Peer review filters and the incentives for high-risk research. Seminar presented at the Santa Fe Institute "New Synthesis for the Science of Science" workshop, May 4-6 2022.

1. A New Synthesis for
the Science of Science
May 4-6, 2022
Peer review filters
and the incentives
for high-risk research
Carl T. Bergstrom
Photo: Carl Bergstrom

2. Peer review filters and the
incentives for high-risk
research
Carl T. Bergstrom
Department of Biology
University of Washington
Kevin Gross
Department of Statistics
North Carolina State University
Kevin Gross, NCSU
A New Synthesis for the Science of Science
May 4-6, 2022

3. Image: Hubble space telescope (cc) Image: Environmental Molecular Sciences Lab

4. (cc) Image Wikimedia CTB
Photo: United Airlines Photo: Luis Acosta

6. If bees did science,
it would likely look
very different from
what we do!

7. What
motivates
scientists?
Imagination Reality
Epistemically pure Epistemically sullied

8. Norms
and
Institutions
Incentives
create
Nature to generate
which are used to query
Knowledge
Scientists
respond to
Research
strategies
in selecting

9. Ideas Proposals
Shall I
propose
this?
Experiments
Shall we
fund
this?
Manuscripts
Shall I
write
this up?
Publications
Shall we
publish
this?
Readings
Shall I
read
this?
Citations
Shall I
cite
this?
Filters in science

10. Ideas Proposals
Shall I
propose
this?
Experiments
Shall we
fund
this?
Manuscripts
Shall I
write
this up?
Publications
Shall we
publish
this?
Peer review filters
Grant
peer review
Manuscript
peer review

11. Ideas Proposals Experiments Manuscripts Publications
Ex post vs. ex ante review
Grant
peer review
Manuscript
peer review
Ex ante
review:
Results are
unknown
Ex post
review:
Results are
known

12. Funding agencies want to support useful research.
Journals want to publish useful research.
Photo: Carl Bergstrom

13. Funding agencies want to support useful research.
Journals want to publish useful research.
But what defines useful ?
Photo: Carl Bergstrom

14. With all else equal, a scientific result is useful to the degree
that it changes beliefs about some epistemic object*.
*A hypothesis, model, claim, parameter value, etc.
Photo: Carl Bergstrom

15. Informal Justification:
If it doesn’t change anyone’s
beliefs, what was the point of
you doing it?
What is the point of me
reading about it?
Photo: Carl Bergstrom

16. Formal Apparatus:
Forecasting theory.
Photo: Carl Bergstrom
Quantify the accuracy
of probabilistic
forecasts
Elicit honest reports of
probabilistic beliefs

17. A scoring rule quantifies how well a
probabilistic prediction anticipates an
outcome x. Lower scores are better.
A proper scoring rule ensures that a
forecaster maximizes her expected
score by reporting her true beliefs.
Formal Apparatus:
Forecasting theory.
Photo: Carl Bergstrom

18. How well do I understand something?
“How well can I predict the outcomes
of observable events or the truth of
empirical propositions?”
Scientists aim to develop explanatorily-
adequate models of physical phenomena.
Photo: Carl Bergstrom

19. Scoring rules are useful for quantifying
scientific progress because they reward
movement towards beliefs that successfully
anticipate observable phenomena, while also
rewarding faithful awareness of uncertainty.
Both are key virtues in science.
Photo: Carl Bergstrom

20. Example: Is there life on Europa?
Suppose I believe there is a 30% chance that
there is life there (x=1) and 70% there is not
(x=0). I predict p=0.3.
Use a scoring rule known as the Brier score:
S(p,x)=(x-p)2
If there is life on Europa, S=(1-0.3) 2 =0.49.
If there is not life there, S=(1-0.3) 2 =0.09.
Photo: Carl Bergstrom

21. Suppose a new observation (y)
leads me to update my belief in
life on Europa from 30% to 50%.
What is the value of that observation to me?
With the scoring rule
framework, the value is the
expected increase in my score
resulting from this update.
Photo: Carl Bergstrom

22. For a scoring rule S, the cost of using probabilities p to forecast,
when the real probabilities are q, is the divergence d(q||p).
So if based on an observation y I update my beliefs p to q(p,y), I
expect this to improve my score by d(q(p,y)||p).
Photo: Carl Bergstrom

23. Example: Is there life on Europa?
After observing y, I update my beliefs from p=0.3 to p=0.5.
The value of this is the divergence* d(0.5||0.3) = 0.2.
* Divergence under the Brier score is just the change in probability assignment.
Photo: Carl Bergstrom

24. So that’s the ex-post value of an experiment in the scoring rule framework:
The divergence between prior and posterior after observing the outcome.
Photo: Carl Bergstrom

25. Cool digression: A Shannon information scoring rule.
If instead of using the Brier score
S(P
,x)=(x-px)2 we use the ignorance
score (or surprisal) S(P
, x) = -Log(px),
the divergence is the familiar
Kullback-Leibler divergence.
Photo: Carl Bergstrom

26. Given Bayesian updating and a proper scoring rule,
the greater the change in beliefs, the greater the
value of updating.
Photo: Carl Bergstrom

27. Not all research is
basic science.
Sometimes you
have problems you
want to solve.
Then predicting
arbitrary things may
not be a good
measure of value.
Photo: Carl Bergstrom

28. It’s ok.
We can always define the value of an experiment —
for any decision problem we want.
Photo: Carl Bergstrom

30. Frankel and Kamenica:
Every decision problem induces a measure of information/uncertainty
with the properties below
Every information measure with these properties corresponds to a
decision problem.
1. The information from an observation is always non-negative
2. Observations that do not change beliefs carry no information
3. The order in which observations are made do not on average
change the total amount of information obtained.

