Computational Accounts of Decision-Making PDF

11 January 2024 12:01 Main Ideas Notes Types of errors in perceptual decisions ○ Signal detection theory refers to four possible outcomes of a decision as: Notes Notes Quantifying sensitivity and criterion Using signal detection theory means we can measure features of internal distribution directly...

11 January 2024 12:01 Main Ideas Notes Types of errors in perceptual decisions ○ Signal detection theory refers to four possible outcomes of a decision as: Notes Notes Quantifying sensitivity and criterion Using signal detection theory means we can measure features of internal distribution directly from behaviour ○ ▪ Hits ▪ False alarms ▪ Misses ▪ Correct rejection Roc analysis An ROC is a plot of hit vs. false alarm rates obtained at different values of the criterion Simple model of origins of errors ○ Criterion point (c) = threshold ▪ The line between detecting something and not detecting something ○ Even when the stimulus is constant, the internal sensory signal (e.g. firing rate) is variable, and a criterion needs to be applied ○ Sometimes the observer reports “seen” and sometimes “unseen”, for the same stimulus Drift diffusio Uses b Can ac ○ dprime = also distance between gaussian distributions ○ dprime measures signal or noise ratio how good system is from distinguishing signal and noise ○ Model known as the signal detection theory ○ Criteria can be different (i.e., setting a liberal criteria) but d' remains the same ▪ This means don't need much evidence to say signal is present ▪ But will get false alarms depending on criteria ▪ Might miss hits based on criteria The area under the ROC is proportional to d' ▪ Signal detection theory (SDT) ○ ▪ Therefore should measure dprime ○ Negative values of the criterion means that the response is more “liberal” (more likely to say yes), positive values means the response is more “conservative” (more likely to say no) Likelihood ratio ○ The heights of the distributions at each level of evidence are known as the “likelihoods” Deciding the Deliber A stopp Similar How should we set the criterion? Depends on whether you want avoid misses (take a more liberal approach) or whether you want to avoid false alarms (take a more conservative) Non-perceptual factors may affect a subject's tendency to say "seen" or "unseen" Example of liberal criteria Can fit Capture Relating LIP When t a digit-d Attractor ne Attracto a drift r Biases due Criterio Integrating samples over time SDT theory is used with one sample Using the sequential probability ratio test How are rew ** monkey ra A blue On trial criterion ○ Starting Green and Swets (1966) derived the optimal position of the criterion (in units of likelihood ratio) for different prior proba bilities of signal/noise, and values/costs of making different responses: Log likelihood ratio ○ specifies where we should switch from one decision to the other (at zero in the unbiased case) Empirical evidence for integration Neural data suggest brain is accumulating data from a threshold from which a decision is made Biases due People Parieta Speed-accu Type o The dri Summary Key Concepts and Definitions Signal Detection Theory (SDT): ▪ A statistical approach to quantify the ability to differentiate between signal (true events) and noise (false alarms). ▪ SDT is crucial in understanding how noise influences perceptual response errors and allows for the separation of the observer's sensitivity from their decision criterion. Drift Diffusion Model (DDM): ▪ A model that represents a decision-making process as the accumulation of evidence over time, subject to random fluctuations (‘noise’). ▪ The process continues until enough evidence has been gathered to cross a threshold, leading to a decision. ▪ Unlike SDT, DDM can also predict response times, providing a comprehensive framework for modelling how context influences the speed and accuracy of decisions. Criterion: ▪ In the context of SDT, the criterion is a threshold that determines how much evidence is required before a decision is made. ▪ It can be adjusted based on strategic factors, such as the relative costs associated with different types of responses. Sequential Probability Ratio Test (SPRT): ▪ An extension of SDT for integrating multiple samples. ▪ It's a statistical procedure used for decision-making that evaluates evidence as it accumulates. Urgency Signal: ▪ In decision-making processes, particularly under time pressure, urgency signals are hypothesized to increase the starting point and/or drift rate of evidence accumulation, emphasizing speed over accuracy. Real-Time Industry Examples Medical Diagnosis: In contexts like X-ray or MRI analysis, doctors often use principles akin to SDT and DDM. They must decide whether an anomaly is present (signal) or absent (noise), and the decision must be made efficiently and accurately to ensure patient health and optimal use of resources. Military Operations: Decision-making in military operations often resembles the scenarios modelled by SDT and DDM. Commanders need to differentiate between threats and non-threats and make rapid decisions, often based on incomplete or noisy information. Case Studies a. Use of DDM in Understanding Perceptual Decision-Making Tasks: i. The drift-diffusion model provides an excellent fit for behavior in perceptual decision-making tasks. It captures the