Computational Modeling For Understanding Biological Pathways

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Computational Modeling For Understanding
Biological Pathways

• Lisa Tucker-Kellogg
• CS3108A Computational Thinking
• 30 Sept 2008

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-- Pat Philips, Microsoft Research
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TOPICS and sources

• Computational Thinking
• Quotes from Jeanette Wing
• Modeling and Simulation
• What is modeling
• Formalisms must match the data the goal.
• Much of this material quoted or adapted from
  Wikipedia
• My Research
• Modeling Biological Signaling Pathways
• Fallacies in Probabilisitic Reasoning
• Why we need models for simple scenarios
• Much material due to Norman Fenton,Yuval Shahar
• Additional sources are written on the individual
  slides

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Computational Thinking

• doing arithmetic, solving mathematical
  equations by sheer bulldozing power, is not the
  most significant . Computers are thinking aids
  of enormous potentialities. Merely having them
  around is enough to change the way we think, to
  force investigators in all fields to think
  through their problems along new lines. We are at
  the beginning of a trend that is certain to bring
  machines which not only learn, but which will
  accelerate the rate at which we ourselves learn.
  The revolution to come is difficult to appreciate
  fully. We only know that science, government, and
  industry will change swiftly and radically in the
  years ahead. -- The Thinking Machine, 1962.

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Futurism

• People tend to over-estimate how much change will
  occur in 1-3 years.
• People tend to under-estimate how much change
  will occur in 10-30 years.
• The information you learn now might not be
  useful for long, but the way you learn to think
  will endure.

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Coursework is an artificial workload

• Its fantastically beneficial and worth every
  cent youre paying, but its artificial.
• Real jobs are blah blah blah repetitive,
  boring, gruntwork
• Real problems often come with longer time frames,
  greater risk, and more broadly delegated roles.
• Real jobs are sometimes better grounded in the
  philosophical principles of the field.

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The grounding of different fields

• Mathematics what can I prove, given my axioms?
• Engineering what can I build and how does it
  behave?
• Experimental Natural Science design controlled
  experiments
• Observational Natural Science choose what to
  observe

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Computational Thinking

• Computer science interacts with almost every
  other discipline on campus. Computational
  biology, computational chemistry, computational
  design, computational finance, computational
  linguistics, computational logic, computational
  mechanics, computational neuroscience,
  computational physics, and computational and
  statistical learning . Computer science is not
  just about programming, but about thinking. Our
  long-term vision is to make computational
  thinking commonplace for everyone, not just
  computer scientists.
• -- Jeannette Wing (CMU)

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• Robotics CS Mechanical Engineering
  Electrical Engineering
• Language Technologies CS Linguistics
• Human-Computer Interaction CS Design
  Psychology
• Automated Learning and Discovery CS
  Statistics
• Software CS Public Policy Management

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Computational Thinking

• Computational thinking builds on the power and
  limits of computing processes, whether they are
  executed by a human or by a machine.
  Computational methods and models give us the
  courage to solve problems and design systems that
  no one of us would be capable of tackling alone.

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Computational Modeling

• Computer models have some of the characteristics
  of mental modeling as well as some of the
  characteristics of math modeling and the types of
  modeling done in other disciplines. If a problem
  lends itself to computer modeling, then the
  computer may well be able to carry out the steps
  (procedures, symbol manipulations) needed to
  solve the problem.

From www.iae-pedia.org
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Modeling

• A model is a physical, mathematical, or
  logical representation of a system of entities,
  phenomena, or processes. Basically a model is a
  simplified abstract view of the complex reality.
  It may focus on particular views, enforcing the
  "divide and conquer" principle for a compound
  problem. 
• A model is a formalized interpretation which
  deals with empirical entities, phenomena, and
  physical processes in a logical, mathematical, or
  systematic way.
• A model is also a way in which the human thought
  processes can be amplified.  Models that are
  rendered in software allow scientists to leverage
  computational power to simulate, visualize,
  manipulate and gain intuition about the entity,
  phenomenon or process being represented

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Modeling

• Scientific modeling is the process of generating
  abstract, conceptual, graphical, and/or
  mathematical models. Science offers a growing
  collection of methods, techniques and theory
  about all kinds of specialized scientific
  modeling.
• Modeling is an essential and inseparable part of
  all scientific activity, and many scientific
  disciplines have their own ideas about specific
  types of modeling. 

