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Peter Killeen

Arizona State University, Psychology, Post-Doc

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Interested in ontologies, epistemologies, and models. I write on time, motivation, learning, schedules of reinforcement, ADHD, hypnosis, statistics, and discount functions. Recent interest in tobacco addiction.
Supervisors: David Hestenes, BF Skinner, Howard Rachlin, and Dave Cross
Address: Psychology
ASU
Tempe AZ
85287-1104

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Papers by Peter Killeen

Prospective & Retrospective Timing Fetterman & Killeen

Learning & Behavior, 2010

Pigeons discriminated between two pairs of durations: a short set (2.5 and 5 sec) and a long set ... more Pigeons discriminated between two pairs of durations: a short set (2.5 and 5 sec) and a long set (5 and 10 sec). The pairs were intermixed within sessions and identified by the colors on the signal and choice keys. Once the task was learned, the pigeons experienced the following three conditions seriatim: (1) The signal key was made ambiguous about the test change, but the choice keys were informative (retrospective); (2) the signal key identified the test range, but the choice keys did not (prospective); (3) probe trials were introduced in which the color of the center key signaled one test range, but the color of the choice keys signaled the other test range (inconsistent). Accuracy of choice decreased in the retrospective condition and, returned to baseline levels, was higher under the prospective condition than under the retrospective condition. In a final condition, referred to as conflict trials, the center-key color signified one test range and the choice-key colors the other range. The results from these conflict-inconsistent tests indicate that choice behavior was largely controlled by the signal-key color and not by the choice-key color. We relate these findings to different approaches to timing in animals.

How reinforcement context affects temporal production and categorization

Animal Learning & Behavior, 1998

The behavioral theory of timing assumes that timing is governed by a pacemaker whose pulses move ... more The behavioral theory of timing assumes that timing is governed by a pacemaker whose pulses move organisms from one state to the next, and that the speed of the pacemaker covaries with the rate of reinforcement in the experimental context. The goal of the present experiments was to clarify just what constitutes that context. In Experiment 1, pigeons responded on signaled fixed-interval20-sec and 40sec schedules offood reinforcement that were presented randomly within sessions (alternating condition) or between sessions (isolated condition). In Experiment 2, pigeons categorized the duration of a short or a long set of intervals in the alternating or the isolated condition. Performance in both experiments was under strong control by the signals, with scalar timing between long and short sets, but no significant differences between the alternating and isolated conditions. The context of reinforcement that determines pacemaker period can thus be specific to a particular timing task and signal.

Killeen, P. R., & Bizo, L. A. (1998). The mechanics of reinforcement. Psychonomic Bulletin & Review, 5, 221-238.

by Lewis Bizo and Peter Killeen

Psychonomic Bulletin & Review, 1998

Motivation, association, and response constraints are central phenomena in learning and performan... more Motivation, association, and response constraints are central phenomena in learning and performance. A recent theory of reinforcement-a mechanics of reinforcement (Killeen, 1992)-offers a formal description of these processes in terms of three principles. This paper summarizes the principles, elaborates them so as to generate clear predictions, and reports new data that bear on their evaluation. In particular, the action of the principles are represented in a behavior space, in which changes in the relation between target or operant behaviors and other activities appear as behavioral trajectories.

Bizo, L. A., Kettle, L., & Killeen, P. R. (2001). Rats don't always respond faster for more food: The paradoxical incentive effect. Animal Learning & Behavior, 29, 66-78.

by Lewis Bizo and Peter Killeen

Animal Learning & Behavior, 2001

Rats' lever-pressing was reinforced on variable-ratio schedules. As ratio values increased, respo... more Rats' lever-pressing was reinforced on variable-ratio schedules. As ratio values increased, response rates initially increased with them, then eventually decreased. In Exp 1, rates were uniformly higher with 1-pellet reinforcers than with two-pellet reinforcers—the paradoxical incentive effect. In Exp 2, rats received 1-, 2-, and 3-pellet reinforcers with counterbalanced preloads of pellets; the continued superiority of the smaller reinforcers ruled out a satiation explanation. Exp 2 introduced a 20-sec intertrial interval (ITI), and Exp 4 filled the ITI with an alternate response to test a memorial/overshadowing explanation. In Exp 5, the rats received 1 or 2 standard grain pellets or 1 sucrose pellet as reinforcers over an extended range of ratios. The diminution of the effect in Exp 3 and its reversal in Exp 4 and Exp 5 at large ratios provided evidence for overshadowing and reconciled the phenomenon with mathematical principles of reinforcement.

