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A Bayesian Recognitional Decision Model
Shane T. Mueller
Applied Research Associates, Inc.
ABSTRACT: The recognition-primed decision (RPD) model (Klein, 1993) is an account
of expert decision making that focuses on how experts recognize situations as being
similar to past experienced events and thus rely on memory and experience to make
decisions. A number of computational models exist that attempt to account for similar
aspects of expert decision making. In this paper, I briefly review these extant models
and propose the Bayesian recognitional decision model (BRDM), a Bayesian implemen-
tation of the RPD model based primarily on models of episodic recognition memory
(Mueller & Shiffrin, 2006; Shiffrin & Steyvers, 1997). The proposed model accounts for
three important factors used by experts to make decisions: evidence about a current
situation, the prior base rate of events in the environment, and the reliability of the
information reporter. The Bayesian framework integrates these three aspects of
information together in an optimal way and provides a principled framework for
understanding recognitional decision processes.
Introduction and Background
THE RECOGNITION-PRIMED DECISION (RPD) MODEL (KLEIN, 1989, 1993, 1998) IS A
conceptual model that arose from naturalistic observation of expert human decision
makers. Its basis in naturalistic settings and applied research helps to identify the
types of decisions and situations that appear most relevant to expert decision makers
in their work. These situations often involve “time pressure, uncertainty, ill-defined
goals, high personal stakes, and other complexities” (Lipshitz, Klein, Orasanu, &
Salas, 2001, p. 332).
The main insight of the RPD model is that the skill of expert decision making
lies in making sense of the current situation, identifying past situations that were
similar, and using the workable actions that were taken in the past to guide cur-
rent choices. In contrast to the processes hypothesized by more classic theories of
decision making, naturalistic decision making is not about balancing trade-offs
between choices, estimating probabilities, or assessing the expected utility of fea-
tures or options.
The RPD model describes a fairly complex set of processes used by experts to
make decisions. Despite the fact that the model incorporates concepts such as pat-
tern matching, recognition memory, and situation-action decision rules (all of
which constitute psychological theories that have been embedded or implemented
in computational and mathematical models), it is fundamentally a conceptual model
ADDRESS CORRESPONDENCE TO: Shane T. Mueller, Klein Associates Division, ARA Inc., 1750 N.
Commerce Center Blvd., Fairborn, OH; smueller@ara.com.
Journal of Cognitive Engineering and Decision Making, Volume 3, Number 2, Summer 2009, pp. xxx–xxx.
DOI 10.1518/155534309X441871. © Human Factors and Ergonomics Society. All rights reserved.
1
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of decision making, without a computational or mathematical implementation. Yet
there are aspects of the RPD theory that are similar to a number of computational
models of decision making, and so these other models may be able to provide rea-
sonable mechanistic and formal models of the RPD theory.
For example, at a high level, random walk and accumulator models arising out
of the stochastic process tradition (Busemeyer & Townsend, 1993; Ratcliff, 1978;
Usher & McClelland, 2001) offer explicit computational mechanisms for dealing
with time-pressured decision making. Although typical descriptions of stochastic
models such as decision field theory (Busemeyer & Townsend, 1993) focus on the
use of a decision threshold to drive a response, these models typically allow decisions
to be made at arbitrary deadlines using the current balance of information. This is
a fundamental aspect of such models that separates them from all-or-nothing
decision processes (cf. Meyer, Yantis, Osman, & Smith, 1985, for discussion).
These models accumulate evidence for different options in microsteps and
come to a decision when evidence for an option passes some boundary. To the
extent that RPD was born out of situations requiring immediate, time-sensitive
action, these models may offer insights into a similar domain and provide natural
accounts of satisficing (making a decision that is good enough) that are central to
the RPD model. Furthermore, some of these models have been closely connected
to models of memory retrieval, which is also central to the RPD model. For exam-
ple, Ratcliff’s (1978) seminal paper introducing the diffusion model was entitled
“A Theory of Memory Retrieval” (and see also Shiffrin, Ratcliff, & Clark, 1990).
However, these stochastic models typically require multiple well-defined choice
alternatives to be available at the outset of the process. In contrast, the RPD model
needs to retrieve only a single option to begin evaluating it, and this option is
often good enough that it does not need to be compared with alternatives.
In the stochastic modeling tradition, many of the processes described by the
RPD model have been given names such as “option generation” (Johnson & Raab,
2003; Raab & Johnson, 2007). This approach treats option generation as a pre-
processing step along the way to decision making, which is reasonable for theories
based on empirical paradigms in which research participants are given carefully
crafted, clearly defined options to choose among in laboratory settings. However,
even when option generation is considered, the focus remains on choice among
options, rather than evaluation of individual options.
As an example of this focus, although typical random walk models of decision
making (e.g., Ratcliff, 1978) require the comparison of two and only two options,
some alternatives (e.g., Usher & McClellend, 2001) have developed alternative
architectures to get around this limitation. However, this was done by increasing
the comparison process to three, four, or more options, rather than decreasing it
to evaluating the goodness of a single option. In contrast, in many natural situa-
tions, the world does not present decision makers a set of clear alternatives from
which to choose.