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Modeling

• Modeling is a comparatively new area of activity
  involving the marriage of ideas from various
  disciplines.
• Modeling techniques include statistical methods,
  computer simulation, system identification, and
  sensitivity analysis. An important issue is to
  understand the underlying dynamics of a complex
  system. (chaos theory)
• Must assess whether the assumptions of a model
  are correct and complete. Does a model
  reflects reality? Deal with divergences between
  theory and data.

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Modeling

• One of the main aims of scientific modelling,
  according to Silvert (2001), is to apply
  quantitative reasoning to observations about the
  world, in the hope of seeing aspects that may
  have escaped the notice of others.
• Typical Steps
• characterize the system,
• make some assumptions about how it works
• translate these into equations and a simulation.
• validate the results or check the models
  predictions.

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Generating a Model

• Typically a model will refer only to some aspects
  of the phenomenon in question, and two models of
  the same phenomenon may be essentially different.
  This may be due to differing requirements of the
  model's end users or to conceptual or aesthetic
  differences by the modelers and decisions made
  during the modeling process.
• Users of a model need to understand the model's
  original purpose and the assumptions that it is
  based on.

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Assumptions and Scope

• Identify abstract principles that are
  approximately true (or true enough for modeling
  purposes).
• Remove issues that are higher and bigger than you
  are willing to take on (such as organism-wide
  cancer from medical viewpoint). Remove issues
  that are too low-level (exact details of variants
  forms, or exact details of how the DNA unwinds if
  all you care about is the behavior of a whole
  organ.)
• Computational thinking what information will
  suffice? what information is missing? What is
  happening that doesnt have a cause?

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Ways to Validate a Model

• Ability to explain past observations
• Ability to predict future observations
• Ability to control events
• Cost of use, especially in combination with other
  models
• Refutability, enabling estimation of the degree
  of confidence in the model
• Simplicity, or even aesthetic appeal

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Computational Modeling

• a computational model is a program that attempts
  to simulate an abstract model of a particular
  system. 
• Computational models can be mathematical models,
  or can be any otherexecutable form.
• computational models can also use external
  inputs, with only part of the system being
  modeled, such as flight simulators.

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Computational Modeling

• What is the point of modeling and simulation?
• Dont want to repeat a prediction that is already
  essentially obvious.
• Dont want to build a model of something thats
  so poorly understood that you dont really know
  anything yet.
• Need to find a middle ground.
• In biology thats particularly hard because
  biologists informally have a lot of intuitive
  knowledge that helps them get the individual
  results.
• Can you formalize the published and unpublished
  knowledge?

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Choice of Formalism

• Determines what information you can represent in
  your modeling.
• Represent encode, capture.
• Affects input data, output results, and
  everything else between.
• Key questions for choosing formalisms amount of
  detail, scale(s), dimensions of variation.
• Scope
• Should we build complex models than incorporate
  everything we know?
• Should be build simple models that incorporate
  only what were sure of?

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Spectrum of Computational Mining / Modeling
Methods
SPECIFIED
ABSTRACTED
differential equations
Markov chains
Bayesian networks
Boolean/fuzzy logic models
mechanisms
statistical mining
(including molecular structure-based computation)
influences and logic
components and relationships
Appropriate approach depends on question and data
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Adapted from Nature Cell Biology, 8 1195 - 1203
(2006) Aldridge et al.
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Why we need mathematical models to understand
biological systems
Weng, Bhalla and Iyengar, Science. 284, 92
(1999).
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Pathway in diagram form
from Nature 407, 789-795
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Pathway knowledge
Time-series measurements of concentrations
Reaction equations with unknown parameters
Parameter estimation
Computational model of pathway dynamics
Biological Predictions
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Semi-precise format
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To be 100 precise we need each step to have a
reaction equation with defined kinetics

• Mass action
• caspase-3 IAP ? caspase-3IAP
• Irreversible mass action
• Ligand Receptor ? LigandReceptor
• Michaelis-Menten
• procaspase-3 ? caspase-3, catalyzed by
  caspase-8. Two parameters, k and Km.