influence of evidence strength on both accuracy and response times, as detailed in studies by Gold & Shadlen (2007). b. Influence of Reward and History Biases on Evidence Accumulation: i. Studies like those by Rorie et al. (2010) in PLoS Computational Biology explore how reward biases and history biases (such as previous experience or memory) influence the process of evidence accumulation and decision-making. Statistics The document includes various statistical analyses and visual representations (graphs, charts) to illustrate the behavior of SDT and DDM in different scenarios. For example, it discusses how the drift-diffusion model provides a good fit for behavior in perceptual decision-making tasks, highlighting the relationship between motion strength, accuracy, and mean response time. Hypothetical Scenarios and Analogies a. Buridan's Ass Dilemma in Decision-Making: The dilemma illustrates the decision paralysis that occurs when faced with two equally valuable options. This analogy can be related to the need for a stopping rule in decision-making Summary models, signifying the point at which enough evidence has been gathered to make a choice. Signal detection theory (SDT) provides a principled framework for understanding how noise leads to perceptual response errors SDT allows separation of the sensitivity (d’) of the observer from the criterion for responding Criteria may be adjusted based on strategic factors (e.g. relative costs associated with each response type) SDT can be extended out to integration of multiple samples; this is the serial probability ratio test (SPRT) The drift-diffusion model is a general framework for modelling how context affects the speed and accuracy of the decision process Reward and history biases modulate evidence accumulation; memory biases are mediated by posterior parietal cortex (at least in rodents) Emphasising speed over accuracy can be achieved by adding an “urgency signal” to the starting point and/or drift rate PSYC0032 The Brain in Action Page 1 Notes e threshold ration is costly - so need a rule that tells you when to stop ping rule quantifies when you have enough evidence to SDT criterion but rule for integration over time on model bounds ○ Bound height controls speed-accuracy trade-offs How is the criterion/bound set? These urgency signals are themselves under "top-down" control People with greater change in pre-SMA activation also show the greatest changes in response caution when given “accuracy” vs. “speed” instructions Key Points: Signal Detection Theory (SDT) Four possible outcomes: hits, false alarms, misses, and correct rejections. Different error types result in various real-world consequences. Performance limitations can be characterized by assessing false alarms and misses. Perceptual Decision-Making Involves decision-making based on sensory stimuli and internal perceptions of signal presence. Asymmetric costs are associated with different kinds of decision errors. ccount for response times unlike SDT Drift-Diffusion Model (DDM) Integrates evidence from sensory information over time. Accuracy and response times are influenced by the strength of evidence. The model fits well to behavior in perceptual decision-making tasks. to behaviour in perceptual decision-making tasks es influence of evidence strength both accuracy and response times P activity to the DDM the firing rates are aligned to the eye movement response, they reach a common level - similar to hitting a bound in diffusion model etworks or networks also show “diffusion-to-bound” behaviour - but driven by emergent dynamics rather than computation of rate (cf. Sherringtonian vs. Hopfieldian views) to rewards or memory on shifts if one category becomes more valuable or probable ward biases implemented? andom dot motion task target indicates a low magnitude reward, whereas a red target indicates a high magnitude reward ls where one option is more rewarding than the other, the monkey shifts his psychometric function (moves his n) in the direction of the rewarded target (note sensitivity - the slope of the function - remains unchanged) Likelihood Ratios Ratio of probabilities for signal-presence vs. absence. Used in decision-making to determine the presence of signals based on evidence. Sensitivity and Criterion in SDT Sensitivity (d'): Measure of signal-to-noise ratio or perceptual sensitivity. Criterion: The threshold set by the observer that affects decision outcomes (liberal vs. conservative responses). Notes 1. SDT and X-Ray Diagnosis: Signal Detection Theory (SDT) is a psychological theory used to explain and quantify how decisions are made under conditions of uncertainty. The fundamental assumption of SDT is that decision-making involves a sensory signal that is embedded in noise. The theory posits that when a decision-maker tries to detect a signal (e.g., a tumour in an x-ray), they must distinguish it from the noise (normal x-ray patterns). The decision is influenced by the 'sensitivity' of the observer to the signal and their 'criterion' or threshold for deciding that a signal is present. 2. Errors in Perceptual Decisions: This concept extends SDT to various contexts, highlighting that decisions often involve interpreting uncertain or ambiguous information. The logic here is that all perceptual decisions are prone to errors due to the presence of noise, and the type of error (false alarm vs miss) depends on the observer's criterion. 