Shapiro and Kacelnik (2007) provided an interesting example of single-option
choices among starlings. Choice behavior for these birds appears to be optimized
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for sequential rather than simultaneous encounters with feeding opportunities,
because rarely does the world present a starling with two alternative feeding
opportunities it must choose between. Instead, the starling must decide whether
taking advantage of the current opportunity is worthwhile in comparison with
other unknown opportunities. The starling’s decision problem is similar to that
faced in the so-called secretary problem (e.g., Seale & Rapoport, 1997), in which
a person must make a series of sequential decisions about whether to take a course
of action (to hire a secretary). In both cases, as in the RPD model, a rich back-
ground knowledge of what constitutes a good option eliminates the need for (and
is preferable to) comparison between options.
For the RPD model, option generation is the tail that wags the dog of classical
decision making. The skills that make experts good at their decisions consist of
their ability to generate good options—perhaps so much so that there is often no
need to generate multiple options—and to evaluate them against one another.
Consequently, these stochastic models of decision making remain rooted in a tra-
dition of comparison and choice among options and may not be well suited for
developing a computational model of naturalistic expert decisions.
One domain of computational models that is perhaps more relevant to RPD
involves episodic and semantic memory. The RPD model assumes that decision
making is rooted in past experiences, and so the process is essentially a question
of identifying memories for previous events or situations that are similar to the
current situation. A number of computational models have explored such decisions
in the context of episodic memory, memory for lists of words or pictures, categoriza-
tion, priming, lexical decision, and other related phenomena. Two prominent mod-
els are MINERVA 2 (Hintzman, 1984), and retrieving effectively from memory
(REM; Shiffrin & Steyvers, 1997).
The core assumptions of these models are that memories for events take on
feature-based representations and are stored as individual traces. MINERVA 2 stores
past memory entirely as episodes and uses similarity-matching rules to determine
what is retrieved or recalled. The REM model allows for long-term memory proto-
types as well as individual episodic traces to exist. This notion is somewhat more
consistent with the originally articulated RPD model, which assumes that past sit-
uations eventually merge into prototypes that are used to mediate decisions. REM
also frames the memory retrieval process as a Bayesian decision problem, which
allows evidence, uncertainty, and prior probabilities to be incorporated in princi-
pled (and even optimal) ways.
This Bayesian framing was at least partly inspired by Anderson’s (1990)
development of the Adaptive Control of Thought – Rational (ACT-R) computa-
tional architecture, another model that embeds theories of memory retrieval
with close connections to decision making. Although ACT-R uses mechanisms
for decision making and choice that are fundamentally different from those of
the REM and RPD models, it has been used to develop instance-based decision
models (e.g., Gonzalez, Lerch, & Lebiere, 2003) that are similar in spirit to the
RPD model.
A Bayesian Recognitional Decision Model 3
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Following Hintzman’s (1988) extension of MINERVA 2 to a decision realm,
Dougherty and colleagues (e.g., Dougherty, 2001; Dougherty, Gettys, & Ogden,
1999) developed the MINERVA-DM decision-making model rooted in episodic
memory theory. MINERVA-DM resembles aspects of the RPD model in that past
experiences are used as a basis for decision making. However, the goal of that
model was to account for human errors in frequency, likelihood, and probability
estimation. This motivation places the model outside the domain of RPD, as it
focuses on tasks that are not relevant to much of expert decision making. Yet the
essence of the model is to explore connections between decision making and mem-
ory, which is a critical insight of the RPD model. Recent updates of this modeling
approach have focused on hypothesis generation (Thomas, Dougherty, Sprenger, &
Harbison, 2008), which provides insight into a wide range of diagnostic classifica-
tion tasks in which experts engage.
These previous modeling efforts derive from academic efforts to understand
decision-making processes. Given the RPD model’s basis in naturalistic and applied
settings, it is perhaps not surprising that a number of agent-based modeling
and simulation efforts have adapted or integrated RPD processes to provide more
realistic predictions or simulations of human-like agents. For example, Warwick,
McIlwaine, Hutton, and McDermott (2001) have described a MINERVA 2-based
computational RPD model that resembles Hintzman’s (1988) and Dougherty’s
(2001) models but focuses more on naturalistic decisions, with the goal of provid-
ing realistic predictions of expert decisions in simulated work environments.
Similarly, Yen and colleagues (Fan, Sun, Sun, McNeese, & Yen, 2006; Fan, Sun,
McNeese, & Yen, 2005; Fan, Sun, Sun, et al., 2005; Ji et al., 2007) have reported
on developments of a multiagent modeling system called R-CAST. R-CAST is not a
model of human cognitive processes per se; it is, rather, an artificially intelligent
multiagent system in which agents have RPD decision-making capabilities. It is
intended to model group behavior and to serve as reasonable teammates and deci-
sion aids.
Similar agent-based simulation approaches to adapting RPD processes include
Norling, Sonenberg, and Rönnquist’s (2000) and Norling’s (2004) attempts to inte-
grate RPD decision processes into belief-desire-intention (BDI) agents; Sokolowski’s
(2002, 2003, 2007) composite agent approach to implementing RPD models; Regal,
Reed, and Largent’s (2007) use of an RPD decision module to evaluate command
approach strategies in simulated war-gaming; and Raza and Sastry’s (2007, 2008)
introduction of the RPD-Soar agent, which allows naturalistic decision making
within a computational architecture.