kforward
kbackward
kLR
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Reaction equations are interchangeable with
differential equations that calculate
concentrations over time
kLR

• Receptor Ligand LigandReceptor
• d LR / dt kLR L R
• d L / dt - kLR L R
• d R / dt -kLR L R
• kLR L R velocity

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Pathway knowledge
Time-series measurements of concentrations
Reaction equations with unknown parameters
Parameter estimation
Computational model of pathway dynamics
Biological Predictions
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How much ligand is needed to cause activation of
caspase-8?
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What part of this research is within a
traditional discipline?

• Mathematical equations for the pathway
• Defining the format and parameters of a model
• Experiments for calibrating the model
• Parameter Estimation Method
• Choose the best number for each parameter
• Simulate pathway behaviors
• Biological Experiments

Computer Science
Biology
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Impact of modelingaccording to (Bentele et al.,
2004)

• Communicate interpretations and causes
• Focus debate and avoid pointless argument
• Fewer experiments needed to pinpoint responsible
  regulatory mechanism.
• Probe different scenarios hypotheses.
• They feel they couldnt have gotten the result
  without both model and experiment.

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Benefits of Modeling

• Larger pathways become very complex
• Human intuition isnt good at intuiting dynamics
• Steady states are much easier.
• Help design more efficient experiments.
• Such as choosing timepoints.
• Birds eye view shows possibilities you havent
  considered

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Benefits of Modeling

• Once you set up the model, each thing you try
  with it gives instantaneous results, for free
• And you can try changing ANYTHING.
• Each wet experiment requires a lot of resources.
• Explore a huge number of perturbations
• Each perturbation can be an experimental
  condition.
• Each condition can be a hypothesis, and each
  simulation shows the implications of that
  hypothesis.

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Mental benefits of modeling

• Quantitative awareness
• For example about amount of uncertainty
• Visualize all concentration curves
• Can trace causes, not just correlations
• Many people swear by it
• We limit our thinking unconsciously, especially
  about unmeasurable things
• Complementary to human discussions
• Competitive advantage?

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My Research

• Using differential equations to model the
  dynamics of signaling pathways.

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Nature Cell Biology, 8 1195 - 1203
(2006) Aldridge et al.
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My Research
PI3K active
PI3K inact
PI3K membr
Akt cyto
PIP3
PIP2
? ?
Akt membr
PP2A
RedEnz
PDK1 active
PDK1 membr
PDK1 inact
PTEN
PTENox
p-Akt
DDC
DPI
NOX
catalase
SOD
O2-
H2O2
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O2-
PDK1_inactive
Akt_p
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Whats my modeling for?

• A model cannot be proven correct.
• Modeling cannot disprove anything.
• A model can suggest a view of reality
• Suggest experiments
• Suggest interpretations of datasets
• Suggest implications
• Predict the results of experiments never
  performed before

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Whats my modeling for?

• Proof of Plausibility
• Accounting for the effects of a drug
• Suggesting a missing link
• Hypothesis Management
• Suggesting experiments to differentiate
• Disambiguate Communication
• Meta-study of Existing Reports
• Understand complex dynamics

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Proof of Plausibility

• Drug D causes some mild, subtle upstream effects
  e, f, g, and a massively important downstream
  effect Z.
• D causes large changes in the localization of
  protein e, but the data is noisy. Protein f shows
  15 increased expression, not so big. Etc.
• GOAL QUESTION TO ANSWER Are the effects e,f,g
  sufficient to explain the big downstream effect
  Z?
• Or should we look for D having other effects?

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Proof of Plausibility

• Build a set of differential equations starting
  from reactions D?e, D ? f, D ? g and ending with
  the reactions that create Z.
• Simulate the system computationally. Are the
  effects e,f,g,h sufficient to explain the
  downstream effect Z?
• E.g., Modeling can provide mathematical evidence
  that D?e and D ? f are enough to explain 100 of
  Z, without needing g.

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Hypothesis Management

• Rather than doing experiments to confirm or
  refute the most likely hypothesis
• Provide a systematic list of hypotheses
• According to whatever criteria (e.g. willing to
  measure)
• Simulate each hypothesis
• Automatically filter the results, looking for a
  good match to data, a conclusive result that
  depends on the hypothesis.