3. Asymmetric Costs in Decision Making: This concept recognizes that different types of decision errors have different consequences or costs. The theory assumes that decision-makers are aware of these costs and adjust their decision criteria accordingly to minimize the overall cost or maximize utility. 4. Signal Detection Theory (SDT): SDT distinguishes between an observer's ability to discern between signal and noise ('sensitivity') and their willingness to report observing a signal ('criterion'). The theory assumes that both signal and noise are random variables and that the observer's task is to decide whether a given observation is due to a signal or just noise. 5. Dice Game Example: This analogy is used to simplify the concept of detecting a signal in the presence of noise. The 'world state' represents the true condition (signal present or absent), while the 'noise' represents the random variation that obscures the signal. The sum of dice rolls is an analogy for the decision-making process, where the total score represents the accumulated evidence. 6. Random Dot Motion Task: This experimental task is used to study decision-making under uncertainty. It assumes that subjects can integrate sensory information over time to make a decision. The task demonstrates how evidence accumulates and influences decision-making. Sequential Probability Ratio Test (SPRT) Uses the running sum of likelihood ratios for making static or sequential decisions. 7. Integrating Likelihoods Over Time: This concept is based on the principle that multiple independent pieces of evidence can be combined to strengthen the overall decision. It follows the logic that independent, but concordant, evidence should increase the confidence in a decision. Posterior Parietal Cortex and Sensory History Important for representing and utilizing prior stimulus information in decision-making. Associated with working memory and the processing of sensory-stimulus history. 8. Sequential Probability Ratio Test (SPRT): SPRT is a statistical method used to make decisions by continuously monitoring evidence rather than setting a fixed sample size. The logic is that by accumulating evidence until a threshold is reached, one can make more efficient and quicker decisions. Neural and Computational Aspects of Decision -Making Attractor networks potentially exhibit "diffusion-to-bound" behavior without computing a drift rate. Memory biases can influence perceptual decisions, with memory of sA affecting current evidence interpretation. Biases due to Rewards or Memory Reward biases can be implemented by shifting the psychometric function or the starting point of evidence accumulation. Memory biases manifest as behavioral biases when laboratory experiments are designed to have independent trials. 9. Lateral Intraparietal (LIP) Area Studies: These studies explore how the brain accumulates evidence for decisionmaking. The assumption is that neurons in the LIP area represent the accumulation of evidence in favor of a particular decision, and that this process is crucial for making accurate decisions. 10. Stopping Rule (or Threshold): This concept is about deciding when enough evidence has been collected to make a decision, especially in scenarios where continued deliberation is costly. The logic is that there is a trade-off between the accuracy of a decision and the cost of time and resources spent in making it. 11. Drift Diffusion Model (DDM): DDM is a mathematical model of decision-making that describes how evidence accumulates over time until it reaches a boundary, leading to a decision. It assumes that the accumulation of evidence is subject to random fluctuations (noise), and the time taken to reach a decision (response time) is a crucial part of the decision-making process. g point evidence accumulation is increased for the more rewarded response to memory are influenced when making perceptual decisions al cortex inactivation makes rodents better - because history biases are eliminated uracy tradeoffs f contextual bias that affect overall accuracy and response time (rather than biasing us towards one or other option) ift diffusion model provides framework for think about how these modulation of decision process occur 12. Attractor Networks: This concept in neuroscience suggests that certain networks of neurons can settle into stable patterns (attractors) that represent specific decisions or cognitive states. The theory posits that decision-making can emerge from the dynamics of neural networks rather than just from the linear accumulation of evidence. 13. Speed-Accuracy Tradeoffs: This principle states that decision-making typically involves a trade-off between making fast decisions and making accurate decisions. The logic is that faster decisions are generally less accurate because there is less time to accumulate evidence, and vice versa. 14. Setting the Criterion/Bound: This concept involves adjusting the threshold for making a decision based on the context, such as the need for speed or accuracy. It assumes that decision-makers can strategically manipulate their decision criteria based on their goals or the demands of the situation. PSYC0032 The Brain in Action Page 2 Notes PSYC0032 The Brain in Action Page 3 Notes Notes PSYC0032 The Brain in Action Page 4 PSYC0032 The Brain in Action Page 5