Sanabria, F, Acosta, J. I., Killeen, P. R., Neisewander, J. L., & Bizo, L. A. (2008). Modeling the effects of fluoxetine on food-reinforced behavior. Behavioural Pharmacology, 19, 61-70.

by Peter Killeen, Janet Neisewander, and Lewis Bizo

Behavioural Pharmacology, 2008

We propose a novel method to dissociate incentive motivation from memory and motor processes in i... more We propose a novel method to dissociate incentive motivation from memory and motor processes in instrumental performance. Components of a multiple fixed-ratio schedule of food reinforcement were adjusted to envelop the range of response requirements that maintained lever pressing by rats. We sought to manipulate motivation for food rewards with acute administrations of various doses (0–10 mg/kg) of fluoxetine, a 5-HT reuptake inhibitor that reduces food intake. A quantitative model of fixed-ratio performance derived from Killeen's (1994) Mathematical Principles of Reinforcement (MPR) provided an adequate account of data from individual rats. Decreases in response rate resulting from fluoxetine were reflected in changes in estimates of activation, indexed by MPR parameter a; estimates of working memory capacity and lever pressing duration were not systematically affected. These results support the use of MPR parameter a to index incentive motivation using multiple fixed-ratio schedules that are adjusted to individual performance.

A Ludic Appreciation of Mechner's Aesthetics

Psychological Record, 2018

We can imagine many of our emotions in our family pet: hunger, fear, anger, lust, and even the bo... more We can imagine many of our emotions in our family pet: hunger, fear, anger, lust, and even the bonding that we call love. But not
the appreciation of a sunset, sonnet, musical passage, or good joke. Mechner takes on the gamut of such aesthetic appreciations,
removed from the urgency of the primal ones, and gives us the first thorough attempt at a behavioral explication. Because he has
been so thorough and apt, my commentary can add little value to his thesis, only subtract from it. Therefore, rather than critique, I
exemplify, and then simplify. By reducing his voluminous report to two lines: a theorem and an equation, I thereby encapsulate
aesthetics in a sweet pill of spire. Aesthetic appreciation of this note may require a willing suspension of disbelief.

The non-Darwinian evolution of behavers and behaviors

Behavioral Processes, 2019

Darwinian evolution and Skinnerian psychology, have in common the vision of powerful control of t... more Darwinian evolution and Skinnerian psychology, have in common the vision of powerful control of their subjects by their sequalae. Individuals of species that generate more successful offspring come to dominate their habitat; responses of those individuals that generate more reinforcers come to dominate the repertoire of the individual in that context. This is unarguable. What is questionable is how large a role these forces of selection play in the larger landscape of existing organisms and the repertoires of their individuals. Here it is argued that non-Darwinian and non-Skinnerian selection play much larger roles in both than the reader may appreciate. The argument is based on the history of, and recent advances in, microbiology. Lessons from that history re-illuminate the three putative domains of selection by consequences: The evolution of species, response repertoires, and cultures. It is argued that before, beneath, and after the cosmically brief but crucial epoch of Darwinian evolution that shaped creatures such as ourselves, non-Darwinian forces pervade all three domains.

The Futures of EAB

Killeen, P. R. (2018). The Futures of Experimental Analysis of Behavior. Behavior Analysis: Resea... more Killeen, P. R. (2018). The Futures of Experimental Analysis of Behavior. Behavior Analysis: Research and Practice. http://dx.doi.org/10.1037/bar0000100
For 50 years Experimental Analysts of Behavior (EAB) have been riding the crests of waves raised by BF Skinner. His technical innovations and conceptual simplifications were a powerful breath of fresh air, and the large effect sizes engineered with contingencies of reinforcement
gave its practitioners confidence in their methods. The goals of EAB meanwhile went unexamined, its antimentalistic philosophy untested, and the gap between laboratory and life inevitably widened. This gap can only be bridged by renewed conversations on the fundamentals of our field, and new technologies to examine behavior that we have largely ignored. Interpretative accounts—showing that reinforcement may have played an important role in some complex or exceptional behavior—is no longer enough. To ensure a future for EAB several things must happen. We must learn that data have little value until embedded in a coherent
narrative; and the best of those are called theories. The biological EAB must reach levels up to biology/ethology/ecology; and levels down to physiology/neuroscience. The psychological EAB must recognize the value of bringing into our tool-box treatments of states such as affects and dispositions; operations such as attention, rumination, goal-setting, and reframing; and craft a better understanding of belief systems in general. The social EAB must strive to generalize basic laws formulated in open-loop controlled laboratory settings to dynamic interactive closed-loop processes with two or more interacting systems. To be successful these endeavors require respect for other approaches to these phenomena, and collaborations with scientists who know more about them than we yet do.