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inactiveReducingEnzyme
O2-
Too Presumptious?
ReducingEnzyme(oxidizedactive)
?
Wrong! Whats better?
?
PPaseNHEox
PPaseNHE1(active)
inactiveNHE1
NHE1 (active)
PPaseAkt
PPaseAktox
inactivePDK1
?
Aktcytosol
PIP3
PIP3PDK1(active)
Akt-P
Aktmembrane
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Hypothetical influences of O2- on Akt lifecycle
expression activation
NHE1
PIP3
via PTEN
Akt_m
PDK1
p-Akt_m
via ERM scaffolding
Akt_cytosol
reduced p-Akt_cytosol
p-Akt_cytosol with disulfide
PP2A
?
S-NO activation
thioredoxin
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Hypothesis Management

• Suppose we have a set of several very closely
  related hypotheses about the connectivity in a
  signaling pathway.
• Experimental measurements seem to give
  approximately the same results for each case.
• Design a combination of experimental
  perturbations that will maximize the differences
  between the behaviors of the system under the
  different hypotheses.
• Modeling was successful for suggesting a
  combination of knockout and si-RNA perturbations
  for highlighting the phenomenon we wanted to
  study.

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Disambiguate Communication

• Certain types of complex concepts are hard to
  express in text.
• High-dimensional or dynamic or nested
• If your data provides evidence for something
  complex happening, how do you communicate this
  interpretation unambiguously to your audience?
• Even if you can contruct the logic in your head,
  your reviewers and editors and audience need to
  be able to follow your logic, reproducibly.

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Meta-Study of Existing Studies

• (Future project, not succeeded yet).
• Basic idea
• Everybody accepts that A?B?C?D.
• 4 papers show that A?X in some cell types.
• 2 papers show that X?Y in some cell types.
• 8 papers show that Y?D in some cell types.
• Use modeling to show what fraction of the A?D
  effect could theoretically be explained by
  A?X?Y?D. (Which might shock people.)

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Example a study of dynamics
Urokinase

• AIM 1
• Characterize dynamic behavior of Urokinase
  mediated plasmin, in silico and in vitro.
• AIM 2
• Model the role of plasmin dynamics in liver
  fibrosis
• AIM 3
• Experimentally validate model predictions

TSP1
Plasmin
LTGF-ß1
TGF-ß1
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Detail about first aim

• CONCEPT The mechanism of activation of plasmin
  from urokinase allows for bistability in plasmin.
  
• 1a Model development Define the differential
  equations and the parameters.
• 1b Model simulation Simulate the model in
  MATLAB, under different initial conditions.
• Phase plane and Nullcline analysis Steady state
  analysis of the reduced system of ODEs.
• Bifurcation analysis Analyzing the steady state
  behavior of the system with changes in
  parameters.
• Experimental validation Experimental validation
  of bistable behavior.

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Then study larger implications
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Common Human Errors in Prob/Stat Reasoning

• Slide Credits
• Norman Fentons BBN web site http//www.dcs.qmul.a
  c.uk/norman
• Yuval Shahars class on medical decision-making
  http//www.ise.bgu.ac.il/courses/mdss/

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Probabilistic Reasoning

• Probabilistic reasoning is used extensively in
  computer science, especially in the design of
  algorithms and in artificial intelligence, and
  CompSci is one of the few undergraduate degrees
  outside math that teaches probabilistic
  inference.
• The following fallacies are to help us appreciate
  the importance of using formal methods and not
  just common sense and gut instincts for solving
  problems.
• These are the sorts of things where humans tend
  to intuit the wrong conclusions, and where
  automated reasoning about outcomes, or
  simulations of outcomes, can be particularly
  important.

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Here is a list of names from Hollywood movies

• Tom Hanks
• Ruth Gordon
• George Clooney
• Meg Ryan
• Natalie Wood
• Jackie Chan

Judy Davis Bruce Willis Arnold Schwarzenegger Laur
en Bacall
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Memory Test

• How many names were in the list?
• How many were male
• How many were female
• When given an equal number of each gender in the
  list, if the men in the list are more famous than
  the women in the list, then subjects usually
  think the list has more men than women.
• Increased familiarity makes some names more
  retrievable.

