judging whether two line segments separated by an occluder are collinear. We manipulate sensory uncertainty by varying retinal eccentricity. A Bayes-optimal observer would take the level of sensory uncertainty into account-in a very specific way-in deciding whether a measured offset between the line segments is due to non-collinearity or to sensory noise. We find that people deviate slightly but systematically from Bayesian optimality, while still performing "probabilistic computation" in the sense that they take into account sensory uncertainty via a heuristic rule. Our work contributes to an understanding of the role of sensory uncertainty in higher-order perception.
Project description:In the immediate aftermath of a strong earthquake and in the presence of an ongoing aftershock sequence, scientific advisories in terms of seismicity forecasts play quite a crucial role in emergency decision-making and risk mitigation. Epidemic Type Aftershock Sequence (ETAS) models are frequently used for forecasting the spatio-temporal evolution of seismicity in the short-term. We propose robust forecasting of seismicity based on ETAS model, by exploiting the link between Bayesian inference and Markov Chain Monte Carlo Simulation. The methodology considers the uncertainty not only in the model parameters, conditioned on the available catalogue of events occurred before the forecasting interval, but also the uncertainty in the sequence of events that are going to happen during the forecasting interval. We demonstrate the methodology by retrospective early forecasting of seismicity associated with the 2016 Amatrice seismic sequence activities in central Italy. We provide robust spatio-temporal short-term seismicity forecasts with various time intervals in the first few days elapsed after each of the three main events within the sequence, which can predict the seismicity within plus/minus two standard deviations from the mean estimate within the few hours elapsed after the main event.
Project description:Reinforcement learning causes an action that yields a positive outcome more likely to be taken in the future. Here, we investigate how the time elapsed from an action affects subsequent decisions. Groups of C57BL6/J mice were housed in IntelliCages with access to water and chow ad libitum; they also had access to bottles with a reward: saccharin solution, alcohol, or a mixture of the two. The probability of receiving a reward in two of the cage corners changed between 0.9 and 0.3 every 48 hr over a period of ~33 days. As expected, in most animals, the odds of repeating a corner choice were increased if that choice was previously rewarded. Interestingly, the time elapsed from the previous choice also influenced the probability of repeating the choice, and this effect was independent of previous outcome. Behavioral data were fitted to a series of reinforcement learning models. Best fits were achieved when the reward prediction update was coupled with separate learning rates from positive and negative outcomes and additionally a "fictitious" update of the expected value of the nonselected choice. Additional inclusion of a time-dependent decay of the expected values improved the fit marginally in some cases.
Project description:Bayesian theories of neural coding propose that sensory uncertainty is represented by a probability distribution encoded in neural population activity, but direct neural evidence supporting this hypothesis is currently lacking. Using fMRI in combination with a generative model-based analysis, we found that probability distributions reflecting sensory uncertainty could reliably be estimated from human visual cortex and, moreover, that observers appeared to use knowledge of this uncertainty in their perceptual decisions.
Project description:The pharmacokinetic parameters derived from dynamic contrast-enhanced (DCE) MRI have been used in more than 100 phase I trials and investigator led studies. A comparison of the absolute values of these quantities requires an estimation of their respective probability distribution function (PDF). The statistical variation of the DCE-MRI measurement is analyzed by considering the fundamental sources of error in the MR signal intensity acquired with the spoiled gradient-echo (SPGR) pulse sequence.The variance in the SPGR signal intensity arises from quadrature detection and excitation flip angle inconsistency. The noise power was measured in 11 phantoms of contrast agent concentration in the range [0-1] mM (in steps of 0.1 mM) and in onein vivo acquisition of a tumor-bearing mouse. The distribution of the flip angle was determined in a uniform 10 mM CuSO4 phantom using the spin echo double angle method. The PDF of a wide range of T1 values measured with the varying flip angle (VFA) technique was estimated through numerical simulations of the SPGR equation. The resultant uncertainty in contrast agent concentration was incorporated in the most common model of tracer exchange kinetics and the PDF of the derived pharmacokinetic parameters was studied numerically.The VFA method is an unbiased technique for measuringT1 only in the absence of bias in excitation flip angle. The time-dependent concentration of the contrast agent measured in vivo is within the theoretically predicted uncertainty. The uncertainty in measuring K(trans) with SPGR pulse sequences is of the same order, but always higher than, the uncertainty in measuring the pre-injection longitudinal relaxation time (T10). The lowest achievable bias/uncertainty in estimating this parameter is approximately 20%-70% higher than the bias/uncertainty in the measurement of the pre-injection T1 map. The fractional volume parameters derived from the extended Tofts model were found to be extremely sensitive to the variance in signal intensity. The SNR of the pre-injection T1 map indicates the limiting precision with which K(trans) can be calculated.Current small-animal imaging systems and pulse sequences robust to motion artifacts have the capacity for reproducible quantitative acquisitions with DCE-MRI. In these circumstances, it is feasible to achieve a level of precision limited only by physiologic variability.
Project description:Circadian clocks generate 24-hr rhythms in physiology and behavior. Despite numerous studies, it is still uncertain how circadian rhythms emerge from their molecular and neural constituents. Here, we demonstrate a tight connection between the molecular and neuronal circadian networks. Using fluorescent transcriptional reporters in a Drosophila ex vivo brain culture system, we identified a reciprocal negative regulation between the master circadian regulator CLK and expression of pdf, the main circadian neuropeptide. We show that PDF feedback is required for maintaining normal oscillation pattern in CLK-driven transcription. Interestingly, we found that CLK and neuronal firing suppresses pdf transcription, likely through a common pathway involving the transcription factors DHR38 and SR, establishing a direct link between electric activity and the circadian system. In sum, our work provides evidence for the existence of an uncharacterized CLK-PDF feedback loop that tightly wraps together the molecular oscillator with the circadian neuronal network in Drosophila.
Project description:Cortical computation is distributed across multiple areas of the cortex by networks of reciprocal connectivity. However, how such connectivity contributes to the communication between the connected areas is not clear. In this study, we examine the communication between sensory and motor cortices. We develop an eye movement task in mice and combine it with optogenetic suppression and two-photon calcium imaging techniques. We identify a small region in the secondary motor cortex (MOs) that controls eye movements and reciprocally connects with a rostrolateral part of the higher visual areas (VRL/A/AL). These two regions encode both motor signals and visual information; however, the information flow between the regions depends on the direction of the connectivity: motor information is conveyed preferentially from the MOs to the VRL/A/AL, and sensory information is transferred primarily in the opposite direction. We propose that reciprocal connectivity streamlines information flow, enhancing the computational capacity of a distributed network.