My goal in this paper is to present a new computational model of recognitional
decision making, implemented as a Bayesian decision process. Bayesian theory is a
way to perform inference about different hypotheses based on both evidence and
prior knowledge. A number of Bayesian models of psychological processes exist,
and they offer principled approaches to understanding how evidence is used in
various decision processes. These include decisions about episodic memory (REM:
Shiffrin & Steyvers, 1997; BCDMEM: Dennis & Humphreys, 2001), semantic
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knowledge (REM-II: Mueller & Shiffrin, 2006), perceptual judgment (ROUSE:
Huber, Shiffrin, Lyle, & Ruys, 2001), and word recognition (the Bayesian reader:
Norris, 2006).
Although there are many ways to develop models using Bayesian principles,
these models share the property that they hypothesize prior probabilities of differ-
ent events and use observed evidence to perform inference about the true likeli-
hood of those events (called the posterior likelihood). They also allow principled
use of information. For example, in comparison with a somewhat arbitrary simi-
larity-matching process employed by MINERVA 2, REM equates similarity with
the probability that one memory trace generated another.
Such models are not optimal in the sense that they are always correct; rather,
they allow for optimal use and combination of information, under specified limi-
tations (such as memory errors or biases). These models suggest methods for
implementing a Bayesian computational model of recognitional decision making.
Along with allowing prior expectations to be combined with observed evidence,
the Bayesian framework also allows one to specify directly a decision maker’s
model of how the evidence was generated. Consequently, the trust in the reporter
or perceived reliability of a sensor can be incorporated as well. These concepts
form the basis of the Bayesian recognitional decision model I describe next.
A Bayesian Recognitional Decision Model
The Bayesian recognitional decision model (BRDM) adopts a Bayesian frame-
work for both theoretical and practical reasons. (The RPD model described by Klein,
1993, 1998, is fairly extensive and covers processes such as pattern matching,
action selection, analogy, and mental simulation. The aspect of the model covered
in this paper is focused on the process of recognizing relevant past events, and I use
the term recognitional decision to highlight the fact that this model does not incor-
porate many of the more complex and interesting aspects of behavior described by
the RPD model.) Many computational decision models offer a number of free
parameters with which to explain data. These can represent processes such as evi-
dence sampling, decision thresholds, and intrinsic noise. Often, different sources
of noise can masquerade as one another, and so the true source of effects can be
difficult to determine (cf. Mueller & Weidemann, 2008).
The Bayesian approach makes a default assumption that evidence is used opti-
mally and, thus, the interesting processes lie elsewhere. This is reasonable as a
default assumption because there are many ways to be suboptimal but only one
way to be optimal. As such, it is perhaps the most parsimonious default assump-
tion. In addition, many of the optimality assumptions can be relaxed if the cir-
cumstances warrant. Thus, although naturalistic decision making research was in
part a reaction against classic models of optimal decision making (cf. Lipshitz et
al., 2001), the BRDM does not violate these basic insights simply by virtue of its
Bayesian nature. Rather, it may indeed help focus theory on identifying informa-
tion and knowledge used by experts to make decisions.
A Bayesian Recognitional Decision Model 5
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Empirical Context of Model Development
This research is based partially on interviews with U.S. Army and U.S. Air
Force officers responsible for chemical/biological defense. Their primary role is to
evaluate sensor and human reports regarding the presence of chemical or biologi-
cal threats and attacks. Because the incidence of actual events is very rare (many
officers will not witness a true positive event during their entire careers), this
might be considered an ultravigilance task. I will not provide a detailed account of
their decision-making process but will summarize the three types of information
these officers used to determine the validity of a threat: background information,
the cues in the reports, and the reliability of the source of the reports.
The interviews suggested that once a situation is identified, a fairly scripted
sequence of events is executed for addressing that situation. This script is often
part of doctrine and of the local techniques, tactics, and procedures, and indeed it
is often preplanned. These scripts are well practiced and exercised, and although
they are unlikely to fit a situation exactly, their execution is routinized once a situ-
ation is identified. The interviews suggested that an suspected attack is typically
treated as a true chemical/biological incident until a convincing level of evidence
can be established to eliminate the possibility. Next, I will describe the mecha-
nisms by which the BRDM identifies a situation based on background informa-
tion, environmental cues, and the reliability of the reporter.
Model of the Environment
For the BRDM to operate, one must first make assumptions about how events
occur in the environment, are reported to the decision maker, and are represented
by the decision maker. First, assume that a number of classifiable events might
occur. In the chemical/biological weapons protection domain, these event classes
might correspond to things such as conventional missile attacks, false alarms from
environmental dust, or specific nerve agents delivered through ballistic missiles.
These event classes have typical sets of features associated with them.
The header row of Table 1 illustrates some of the potential features that signal
different types of chemical attacks. For the example simulations in the next sec-
tion, assume that each event class has a binary feature prototype (as in the first
row of Table 1), in which each feature is either present or absent. In fact, even this
6 Journal of Cognitive Engineering and Decision Making / Summer 2009
TABLE 1. Example Feature-Based Representations of Events and Reports About Events
Chemical Mortar Garlic
Possible Features Odor Radiation Explosion Smell Coughing
Binary event prototype 1 0 0 0 1
Probabilistic event prototype .9 .01 .2 .1 .95
Report about event 1 0 0 1 1
Feature base rate .8 .3 .2 .1 .6
Note. The features and numbers in the table do not reflect the actual rate of feature occurrence in
real-world settings.