The_Modulated_Contingency_Killeen&Jacobs_tBA_(2017).pdf

Killeen, P. R., & Jacobs, K. W. (2017). The modulated contingency. The Behavior Analyst, 1-20. do... more

Killeen VITÆ.docx

my CV thru 2018

Models of Ratio Schedule Performance

Predictions of Killeen's (1994) mathematical principles of reinforcement (MPR) were tested for re... more Predictions of Killeen's (1994) mathematical principles of reinforcement (MPR) were tested for responding on ratio reinforcement schedules. The type of response key, the number of sessions per condition, and first vs. second half of a session had negligible effects on responding. Longer reinfbrcer durations and larger grain types engendered more responding, affecting primarily the parameter a (specific activation). Key pecking was faster than treadle pressing, affecting primarily the parameter S (delta; response time). Longer intertrial intervals led to higher overall response rates and shorter postreinforcement pauses and higher running rates, and ruled out some competing explanations. The treadle data required a distinction between the energetic requirements and rate-limiting properties of extended responses. The theory was extended to predict pause durations and run rates on ratio schedules.

Predicting violations of transitivity when choices involve fixed or variable delays to food

Modelling natural action selection: an international workshop, Edinburgh (eds JJ Bryson, TJ Prescott & AK Seth) , 2005

Incentive theory, an established model of behaviour, predicts how animals should choose between a... more Incentive theory, an established model of behaviour, predicts how animals should choose between alternatives that differ in the amount of food delivered, and the delay until it is delivered. Choice behaviour in such situations may be " irrational " , in that it fails to satisfy Strong Stochastic Transitivity (SST). We apply incentive theory within the framework of a standard choice procedure from operant psychology and show that choice behaviour does not satisfy substitutability, and therefore SST does not hold. This occurs because of a change in the context of choice, implicit in the change of experimental conditions necessary to test SST. The predictions from our model are similar to the results of experimental studies of choice behaviour in pigeons. This agreement suggests that behavioural theories may provide insight into other apparent departures from rational behaviour.

Changing rates of reinforcement perturbs the flow of time

This experiment tested the hypothesis that changes in rate of reinforcement affect the rate of an... more This experiment tested the hypothesis that changes in rate of reinforcement affect the rate of an internal pacemaker as suggested by the Behavioral Theory of Timing (BeT: Killeen and Fetterman, 1988). Pigeons were trained to discriminate durations of 10 s and 20 s, and then exposed to higher or lower rates of freely delivered reinforcers. When returned to the' discrimination task, judgments were reliably biased in the predicted directions: those returning from a richer context judged standard durations to be longer than did those returning from a poorer context. These results validate a key assumption of BeT, and provide an explanation of how changing tempos of life bias the perception of time.

Foraging by rats- Intuitions, models, data.pdf

Killeen, P R. and Riggsford, M., 1989. Foraging by rats: Intuitions, models, data. Behav. Process... more Killeen, P R. and Riggsford, M., 1989. Foraging by rats: Intuitions, models, data. Behav. Process., 9:95-05. Rats R. norvegicus were trained to press levers to accumulate food at distant sites. The size of the hoard increased with the distance to the site, but old not vary when the rats had to run uphill or downhill to get it. Persistence in a patch depended on the richness of the alternative patch. Optimality models were developed and modified in light of these data.