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Search Effects

• Think of English words that have at least three
  letters.
• For a word picked at random that contains the
  letter r,
• Is it more likely that the word would start with
  letter "r, or more likely that r would be the
  third letter?

• "r" is more frequently found in the third
  position of English words than in the first
  position. Subjects usually choose the reverse.
• It is easier to search for words by their first
  letter than by their third, so the first case is
  more available, despite being less numerous.

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• You are given the following information
• Ken is an extremely athletic-looking young man
  who drives a fast car and has an attractive
  girlfriend.
• Is Ken more likely to be a professional football
  player or a nurse?

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Representativeness

• We often judge whether object X belongs to class
  Y by how representative X is of class Y
• Despite differences in the prior probability of
  each profession, subjects usually order the
  probability of potential occupations by
  similarity to representatives.
• Prob(famouspopular) ? Prob(popularfamous)
• Prior probabilities of diseases are often ignored
  when the patient seems to fit the description of
  a rare disease.
• Eastern Equine Encephalitis

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•  Steve is very shy and withdrawn, invariably
  helpful, but with little interest in people, or
  in the world of reality.  A meek and tidy soul,
  he has a need for order and structure, and a
  passion for detail.
• Is Steve a farmer, a librarian, a physician, an
  airline pilot, or a salesman?
• Farmers are half the worlds population. How
  many librarians are there?

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• Write down the last two digits of your student ID
  number on a piece of paper.
• Or passport number if you dont have a student ID
  number.
• Digits only. Please ignore characters.

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Anchoring

• Please write down your estimate
• What percentage of Singapore households own at
  least one iPod?
• Anchoring describes the phenomenon where
  previous estimates (including random or
  uncorrelated numbers) bias later estimates and
  revisions.
• Are your ID numbers correlated with your
  predictions of iPod ownership?

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Insufficient Adjustment  Anchoring

• Anchoring occurs even when initial estimates
  (e.g., percentage of African nations in the UN)
  were explicitly made at random by spinning a
  wheel!
• Anchoring may occur due to incomplete
  calculation, such as estimating by two
  high-school student groups
• the expression  8x7x6x5x4x3x2x1 (median answer
  512)
• with the expression 1x2x3x4x5x6x7x8 (median
  answer 2250)
• Anchoring occurs even with outrageously extreme
  anchors (Quattrone et al., 1984)
• Anchoring occurs even when experts (real-estate
  agents) estimate real-estate prices (Northcraft
  and Neale, 1987)

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Illusory Correlations

• The probability that two events will co-occur
• Is often judged not on the number of
  co-occurrences (which would be correct)
• But mistakenly its judged on the strength/degree
  of their association, from the instances when
  they do co-occur. Even if the number of
  co-occurrences is small.

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• People expect random sequences to be
  representatively random even locally
• E.g., they consider a coin-toss run of HTHTTH to
  be more likely than HHHTTT or HHHHTH
• The Gamblers Fallacy
• the mistaken belief that past events will affect
  future events when dealing with random activities
  
• After there has been a run of reds in roulette,
  people think black is more (or less) likely to be
  next.

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The Illusion of Validity 

• A good match between input information and
  outcome causes people to over-estimate their
  confidence in a prediction.
• Internal consistency of input pattern increases
  confidence
• Redundant, correlated data increases peoples
  confidence in a prediction.
• A series of Bs seems more predictive of a final
  grade-point average than a set of As and Cs

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Misconceptions of Regression 

• People tend to ignore the phenomenon of
  regression towards the mean
• Correlation between parents and childrens
  heights or IQ.
• People expect predicted outcomes to be as
  representative of the input as possible.

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Prep for Exam

• Suppose performing well on an exam requires that
  I set my alarm properly (95 probable), that I
  wake up when my alarm sounds (90 probable), that
  I dont have a headache (95 probable), that my
  bus isnt late (80 probable), and that Im not
  sitting next to somebody who taps their pencil
  (80 probable).
• Probability of performing well is 52. People
  tend to overestimate the probability of
  conjunctive events