scholarly journals Analyzing the misperception of exponential growth in graphs.

2021 ◽  
Author(s):  
Lorenzo Ciccione ◽  
Mathias Sablé-Meyer ◽  
Stanislas Dehaene
Keyword(s):  
Exponential Growth ◽  
Social Cost ◽  
Noisy Data ◽  
Ideal Observer ◽  
Logarithmic Scale ◽  
Linear Extrapolation ◽  
Exponential Curve ◽  
Response Modality ◽  
Observer Model ◽  
Human Capacity

Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants’ math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.

Object Detection Using an Ideal Observer Model

2020 ◽  
Vol 2020 (16) ◽  
pp. 41-1-41-7
Author(s):  
Orit Skorka ◽  
Paul J. Kane
Keyword(s):  
Object Detection ◽  
Matched Filter ◽  
Image Sensors ◽  
Ideal Observer ◽  
Noise Power ◽  
Relative Evaluation ◽  
Detection And Identification ◽  
Cross Correlation Analysis ◽  
Observer Model ◽  
The Ideal

Many of the metrics developed for informational imaging are useful in automotive imaging, since many of the tasks – for example, object detection and identification – are similar. This work discusses sensor characterization parameters for the Ideal Observer SNR model, and elaborates on the noise power spectrum. It presents cross-correlation analysis results for matched-filter detection of a tribar pattern in sets of resolution target images that were captured with three image sensors over a range of illumination levels. Lastly, the work compares the crosscorrelation data to predictions made by the Ideal Observer Model and demonstrates good agreement between the two methods on relative evaluation of detection capabilities.

scholarly journals How Optimal is Word-Referent Identification Under Multimodal Uncertainty?

2018 ◽  
Author(s):  
Abdellah Fourtassi ◽  
Michael C. Frank
Keyword(s):  
Visual Cues ◽  
Word Meaning ◽  
Spoken Word ◽  
Ideal Observer ◽  
Optimal Model ◽  
Sources Of Uncertainty ◽  
Multimodal Information ◽  
Model Predictions ◽  
Observer Model ◽  
Novel Words

Identifying a spoken word in a referential context requires both the ability to integrate multimodal input and the ability to reason under uncertainty. How do these tasks interact with one another? We study how adults identify novel words under joint uncertainty in the auditory and visual modalities and we propose an ideal observer model of how cues in these modalities are combined optimally. Model predictions are tested in four experiments where recognition is made under various sources of uncertainty. We found that participants use both auditory and visual cues to recognize novel words. When the signal is not distorted with environmental noise, participants weight the auditory and visual cues optimally, that is, according to the relative reliability of each modality. In contrast, when one modality has noise added to it, human perceivers systematically prefer the unperturbed modality to a greater extent than the optimal model does. This work extends the literature on perceptual cue combination to the case of word recognition in a referential context. In addition, this context offers a link to the study of multimodal information in word meaning learning.

scholarly journals Evidence accumulation and change rate inference in dynamic environments

2016 ◽  
Author(s):  
Adrian E Radillo ◽  
Alan Veliz-Cuba ◽  
Kresimir Josic ◽  
Zachary Kilpatrick
Keyword(s):  
Rate Of Change ◽  
Ideal Observer ◽  
Moment Closure ◽  
Dimensional System ◽  
Change Rate ◽  
Observer Model ◽  
Low Dimensional ◽  
State Of The Environment ◽  
Rate Correlation ◽  
Moment Closure Approximation

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an ideal observer model capable of inferring the present state of the environment along with its rate of change. Key to this computation is updating the posterior probability of all possible changepoint counts. This computation can be challenging, as the number of possibilities grows rapidly with time. However, we show how the computations can be simplified in the continuum limit by a moment closure approximation. The resulting low-dimensional system can be used to infer the environmental state and change rate with accuracy comparable to the ideal observer. The approximate computations can be performed by a neural network model via a rate-correlation based plasticity rule. We thus show how optimal observers accumulates evidence in changing environments, and map this computation to reduced models which perform inference using plausible neural mechanisms.

Mr. Chips: An ideal-observer model of reading.