SQAB 2001: an abundance of riches.

by Peter Killeen and Armando Machado

Behavioural processes, Jan 1, 2002

Better statistics for better decisions: Rejecting null hypotheses statistical tests in favor of replication statistics.

by Federico Sanabria and Peter Killeen

Despite being under challenge for the past 50 years, null hypothesis significance testing (NHST) ... more Despite being under challenge for the past 50 years, null hypothesis significance testing (NHST) remains dominant in the scientific field for want of viable alternatives. NHST, along with its significance level p, is inadequate for most of the uses to which it is put, a flaw that is of particular interest to educational practitioners who too often must use it to sanctify their research. In this article, we review the failure of NHST and propose p(rep), the probability of replicating an effect, as a more useful statistic for evaluating research and aiding practical decision making.

The dynamics of conditioning and extinction.

by Federico Sanabria and Peter Killeen

Pigeons responded to intermittently reinforced classical conditioning trials with erratic bouts o... more Pigeons responded to intermittently reinforced classical conditioning trials with erratic bouts of responding to the conditioned stimulus. Responding depended on whether the prior trial contained a peck, food, or both. A linear persistence-learning model moved pigeons into and out of a response state, and a Weibull distribution for number of within-trial responses governed in-state pecking. Variations of trial and intertrial durations caused correlated changes in rate and probability of responding and in model parameters. A novel prediction-in the protracted absence of food, response rates can plateau above zero-was validated. The model predicted smooth acquisition functions when instantiated with the probability of food but a more accurate jagged learning curve when instantiated with trial-to-trial records of reinforcement. The Skinnerian parameter was dominant only when food could be accelerated or delayed by pecking. These experiments provide a framework for trial-by-trial accounts of conditioning and extinction that increases the information available from the data, permitting such accounts to comment more definitively on complex contemporary models of momentum and conditioning.

Is Breathing Safe?

This Wallethub note looks at the pros and cons of vaping; click on the URL.

Counting the Minutes Killeen 1992.pdf

Models of pacemaker-counter timing systems. Predicts generalized Weber's Law and underprediction.

Symmetric receiver operating characteristics

For receiver operating characteristic curves to be symmetric the signal distribution must be an o... more

Prospective & Retrospective Timing Fetterman & Killeen

Learning & Behavior, 2010

Pigeons discriminated between two pairs of durations: a short set (2.5 and 5 sec) and a long set ... more Pigeons discriminated between two pairs of durations: a short set (2.5 and 5 sec) and a long set (5 and 10 sec). The pairs were intermixed within sessions and identified by the colors on the signal and choice keys. Once the task was learned, the pigeons experienced the following three conditions seriatim: (1) The signal key was made ambiguous about the test change, but the choice keys were informative (retrospective); (2) the signal key identified the test range, but the choice keys did not (prospective); (3) probe trials were introduced in which the color of the center key signaled one test range, but the color of the choice keys signaled the other test range (inconsistent). Accuracy of choice decreased in the retrospective condition and, returned to baseline levels, was higher under the prospective condition than under the retrospective condition. In a final condition, referred to as conflict trials, the center-key color signified one test range and the choice-key colors the other range. The results from these conflict-inconsistent tests indicate that choice behavior was largely controlled by the signal-key color and not by the choice-key color. We relate these findings to different approaches to timing in animals.

How reinforcement context affects temporal production and categorization

Animal Learning & Behavior, 1998

The behavioral theory of timing assumes that timing is governed by a pacemaker whose pulses move ... more The behavioral theory of timing assumes that timing is governed by a pacemaker whose pulses move organisms from one state to the next, and that the speed of the pacemaker covaries with the rate of reinforcement in the experimental context. The goal of the present experiments was to clarify just what constitutes that context. In Experiment 1, pigeons responded on signaled fixed-interval20-sec and 40sec schedules offood reinforcement that were presented randomly within sessions (alternating condition) or between sessions (isolated condition). In Experiment 2, pigeons categorized the duration of a short or a long set of intervals in the alternating or the isolated condition. Performance in both experiments was under strong control by the signals, with scalar timing between long and short sets, but no significant differences between the alternating and isolated conditions. The context of reinforcement that determines pacemaker period can thus be specific to a particular timing task and signal.

Killeen, P. R., & Bizo, L. A. (1998). The mechanics of reinforcement. Psychonomic Bulletin & Review, 5, 221-238.

by Lewis Bizo and Peter Killeen

Psychonomic Bulletin & Review, 1998

Motivation, association, and response constraints are central phenomena in learning and performan... more Motivation, association, and response constraints are central phenomena in learning and performance. A recent theory of reinforcement-a mechanics of reinforcement (Killeen, 1992)-offers a formal description of these processes in terms of three principles. This paper summarizes the principles, elaborates them so as to generate clear predictions, and reports new data that bear on their evaluation. In particular, the action of the principles are represented in a behavior space, in which changes in the relation between target or operant behaviors and other activities appear as behavioral trajectories.