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is probably not accurate and not necessary—environmental events can be defined
probabilistically (e.g., the second row of Table 1). This distinction amounts to
defining an event or object (e.g., a chair) by its most typical features (four legs, a
seat, armrests, and a back) versus defining a chair by the probability of each fea-
ture occurring in chairs you have experienced (four legs 75% of the time, a seat
94% of the time, armrests 52% of the time, and a back 85% of the time). For any
particular event, assume that these features are reported to a decision maker as
either present or absent, as shown in the third row of Table 1.
These events may have different a priori base rates of occurring in the environ-
ment (an example is depicted the fourth row of Table 1). So, for the examples in
Table 1, although the features reported for a particular event (a chemical odor and
coughing) may match the probabilistic prototype for a particular event fairly well,
those features are also likely to occur “naturally” even when that event has not
occurred. Often, naturally occurring classes happen with long-tail distributions,
such that a few very common classes are very frequent, whereas many events hap-
pen rarely (see Zipf, 1949). Assume that this is accurate for this domain in order
to assess the effect that differences in prior probability can have on recognitional
decision making.
In any specific situation, the state of the environment will be reported to the
BRDM by a simulated sensor (either a human reporter or a networked device).
The properties by which a sensor reports the state of the environment are cap-
tured in a probabilistic model, which the decision model later uses as a generative
model to account for the observed data. In the simulation to be discussed, the sen-
sor reports environmental features with a fixed level of reliability, r. When the sen-
sor does not report accurately, the feature value it reports depends upon the base
rate of that feature in the environment (an example of which is shown in the third
row of Table 1). More formally, if B(r) is the result of a Bernoulli trial such that
B(r) ⫽ 1 with probability r and 0 otherwise, and b
r
⑀{0,1} is a particular result of
one such trial, then the generating model for a sensor report (S) can be written as
S
i
⫽ b
r
⫻ B(G
i
) ⫹ (1 ⫺ b
r
) ⫻ B(F
i
). (1)
Here, r is the reliability of a sensor, G
i
is the ground truth of for feature i, F
i
is
the background frequency distribution of each feature i, and S
i
is the resulting fea-
tures reported to the decision model. So, for an event and a feature base rate
shown in Table 1, one might observe a report like the one shown in the fourth row
of Table 1. There, the event prototype was mostly correct; its one incorrect feature
occurred for the fourth feature, which was a likely error to come from the feature
base rate.
Model of the Decision Maker Learning
For the BRDM to operate, it needs to learn about the environment in which it
is operating. In real situations, this experience comes from a number of sources:
from textbook resources, from anecdotes and wisdom passed down by other offi-
cers, and from experienced training exercises and actual events. To simulate this
A Bayesian Recognitional Decision Model 7
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learning process, one exposes the model to a large number of exemplars of each of
the relevant events. The relative probabilities of event classes are specified accord-
ing to Zipf’s law (see a more detailed description in Demonstration 1, as well as in
Zipf, 1949), and reports generated with noise introduced by a probabilistic model
of information reporting, which are described next.
The BRDM learns two primary things about these events: (a) a typical featural
prototype for each event class and (b) a base rate for each event in the environ-
ment. Although individual reports provide an incomplete and unreliable view of
the world, the model learns prototypes by accumulating an average representation
of the observed exemplars. That is, if three exemplars of an event class had fea-
tures [1 1 1 0 0] and two had features [1 1 0 0 0], its composite representation
would be [1 1 .6 0 0]. Thus, an event class prototype becomes the average feature
distribution of events having that label.
The environmental model generates information in a noisy fashion (some-
times erroneously sampling from the base rate of a feature instead of the ground
truth), and so the representations for low-frequency states become contaminated
by features from high-frequency states (see Figure 1). In Figure 1, each row repre-
sents an event class, and each cell shows the relative strength of a feature for that
event, with darker cells indicating greater importance. For five states with 20 fea-
tures, the true environmental prototypes are shown in the top panel. After 10,000
reports, sampled according to the power law distribution and generative model
described earlier, the model’s event prototypes resemble the original environmental
8 Journal of Cognitive Engineering and Decision Making / Summer 2009
Figure 1. Features for five hypothesized states of the world (top panel) and the
corresponding representations learned by the model through experience with those
situations (bottom panel). Each row depicts an event class, and each cell depicts the
relative importance of each feature, with darker cells indicating higher probabilities.
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prototypes, but the high-frequency events (toward the bottom) dominate the base
rate and so features from those high-frequency events bleed into the low-frequency
events because of the error-generating process.
The model also learns the base rate of different threats in the environment. In
specific contexts and situations (domestic vs. deployed; wartime vs. peacetime;
and depending upon the capabilities of the enemy), the officer will have a fairly
clear picture of which threats are most likely, attained via coordination with his or
her intelligence resources and other officers in the region. In practice, much of the
officer’s work involves learning how likely these different threats are (rather than
simply watching for evidence of attacks). In the model, this knowledge is cap-
tured by accumulating an empirical event counter that provides a simple fre-
quency distribution of experienced events. Clearly, if this base rate is inferred from
other sources, behavior may produce biases such as depicted by the representa-
tiveness heuristic (Tversky & Kahneman, 1974).