1997 ◽  
Vol 104 (3) ◽  
pp. 524-553 ◽  
Author(s):  
Gordon E. Legge ◽  
Timothy S. Klitz ◽  
Bosco S. Tjan
Keyword(s):  
Ideal Observer ◽  
Observer Model

Comparisons of thresholds for carcinogenicity on linear and logarithmic dosage scales

2005 ◽  
Vol 24 (6) ◽  
pp. 325-332 ◽  
Author(s):  
William J Waddell
Keyword(s):  
Dose Response ◽  
Mouse Liver ◽  
Goodness Of Fit ◽  
Ethyl Carbamate ◽  
Logarithmic Scale ◽  
Linear Extrapolation ◽  
Human Haemoglobin ◽  
High Background ◽  
Dose Responses ◽  
Comparative Information

Comparisons on a linear and the Rozman logarithmic scale for dosage versus carcinogenicity in rodents are presented for methyl eugenol (ME), nitrosodiethylamine (NDEA), ethyl carbamate (EC) and 2-acetylaminofluorene (AAF). Each of these chemicals has been shown to be carcinogenic in experimental animals and, in addition, humans are regularly exposed to at least three of these compounds (ME, NDEA, EC) in foods. Although the source of adducts from AAF is not known, the aminofluorene (AF) adduct is present in humans. Plotted on the same graphs are either some doses from common foods (ME, NDEA, EC) or adducts (AF) on human haemoglobin, for perspective, with their thresholds for carcinogenesis in animals. Use of a linear scale when comparing doses administered to animals in studies of carcinogenicity with doses of those same chemicals to which humans are exposed does not provide useful, comparative information. On the other hand, the Rozman logarithmic scale for dose allows one to put these relative doses in perspective. It is also evident that forcing a linear extrapolation through the zero, zero origin does not agree with the experimental data. Further analyses for goodness of fit for these dose responses reveal that the dose response for three of these compounds (ME, NDEA, EC) appears to be linear with the logarithm of the dose. However, AAF appears to be linear with the logarithm of the dose for bladder, but not for liver. It is suggested that the high background incidence of tumours in the BALB/c StCrlfC3Hf/Nctr mouse liver may confound the interpretation of dose response from AAF carcinogenesis in mouse liver.

scholarly journals Surprise About Sensory Event Timing Drives Cortical Transients in the Beta Frequency Band

2018 ◽  
Author(s):  
T. Meindertsma ◽  
N.A. Kloosterman ◽  
A.K. Engel ◽  
E.J. Wagenmakers ◽  
T.H. Donner
Keyword(s):  
Frequency Band ◽  
Ideal Observer ◽  
Beta Band ◽  
Statistical Structure ◽  
Population Activity ◽  
Sensory Event ◽  
Event Timing ◽  
Beta Frequency Band ◽  
Observer Model ◽  
Beta Frequency

AbstractLearning the statistical structure of the environment is crucial for adaptive behavior. Humans and non-human decision-makers seem to track such structure through a process of probabilistic inference, which enables predictions about behaviorally relevant events. Deviations from such predictions cause surprise, which in turn helps improve inference. Surprise about the timing of behaviorally relevant sensory events drives phasic responses of neuromodulatory brainstem systems, which project to the cerebral cortex. Here, we developed a computational model-based magnetoencephalography (MEG) approach for mapping the resulting cortical transients across space, time, and frequency, in the human brain (N=28, 17 female). We used a Bayesian ideal observer model to learn the statistics of the timing of changes in a simple visual detection task. This model yielded quantitative trial-by-trial estimates of temporal surprise. The model-based surprise variable predicted trial-by trial variations in reaction time more strongly than the externally observable interval timings alone. Trial-by-trial variations in surprise were negatively correlated with the power of cortical population activity measured with MEG. This surprise-related power suppression occurred transiently around the behavioral response, specifically in the beta frequency band. It peaked in parietal and prefrontal cortices, remote from the motor cortical suppression of beta power related to overt report (button press) of change detection. Our results indicate that surprise about sensory event timing transiently suppresses ongoing beta-band oscillations in association cortex. This transient suppression of frontal beta-band oscillations might reflect an active reset triggered by surprise, and is in line with the idea that beta-oscillations help maintain cognitive sets.Significance statementThe brain continuously tracks the statistical structure of the environment to anticipate behaviorally relevant events. Deviations from such predictions cause surprise, which in turn drives neural activity in subcortical brain regions that project to the cerebral cortex. We used magnetoencephalography in humans to map out surprise-related modulations of cortical population activity across space, time, and frequency. Surprise was elicited by variable timing of visual stimulus changes requiring a behavioral response. Surprise was quantified by means of an ideal observer model. Surprise predicted behavior as well as a transient suppression of beta frequency band oscillations in frontal cortical regions. Our results are in line with conceptual accounts that have linked neural oscillations in the beta-band to the maintenance of cognitive sets.