Bizo, L. A., Kettle, L., & Killeen, P. R. (2001). Rats don't always respond faster for more food: The paradoxical incentive effect. Animal Learning & Behavior, 29, 66-78.

by Lewis Bizo and Peter Killeen

Animal Learning & Behavior, 2001

Rats' lever-pressing was reinforced on variable-ratio schedules. As ratio values increased, respo... more Rats' lever-pressing was reinforced on variable-ratio schedules. As ratio values increased, response rates initially increased with them, then eventually decreased. In Exp 1, rates were uniformly higher with 1-pellet reinforcers than with two-pellet reinforcers—the paradoxical incentive effect. In Exp 2, rats received 1-, 2-, and 3-pellet reinforcers with counterbalanced preloads of pellets; the continued superiority of the smaller reinforcers ruled out a satiation explanation. Exp 2 introduced a 20-sec intertrial interval (ITI), and Exp 4 filled the ITI with an alternate response to test a memorial/overshadowing explanation. In Exp 5, the rats received 1 or 2 standard grain pellets or 1 sucrose pellet as reinforcers over an extended range of ratios. The diminution of the effect in Exp 3 and its reversal in Exp 4 and Exp 5 at large ratios provided evidence for overshadowing and reconciled the phenomenon with mathematical principles of reinforcement.

Sanabria, F, Acosta, J. I., Killeen, P. R., Neisewander, J. L., & Bizo, L. A. (2008). Modeling the effects of fluoxetine on food-reinforced behavior. Behavioural Pharmacology, 19, 61-70.

by Peter Killeen, Janet Neisewander, and Lewis Bizo

Behavioural Pharmacology, 2008

We propose a novel method to dissociate incentive motivation from memory and motor processes in i... more We propose a novel method to dissociate incentive motivation from memory and motor processes in instrumental performance. Components of a multiple fixed-ratio schedule of food reinforcement were adjusted to envelop the range of response requirements that maintained lever pressing by rats. We sought to manipulate motivation for food rewards with acute administrations of various doses (0–10 mg/kg) of fluoxetine, a 5-HT reuptake inhibitor that reduces food intake. A quantitative model of fixed-ratio performance derived from Killeen's (1994) Mathematical Principles of Reinforcement (MPR) provided an adequate account of data from individual rats. Decreases in response rate resulting from fluoxetine were reflected in changes in estimates of activation, indexed by MPR parameter a; estimates of working memory capacity and lever pressing duration were not systematically affected. These results support the use of MPR parameter a to index incentive motivation using multiple fixed-ratio schedules that are adjusted to individual performance.

A Ludic Appreciation of Mechner's Aesthetics

Psychological Record, 2018

We can imagine many of our emotions in our family pet: hunger, fear, anger, lust, and even the bo... more We can imagine many of our emotions in our family pet: hunger, fear, anger, lust, and even the bonding that we call love. But not
the appreciation of a sunset, sonnet, musical passage, or good joke. Mechner takes on the gamut of such aesthetic appreciations,
removed from the urgency of the primal ones, and gives us the first thorough attempt at a behavioral explication. Because he has
been so thorough and apt, my commentary can add little value to his thesis, only subtract from it. Therefore, rather than critique, I
exemplify, and then simplify. By reducing his voluminous report to two lines: a theorem and an equation, I thereby encapsulate
aesthetics in a sweet pill of spire. Aesthetic appreciation of this note may require a willing suspension of disbelief.

The non-Darwinian evolution of behavers and behaviors

Behavioral Processes, 2019

Darwinian evolution and Skinnerian psychology, have in common the vision of powerful control of t... more Darwinian evolution and Skinnerian psychology, have in common the vision of powerful control of their subjects by their sequalae. Individuals of species that generate more successful offspring come to dominate their habitat; responses of those individuals that generate more reinforcers come to dominate the repertoire of the individual in that context. This is unarguable. What is questionable is how large a role these forces of selection play in the larger landscape of existing organisms and the repertoires of their individuals. Here it is argued that non-Darwinian and non-Skinnerian selection play much larger roles in both than the reader may appreciate. The argument is based on the history of, and recent advances in, microbiology. Lessons from that history re-illuminate the three putative domains of selection by consequences: The evolution of species, response repertoires, and cultures. It is argued that before, beneath, and after the cosmically brief but crucial epoch of Darwinian evolution that shaped creatures such as ourselves, non-Darwinian forces pervade all three domains.