Model of the Recognitional Decision Process
Once a reasonable representation for a set of events has been learned, the model
is able to classify new events based on its past experience. It receives a report and
classifies the event by identifying which of its memory prototypes was most likely
to have generated the experienced event. To do so, the model weighs the evidence
inherent in the report with the background probability of such a threat and with
information regarding whether or not the reporter is reliable. The features of
that message are compared in parallel with the relevant prototypes in long-term
memory, and for each, a likelihood is computed, which integrates the reliability of
the sensor, the current information, and the background knowledge about possi-
ble threats.
This is done via a mental model of the reporting process, which corresponds to
the model’s beliefs about the generating process for that report. Assume that the
basic form of this mental model is accurate, although the actual parameters (e.g.,
base rate, reliability, feature strengths) might not be accurate. The basic decision
process is one of determining whether or not the current evidence favors a partic-
ular event class. This is done by computing a posterior likelihood ratio, compar-
ing the likelihood of a particular class (given the evidence) with the likelihood of
nothing happening (given the evidence). This is called the posterior decision like-
lihood ratio, and its formula is
(2)
, (3)
in which denotes the decision likelihood ratio; q
ˆ
(k) is the decision maker’s esti-
mate of the base rate of event class k; G
ˆ
ik
is the estimate of G
ik
, the probability of
feature i for event class k; F
ˆ
is an estimate of F
i
, the probability of feature i across all
kik
i
()
()
=
−
∏
ˆ
ˆ
qk
qk1
ik
ik i
i
(
=
×+−×
⎡
⎣
⎤
⎦
ˆ
ˆ
ˆ
ˆ
ˆ
rG r F
F
1)
A Bayesian Recognitional Decision Model 9
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experiences; and r
ˆ
is the model’s estimate of the reliability with which the sensor
reported the data.
Note that all of the values used in this computation are estimates of the values
used to generate the data: G and F are the model’s long-term memory for the prob-
ability of feature occurrence in given event classes; q
ˆ
is the estimate for the base
rate of event classes; and r
ˆ
is the estimate for the reliability of the sensor. This like-
lihood comparison process allows decisions about events to be made in isolation:
There is no need to choose between specific events. An event class is judged as
satisfactory on its own merits, rather than in comparison with an alternative. An
event that produces a satisfactory result might lead to action, even if there are
other events that are better fits. This aspect of the decision process has some
strong correspondences to the basic decision mechanisms hypothesized by the
RPD model.
If the report was more likely to have come from a specific event class than it
was to have arisen by chance, the likelihood ratio (i.e.,
ik
in Equation 2) is greater
than 1, and the model will consider this option.
For a given report, this process could generate a number of outcomes. If the
report has one prototype whose value is greater than 1.0, and the rest are less
than 1.0, there is clear evidence for that event class. However, this situation might
not always happen. In other situations, no events may have values of that are
greater than 1.0, and so the event with highest value of might be selected as a
working hypothesis, and more evidence will be gathered to corroborate that infor-
mation. In other situations, multiple event prototypes might have values greater
than 1.0. In these cases, the situation is less clear, but one might either choose the
most descriptive option or gather more information that distinguishes between
the attractive options. The particular strategies for disambiguation and corrobora-
tion probably differ across domains, depending on the costs associated with gath-
ering information, the costs of errors, and the benefits of correct identification.
Example Calculation
Table 2 shows an example calculation of the likelihood ratios () for two mes-
sages (A and B), compared with two event prototypes (Events 1 and 2). In this
example, assume that the prior probabilities of these events are all equal to .5 and
that the BRDM estimates this accurately. This has the effect of multiplying the like-
lihood product by (.5)/(1 – .5) which is equal to 1.0, and so has no impact.
In this example, Message A is generated by a more reliable sensor (r ⫽ .9)
than the one generating Message B (r ⫽ .2). Assume that the model accurately
estimates this probability (r
ˆ
⫽ r). Thus, for Message A, matches are given more
positive evidence, and mismatches are given more negative evidence. Message A
shares two feature values with Event 1 and four with Event 2; B shares two fea-
tures with Event 1 and three with Event 2.
The values computed under p(A|Event Class 1) show the probability that the
particular feature of A was generated by the Event 1. The next column shows the
ratio between that probability and the probability of the feature arising from any
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other event (reflected by the feature base rate). When the product of all these val-
ues is found, one obtains the posterior probability that a specific event generated
the observed event.
Both messages provide fairly strong evidence against Event 1. Message A gives
odds of about 100:1 against, and Message B gives odds that are slightly biased against
(.83). However, the odds that Event 2 generated A are close to even (.98), and the
odds that Event 2 generated message B are about 5:4 (1.24) in favor. Thus, Message A
provides equivocal evidence for the two states, but Message B favors Event 2.
This example illustrates the basics of how information is used by the model to
identify the state of the world. Once an event class is identified, this will activate
prototypical action scripts, which will be altered and executed as appropriate.
These mechanisms are outside the domain of the decision model described here.
The example also demonstrates a curious and counterintuitive result. Sensor A is
more reliable than Sensor B, and it matches Event 2 on more features than Sensor B
does, but it ends up being ambivalent about whether Event 2 generated the message.