scholarly journals Touch as an auxiliary proprioceptive cue for movement control

2019 ◽  
Vol 5 (6) ◽  
pp. eaaw3121 ◽  
Author(s):  
A. Moscatelli ◽  
M. Bianchi ◽  
S. Ciotti ◽  
G. C. Bettelani ◽  
C. V. Parise ◽  
...  
Keyword(s):  
Visual Feedback ◽  
Movement Control ◽  
External World ◽  
Ideal Observer ◽  
Proprioceptive Feedback ◽  
Systematic Deviation ◽  
Classical View ◽  
Observer Model ◽  
Perceptual Phenomenon

Recent studies extended the classical view that touch is mainly devoted to the perception of the external world. Perceptual tasks where the hand was stationary demonstrated that cutaneous stimuli from contact with objects provide the illusion of hand displacement. Here, we tested the hypothesis that touch provides auxiliary proprioceptive feedback for guiding actions. We used a well-established perceptual phenomenon to dissociate the estimates of reaching direction from touch and musculoskeletal proprioception. Participants slid their fingertip on a ridged plate to move toward a target without any visual feedback on hand location. Tactile motion estimates were biased by ridge orientation, inducing a systematic deviation in hand trajectories in accordance with our hypothesis. Results are in agreement with an ideal observer model, where motion estimates from different somatosensory cues are optimally integrated for the control of movement. These outcomes shed new light on the interplay between proprioception and touch in active tasks.

Comparing Classification Performance of Mueller Matrix Parameters for Diffuse Materials

2020 ◽  
Vol 2020 (14) ◽  
pp. 263-1-263-7
Author(s):  
Lisa W Li ◽  
Meredith Kupinski ◽  
Madellyn Brown ◽  
Russell Chipman
Keyword(s):  
Operating Characteristic ◽  
Mueller Matrix ◽  
Classification Performance ◽  
Ideal Observer ◽  
Ensemble Average ◽  
Matrix Elements ◽  
Polarization Imaging ◽  
Full Field ◽  
Irradiance Data ◽  
Observer Model

This work compares the material classification performance of Mueller matrix polarization imaging to RGB imaging. White painted wood and white fabric samples are selected to create a classification task that is challenging for RGB imaging. A Mueller Matrix Imaging Polarimeter with a 30° full field of view is used to capture the Mueller Matrix images at nominal red, green, and blue wavelengths across multiple specular scatter angles. A Bayesian ideal observer model is used to evaluate classification performance. Performance is quantified by the Area under (AUC) the Receiver Operating Characteristic (ROC) curve. An AUC = 1 is perfect detection and AUC = 0.5 is the performance of guessing. The ensemble average AUC does not exceed 0.70 for RGB irradiance data. The ensemble average AUC for all 16 individual Mueller elements is greater than 0.95. Various combinations of Mueller matrix elements are also tested. Elements related to diattenuation and polarizance are nearly perfect classifiers for large scatter angles but the AUC minimum is 0.60 at 20°. Depolarization index is the highest performing parameter out of all tested polarization parameters for scatter angles ≥70° where AUC ≥0.98.

scholarly journals Optimality and Saturation in Axonal Chemotaxis

2013 ◽  
Vol 25 (4) ◽  
pp. 833-853 ◽  
Author(s):  
Jiajia Yuan ◽  
Stanley Chan ◽  
Duncan Mortimer ◽  
Huyen Nguyen ◽  
Geoffrey J. Goodhill
Keyword(s):  
Growth Cones ◽  
Quantitative Information ◽  
Ideal Observer ◽  
Response Mechanism ◽  
Neuronal Growth ◽  
Biological Mechanisms ◽  
Chemical Gradients ◽  
Observer Model ◽  
Neuronal Growth Cones ◽  
Insight Into

Chemotaxis (detecting and following chemical gradients) plays a crucial role in the function of many biological systems. In particular, gradient following by neuronal growth cones is important for the correct wiring of the nervous system. There is increasing interest in the constraints that determine how small chemotacting devices respond to gradients, but little quantitative information is available in this regard for neuronal growth cones. Mortimer et al. ( 2009 ) and Mortimer, Dayan, Burrage, and Goodhill ( 2011 ) proposed a Bayesian ideal observer model that predicts chemotactic performance for shallow gradients. Here we investigated two important aspects of this model. First, we found by numerical simulation that although the analytical predictions of the model assume shallow gradients, these predictions remain remarkably robust to large deviations in gradient steepness. Second, we found experimentally that the chemotactic response increased linearly with gradient steepness for very shallow gradients as predicted by the model; however, the response saturated for steeper gradients. This saturation could be reproduced in simulations of a growth rate modulation response mechanism. Together these results illuminate the domain of validity of the Bayesian model and give further insight into the biological mechanisms of axonal chemotaxis.

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