The Futures of EAB

Killeen, P. R. (2018). The Futures of Experimental Analysis of Behavior. Behavior Analysis: Resea... more Killeen, P. R. (2018). The Futures of Experimental Analysis of Behavior. Behavior Analysis: Research and Practice. http://dx.doi.org/10.1037/bar0000100
For 50 years Experimental Analysts of Behavior (EAB) have been riding the crests of waves raised by BF Skinner. His technical innovations and conceptual simplifications were a powerful breath of fresh air, and the large effect sizes engineered with contingencies of reinforcement
gave its practitioners confidence in their methods. The goals of EAB meanwhile went unexamined, its antimentalistic philosophy untested, and the gap between laboratory and life inevitably widened. This gap can only be bridged by renewed conversations on the fundamentals of our field, and new technologies to examine behavior that we have largely ignored. Interpretative accounts—showing that reinforcement may have played an important role in some complex or exceptional behavior—is no longer enough. To ensure a future for EAB several things must happen. We must learn that data have little value until embedded in a coherent
narrative; and the best of those are called theories. The biological EAB must reach levels up to biology/ethology/ecology; and levels down to physiology/neuroscience. The psychological EAB must recognize the value of bringing into our tool-box treatments of states such as affects and dispositions; operations such as attention, rumination, goal-setting, and reframing; and craft a better understanding of belief systems in general. The social EAB must strive to generalize basic laws formulated in open-loop controlled laboratory settings to dynamic interactive closed-loop processes with two or more interacting systems. To be successful these endeavors require respect for other approaches to these phenomena, and collaborations with scientists who know more about them than we yet do.

The_Modulated_Contingency_Killeen&Jacobs_tBA_(2017).pdf

Killeen, P. R., & Jacobs, K. W. (2017). The modulated contingency. The Behavior Analyst, 1-20. do... more

Killeen VITÆ.docx

my CV thru 2018

Models of Ratio Schedule Performance

Predictions of Killeen's (1994) mathematical principles of reinforcement (MPR) were tested for re... more Predictions of Killeen's (1994) mathematical principles of reinforcement (MPR) were tested for responding on ratio reinforcement schedules. The type of response key, the number of sessions per condition, and first vs. second half of a session had negligible effects on responding. Longer reinfbrcer durations and larger grain types engendered more responding, affecting primarily the parameter a (specific activation). Key pecking was faster than treadle pressing, affecting primarily the parameter S (delta; response time). Longer intertrial intervals led to higher overall response rates and shorter postreinforcement pauses and higher running rates, and ruled out some competing explanations. The treadle data required a distinction between the energetic requirements and rate-limiting properties of extended responses. The theory was extended to predict pause durations and run rates on ratio schedules.

Predicting violations of transitivity when choices involve fixed or variable delays to food

Modelling natural action selection: an international workshop, Edinburgh (eds JJ Bryson, TJ Prescott & AK Seth) , 2005

Incentive theory, an established model of behaviour, predicts how animals should choose between a... more Incentive theory, an established model of behaviour, predicts how animals should choose between alternatives that differ in the amount of food delivered, and the delay until it is delivered. Choice behaviour in such situations may be " irrational " , in that it fails to satisfy Strong Stochastic Transitivity (SST). We apply incentive theory within the framework of a standard choice procedure from operant psychology and show that choice behaviour does not satisfy substitutability, and therefore SST does not hold. This occurs because of a change in the context of choice, implicit in the change of experimental conditions necessary to test SST. The predictions from our model are similar to the results of experimental studies of choice behaviour in pigeons. This agreement suggests that behavioural theories may provide insight into other apparent departures from rational behaviour.