In contrast, the unreliable Sensor B provides greater evidence in favor of Event 2.
This happens because errors count against A more than B, and the error that A made
(Feature 3) was one that was unlikely to have occurred by chance. In contrast,
Sensor B mismatched Event 2 on features that were more likely to have matched
by chance. A simulated example of this effect is shown in Demonstration 2. But
first, Demonstration 1 will show the effects that environmental base rate can have
on the probability of accurately classifying events.
A Bayesian Recognitional Decision Model 11
TABLE 2. Sample Calculation of Likelihood Ratio for One Reliable Message (A) and
One Unreliable Message (B)
A [11000] r
⫽
.9 B [10101] r
⫽
.2
p(A|Event Class 1) (A,Event Class 1) p(B|Event Class 1) (B|Event Class 1)
Event Class 1
1 .9*1 ⫹ .1*.8 ⫽ .98 .98/.8 ⫽ 1.225 .2*1 ⫹ .8*.8 ⫽ .84 .84/.8 ⫽ 1.05
0 .9*0 ⫹ .1*.3 ⫽ .03 .03/.3 ⫽ 0.1 .2*1 ⫹ .8*(1⫺.3) ⫽ .76 .76/(1⫺.3) ⫽ 1.09
0 .9*1 ⫹ .1*(1⫺.2) ⫽ .98 .98/(1⫺.2) ⫽ 1.225 .2*0 ⫹ .8*.2 ⫽ .16 .16/.2 ⫽ 0.8
1 .9*0 ⫹ .1*(1⫺.1) ⫽ .09 .09/(1⫺.1) ⫽ 0.1 .2*0 ⫹ .8*(1⫺.1) ⫽ .72 .72/(1⫺.1) ⫽ 0.8
1 .9*0 ⫹ .1*(1⫺.6) ⫽ .04 .04/(1⫺.6) ⫽ 0.1 .2*1 ⫹ .8*.6 ⫽ .68 .68/.6 ⫽ 1.13
Product () 0.0015 0.827
p(A|Event Class 2) (A,Event Class 2) p(B|Event Class 2) (B,Event Class 2)
Event Class 2
1 .9*1 ⫹ .1*.8 ⫽ .98 .98/.8 ⫽ 1.225 .2*1 ⫹ .8*.8 ⫽ .84 .84/.8 ⫽ 1.05
1 .9*1 ⫹ .1*.3 ⫽ .93 .93/.3 ⫽ 3.1 .2*0 ⫹ .8*(1⫺.3) ⫽ .56 .56/(1⫺.3) ⫽ 0.8
1 .9*0 ⫹ .1*(1⫺.2) ⫽ .08 .08/(1⫺.2) ⫽ 0.1 .2*1 ⫹ .8*.2 ⫽ .36 .36/.2 ⫽ 1.8
0 .9*1 ⫹ .1*(1⫺.1) ⫽ .99 .99/(1⫺.1) ⫽ 1.1 .2*1 ⫹ .8*(1⫺.1) ⫽ .92 .92/(1⫺.1) ⫽ 1.02
0 .9*1 ⫹ .1*(1⫺.6) ⫽ .94 .94/(1⫺.6) ⫽ 2.35 .2*0 ⫹ .8*.6 ⫽ .48 .48/.6 ⫽ 0.8
Product () 0.982 1.24
Note. The base rate of features in the environment is (.8, .3, .2, .1, .6).
Vol_3-2-03-Mueller_0900011.qxd 6/1/09 9:24 AM Page 11
Demonstration 1: Base Rate Manipulations
To further demonstrate the basic operation of the model, I next report results
of Monte Carlo simulations of the model operation. In these demonstrations, the
simulated environment contained five states of interest, each defined by a sparse
sampling across 20 binary features. The top panel of Figure 1 shows a typical ini-
tial configuration, with each prototype having five or fewer “on” features. These
five world states occurred with a power law distribution, such that State 1 had the
highest frequency and State 5 had the lowest frequency. In order, the states hap-
pened with probability .39, .22, .16, .13, and .11, such that state i has frequency
proportional to 1/i
␥
(here with ␥⫽.8). This distribution mimics commonly found,
naturally occurring power-law frequency distributions, as has been described by
Zipf (1949).
The system learned concepts based on these environmental prototypes, based
on the sensor generation process described earlier. Because the base rate across fea-
tures is composed mostly of high-frequency items, and the error generation process
produces features from this base rate, concepts tend to grow similar to the base rate
because of errors. The bottom panel of Figure 1 shows the learned representations
based on the world states after 10,000 sampled events. Notice that “phantom” fea-
tures appear in lower frequency event classes because of these errors.
Frequent events have representations that are similar to the base rate, and so the
evidence evaluation process should have trouble distinguishing these particular
events from things that happen all the time. In contrast, rarer events tend to be less
similar to the average, and so they should be easier to identify. But the model also
incorporates its estimates of the environmental base rate of these events. If the base
rate is used optimally, the high-frequency events (which should be harder to iden-
tify) will benefit from being frequent because an optimal model will be willing to
classify the event with less direct evidence. In contrast, lower frequency event
classes will provide stronger evidence for their existence but will be hurt from being
less frequent, as an optimal model will need more evidence to classify the event.