Changing rates of reinforcement perturbs the flow of time

This experiment tested the hypothesis that changes in rate of reinforcement affect the rate of an... more This experiment tested the hypothesis that changes in rate of reinforcement affect the rate of an internal pacemaker as suggested by the Behavioral Theory of Timing (BeT: Killeen and Fetterman, 1988). Pigeons were trained to discriminate durations of 10 s and 20 s, and then exposed to higher or lower rates of freely delivered reinforcers. When returned to the' discrimination task, judgments were reliably biased in the predicted directions: those returning from a richer context judged standard durations to be longer than did those returning from a poorer context. These results validate a key assumption of BeT, and provide an explanation of how changing tempos of life bias the perception of time.

Foraging by rats- Intuitions, models, data.pdf

Killeen, P R. and Riggsford, M., 1989. Foraging by rats: Intuitions, models, data. Behav. Process... more Killeen, P R. and Riggsford, M., 1989. Foraging by rats: Intuitions, models, data. Behav. Process., 9:95-05. Rats R. norvegicus were trained to press levers to accumulate food at distant sites. The size of the hoard increased with the distance to the site, but old not vary when the rats had to run uphill or downhill to get it. Persistence in a patch depended on the richness of the alternative patch. Optimality models were developed and modified in light of these data.

SQAB 2001: an abundance of riches.

by Peter Killeen and Armando Machado

Behavioural processes, Jan 1, 2002

Better statistics for better decisions: Rejecting null hypotheses statistical tests in favor of replication statistics.

by Federico Sanabria and Peter Killeen

Despite being under challenge for the past 50 years, null hypothesis significance testing (NHST) ... more Despite being under challenge for the past 50 years, null hypothesis significance testing (NHST) remains dominant in the scientific field for want of viable alternatives. NHST, along with its significance level p, is inadequate for most of the uses to which it is put, a flaw that is of particular interest to educational practitioners who too often must use it to sanctify their research. In this article, we review the failure of NHST and propose p(rep), the probability of replicating an effect, as a more useful statistic for evaluating research and aiding practical decision making.

The dynamics of conditioning and extinction.

by Federico Sanabria and Peter Killeen

Pigeons responded to intermittently reinforced classical conditioning trials with erratic bouts o... more Pigeons responded to intermittently reinforced classical conditioning trials with erratic bouts of responding to the conditioned stimulus. Responding depended on whether the prior trial contained a peck, food, or both. A linear persistence-learning model moved pigeons into and out of a response state, and a Weibull distribution for number of within-trial responses governed in-state pecking. Variations of trial and intertrial durations caused correlated changes in rate and probability of responding and in model parameters. A novel prediction-in the protracted absence of food, response rates can plateau above zero-was validated. The model predicted smooth acquisition functions when instantiated with the probability of food but a more accurate jagged learning curve when instantiated with trial-to-trial records of reinforcement. The Skinnerian parameter was dominant only when food could be accelerated or delayed by pecking. These experiments provide a framework for trial-by-trial accounts of conditioning and extinction that increases the information available from the data, permitting such accounts to comment more definitively on complex contemporary models of momentum and conditioning.

Is Breathing Safe?

This Wallethub note looks at the pros and cons of vaping; click on the URL.

Counting the Minutes Killeen 1992.pdf

Models of pacemaker-counter timing systems. Predicts generalized Weber's Law and underprediction.

Symmetric receiver operating characteristics

For receiver operating characteristic curves to be symmetric the signal distribution must be an o... more

Is Breathing Safe?

WalletHub Expert Opinion on vaping

It is not so bad--a hellofalot better than sucking tobacco smoke

Macro Information from Micro Data

A complete understanding of a phenomenon requires understanding the four Aristotelian Aspects: Tr... more A complete understanding of a phenomenon requires understanding the four Aristotelian Aspects: Triggers (Efficient Causes), Substrates (Material Causes), Function (Final causes) and Description (Formal Causes). In perfecting Formal Causes (Theories and models) scientific practice is to maximize mutual information between model and data. This is measured the a combination of accuracy (% variance in the data accounted for by the model) and parsimony (% variance in the model accounted for by the data). Examples are given from learning theory, tobacco addiction, and ADHD.

The Joys of Innovation (Review)

Review of Animal Creativity and Innovation, Allison B. Kaufman and James C. Kaufman (eds.). San ... more

A Decade of Contributions to Understanding and Ameliorating Attention Deficit-‐ Hyperactivity Disorder

Selections from, and musings over some of the ADHD articles published in BBF over the decade sinc... more