For any given decision context, it is unclear exactly how prior probabilities are
used by an expert or novice decision maker. Consequently, I will bracket perform-
ance by demonstrating two extremes: one model in which prior odds are not used
at all, and a second in which prior odds are used optimally. If one disregards the
cases in which base rate information may be used antipathetically (which could be
an interpretation of the gambler’s fallacy), the behavior of most experts should fall
somewhere between these two bounds.
To examine this, I simulated 50 sets of event classes as described previously,
then encoded 250 exemplars of each of the five states and computed the likeli-
hood according to the model that each exemplar was generated from each of the
five world states. Figure 2 shows the three measures of decision quality when prior
base rate of event classes is ignored. The left panel shows mean log-likelihood of
the evidence strength. Each line shows the mean value of a message generated
from each event type, compared with each of the five event types. Spikes in the
12 Journal of Cognitive Engineering and Decision Making / Summer 2009
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likelihood occur for each “correct” event-message match, and the mean value of
these matches is typically around 1.0, the “natural” decision bound for this task.
Here, high frequency events produce the weakest evidence on average, whereas
rarer events produce stronger evidence.
The average likelihood for correct decisions is a bit misleading, so the center
panel shows the proportion of events that surpassed this “natural” even-odds
threshold. Thus, if this threshold were used as a decision threshold in this envi-
ronment, the decision maker would take action in response to real events about
8 times out of 10. However, false alarms are also substantial, with roughly 2 out of
every 10 events being falsely classified. The right panel shows how often the high-
est likelihood state was also the correct one. Here, a considerable proportion of
messages would be improperly classified.
The base rate effect in Figure 2 reverses when knowledge of base rates is incor-
porated into the decision process. Figure 3 shows the same three performance
measures as those in Figure 2 when base rate information is taken into account for
the same simulated data. Here, rare items produce lower likelihoods and are less
likely to be chosen.
The results of this simulation illustrate a number of fundamental behaviors.
First, it shows that in principle, the BRDM can produce highly accurate event clas-
sification. Incorrect options rarely provide positive evidence for a specific event
class, but messages with enough noise sometimes do not provide enough evidence
for a specific event. Furthermore, the base rate of events in the environment pro-
duces opposite effects, dependent on how strongly prior evidence is weighted. In
principle, this suggests a testable hypothesis for the BRDM: Manipulating how
strongly prior evidence is considered should reverse frequency-dependent accu-
racy effects.
A Bayesian Recognitional Decision Model 13
Figure 2. Measures of decision quality, unweighted by base rate information (average
over 250 exemplars of each event class for 50 randomly sampled messages per class).
Vol_3-2-03-Mueller_0900011.qxd 6/1/09 9:24 AM Page 13
Demonstration 2: Information Trust
The interviews with domain experts indicated that their confidence and trust
in the source of a report was a strong factor in determining how the evidence pre-
sented should be considered and what actions should be taken. The BRDM offers
an account of how the reliability of an information source might be incorporated
into the decision process, via a mental model of the reporting process.
In the BRDM, a state is classified by computing a posterior likelihood value of
observed data given a specified mental model of the generation process. As dis-
cussed earlier, a sensor reports accurate information with probability r, and other-
wise information is reported in proportion to each feature’s natural occurrence. To
assess the likelihood of evidence given the hypothesized model, the decision
maker incorporates an estimate of this reliability (r
ˆ
) into his or her mental model
of data generation. This assessment may be inaccurate and be lower or higher than
the sensor’s true reliability.
For a report from an unknown sensor, or one with known poor reliability, r
ˆ
might be relatively low (e.g., r
ˆ
⫽ .2). This corresponds to the boy who cried
“wolf.” If the sensor’s reliability truly is low (r ⫽ .2), the model will optimally
account for evidence produced by the sensor. If the sensor’s reliability is higher,
underestimating the reliability will produce distrust for the data, and it will be less
likely to lead to an action. Similarly, for a known reporter with good reliability
(e.g., a verbal report from a trusted member of the team), estimated reliability might
be relatively high (e.g., r
ˆ
⫽ .8). Under typical conditions, this reporter’s “true” reli-
ability might also be similarly high (r ⫽ .8), and so the evidence will be accounted
for optimally by the decision maker. However, if the sensor is temporarily report-
ing inaccurately, or the human reporter is tired, confused, or misled, the reliability
14 Journal of Cognitive Engineering and Decision Making / Summer 2009
Figure 3. Measures of decision quality, weighted by base rate information (average over
250 exemplars of each event class for 50 randomly sampled messages per class).
Vol_3-2-03-Mueller_0900011.qxd 6/1/09 9:24 AM Page 14
of a report might in fact be lower. Here, the reliability would be overestimated,
and the evidence would be given more strength than is warranted.
A simulated example of these effects is shown in Figures 4 and 5. One interest-
ing result of this model is that it makes a somewhat counterintuitive prediction.
One might think that overestimating the reliability of a report will be more likely
to lead to action, yet this will happen only if the sensor is reporting environmental
cues accurately. A higher value of r
ˆ
will give stronger weight to all the cues,
including those that mismatch. Consequently, for a relatively erroneous report,
using a lower estimate for r
ˆ
can be more likely to lead to action.
The way in which the BRDM handles reliability can be illustrated by consider-
ing the following example. Suppose you want to know whether to buy what looks
like a rare antique clock offered for sale at a local junk shop. To understand the
true value, you can either obtain the value assessed by an appraiser or try to find
information on the Internet. You might find the same information from both sources
(e.g., that it is a rare clock and is worth 10 times the offered price), but the assess-
ment of a trusted expert would lead you to purchase the clock, whereas the advice
you get online may make you hesitant. This describes the basic reliability effect.
Now, suppose the appraiser’s estimate says, “This is an beautiful antique clock.
Its inner workings are intact and preserved. It is made of a rare South American
hardwood. But it is an example of a period reproduction, and it has little value.”
A Bayesian Recognitional Decision Model 15
Figure 4. Mean log-likelihood of correct identification for sensors with high- and
low-reliability r and for which the reliability is overestimated and underestimated.
Unreliable sensors tend to produce reports with lower log likelihood values, whereas
underweighting or overweighting the reliability of a sensor impacts the mean likelihood
of the reports as well.
Vol_3-2-03-Mueller_0900011.qxd 6/1/09 9:24 AM Page 15
When you read this, you begin to wonder whether the appraiser is trying to con-
vince you that the relic it is worthless, in order to acquire it behind your back.
Now, if you place high trust in the appraiser, you might not purchase the clock.
However, if you mistrust the appraiser, this negative evidence might be ignored
and you might purchase the clock anyway. This is the essence of how misestimat-
ing the reliability of a source can have counterintuitive effects.
Summary and Future Extensions
Although the model described here was designed to account for some of the
decision-making processes of an expert monitoring sensor reports about chemical
and biological weapons activity, it has wider applications in other contexts. Most
obviously, it has natural implications for understanding the human factors involved
in many sensor monitoring and information fusion tasks. Furthermore, it provides
a new implementation for the recognition component of the RPD model and, in
particular, brings into the picture notions of (a) the decision maker’s understand-
ing of the base rate of events; (b) the decision maker’s mental model of a sensor
(and its reliability); (c) the notion of evaluating an option on its own merits, rather
than requiring the comparison between alternatives; and (d) the use of knowledge
prototypes to make decisions rather than the use of just exemplar-based or case-
based reasoning (cf. Gonzalez et al., 2003; Hintzman, 1988).
16 Journal of Cognitive Engineering and Decision Making / Summer 2009
Figure 5. Probability of correct identification for sensors with high- and low-reliability
r and for which the reliability is overestimated and underestimated. Unreliable sensors
tend to produce reports with lower accuracy than do reliable sensors, but overweighting
the reliability of those sensors has counterintuitive effects: Highly reliable sensors, when
overweighted, produced lower accuracy in some conditions.
Vol_3-2-03-Mueller_0900011.qxd 6/1/09 9:24 AM Page 16
Although the BRDM combines evidence optimally, the demonstrations I reported
showed how errors can stem from a number of sources. For example, the report
used by the decision maker is a noisy representation of the environment. This
constitutes a major source of error in the model. Next, the BRDM uses learned
representations for the events it knows about and learned base rate distributions
across both features and events. These representations can be distorted for a num-
ber of reasons. Also, the BRDM uses a mental model of the evidence-reporting
process, which could theoretically be misspecified in many ways, but which in
the present example could be misspecified by having an inaccurate assessment of the
reliability of the sensor. Together, these offer a number of sources of error in the
model and, perhaps, for decision makers as well.
The prior modeling of REM-II (e.g., Mueller & Shiffrin, 2006) provided some
suggestions about new directions for the BRDM. That model was specifically devel-
oped to account for how information from an event is incorporated into knowledge
structures to be used on later events. Furthermore, it was successfully deployed to
learn meaningful contextual representations based on processing naturalistic text
corpora (Mueller & Shiffrin, 2007). Thus, it is in principle possible to allow a
model to learn the semantic context of a decision maker, in order to better predict
his or her choices and to provide a better simulated teammate. In addition, the
Bayesian framework enables alternative representations to be used and, so, has the
opportunity to extend beyond simple feature-based representations of knowledge.
The BRDM provides a formulation for the recognitional pattern-matching aspect
of the RPD model. However, the original descriptions of the RPD model (e.g., Klein,
1993) go far beyond what the current generation of computational implementations
capture. Most specifically, the model suggests that mental simulation is important
for identifying whether a possible course of action is tenable. An important aspect
of mental simulation is the need to have a mental model of the situation, so that
potential results of actions can be assessed and either accepted or rejected. Small
strides toward that goal have been made by the BRDM model by incorporating
explicit mental models of how information is reported. I anticipate that develop-
ing these notions further, and allowing mental models to be a first-class aspect of
knowledge, will increase understanding of how experts engage in mental simula-
tion and how mental simulation supports decision making.
Acknowledgments
Part of this research was presented at the Workshop on Developing and
Understanding Computational Models of Macrocognition, Havre de Grace, Maryland,
June 3–4, 2008, organized by Laurel Allender and Walter Warwick. This work
was partly funded by the Defense Threat Reduction Agency. The author thanks
Anna Grome and Beth Crandall for conducting interviews and developing qualita-
tive models of chemical officers, upon which some of the present model is based,
and Gary Klein and Rich Shiffrin for developing many of the ideas on which this
model was based.
A Bayesian Recognitional Decision Model 17
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