31. To summarize, any decision problem induces
an information measure such that the more
information you acquire, the better.

32. When the decision problem involves
prediction, the more it makes you
change your beliefs, the more
valuable the information.

33. With all else equal, a scientific result is useful to the degree
that it changes beliefs about some epistemic object*.
*A hypothesis, model, claim, parameter value, etc.
Photo: Carl Bergstrom

34. Thus far we have considered the
ex post value of an experiment.
But we often have to make make
decisions on what to do ex ante.

35. So what is the value of an experiment, ex ante?
Simple: The expected ex post value, given beliefs.
Photo: Carl Bergstrom

36. Cool digression: Shannon
information scoring rule.
If we use the S(P
, x) = -Log(px),
ex ante value of an experiment
is the mutual information
between what an investigator
believes will happen and what
will actually happen.
Photo: Carl Bergstrom

37. Whose beliefs do we use
to set these probabilities?
Whose beliefs do we measure the shift in?

38. What is the ex ante value of an experiment
to an investigator?

39. Example: binary hypothesis test.
Experiment returns an observationY drawn from a normal distribution
with mean μ0 if H0 is true and mean μ0 if H0 is true.

40. Example: binary hypothesis test.
Experiment returns an observationY drawn from a normal distribution
with mean μ0 if H0 is true and mean μ0 if H0 is true.

41. The most useful experiment to the
investigator is the most uncertain one.
But that’s the value of the result to
the investigator themselves.
To get published, the investigator needs to come up
with a result that is useful to their peers, not to
themself.

42. The investigator can leverage their private
beliefs.
Investigator’s probabilities
Reviewers’ probabilities

43. The investigator can leverage their private
beliefs.
Investigator’s probabilities
Reviewers’ probabilities

44. The investigator should pick
an experiment where their
expectations different from
that of the community.
But not one that the
community will consider wildly
improbable, and just ignore.

45. Ex ante review doesn’t allow the investigator
to leverage private beliefs.
The reason is that the reviewers don’t know the result of the
experiment when they evaluate the merits of conducting it.
Reviewers never expect to be surprised, ex ante.
Ex ante, investigators have to propose experiments that
reviewers think will work.

46. Ideas Proposals Experiments Manuscripts Publications
Ex post vs. ex ante review
Grant
peer review
Manuscript
peer review
Investigator wants an
experiment the reviewers
expect will be useful
Investigator wants an
experiment that reviewers will
find surprising (and thus
probably would not have
expected to be useful ex

47. How do reviewers evaluate an experiment
ex ante?

48. Shared uncertainty vs. scientific controversy
Shared Uncertainty: Everyone agrees it’s a 50-50 proposition.
Scientific Controversy: Half of the reviewers think it’s almost certain in
one direction, half think it’s almost certain in the other.
Which do ex ante reviewers prefer to resolve?

49. Shared uncertainty vs. scientific controversy
In a scientific controversy, no one expects to be surprised and thinks
private value is low. But they expect the experiment will be highly
informative to their opponents and thus public value is high.
In a shared uncertainty, everyone expects the result to be somewhat
information to everyone. Public and private value are both moderate.
Private value favors shared uncertainty.
Public value favors scientific controversy.

50. Simulation: problem selection
Large population of binary hypotheses H.
Large population of investigators I.
Each investigator has belief IH about the probability of hypothesis H.
We simulate 50 investigators.
Each investigator samples 15 hypotheses and, knowing the
distribution of others’ beliefs chooses to test the one with the highest
expected value.

51. Ex post review
If investigators are concerned only
about ex-post review they would like
to test hypotheses they find likely but
others uniformly consider unlikely but
not impossible.
Such hypotheses are thin on the
ground and so investigators do the
best they can.
Mean community belief in hypothesis
favored by the investigator
SD
belief
in
hypothesis

52. Ex ante review: private value
With ex ante review by reviewers
concerned with private value,
investigators seek experiments with
mean belief around 50% and minimal
heterogeneity
Investigators can find something close
to this and do so.
Mean community belief in hypothesis
favored by the investigator
SD
belief
in
hypothesis

53. Ex ante review: public value
With ex ante review by reviewers
concerned with private value,
investigators seek experiments with
mean belief around 50% and
substantial heterogeneity.
Investigators can find something close
to this and do so.
Mean community belief in hypothesis
favored by the investigator
SD
belief
in
hypothesis

54. Proposition
Given any proper scoring rule S, an average belief P about some
proposition, and a proposal for a definitive experiment E:
1. If reviewers value the proposal according to what they will learn
themselves, any heterogeneity in beliefs will decrease their ex ante
valuation of E.
2. If reviewers value the proposal according to what others will learn,
any heterogeneity in beliefs will increase their ex ante valuation of E.

55. Implications
Experiments are valuable to the
degree that they change beliefs.
We can formalize this intuition
using the theory of scoring rules.
Photo: Carl Bergstrom

56. Implications
Investigators can leverage private beliefs in
ex post review, to choose experiments they
consider likely to surprise their colleagues.
In ex ante review, investigators can’t. They
have to choose experiments that reviewers
consider likely to be informative.
This creates a tension between the two
filter stages.
Photo: Carl Bergstrom

57. Implications
Because grants are reviewed ex
ante, researchers cannot afford
to submit risky grant proposals
— reviewers expect them to fail.
Other modes of ex ante review,
such as registered reports, may
similarly discourage risky work.
Photo: Carl Bergstrom

58. Implications
Ex ante reviewers will favor
resolving shared uncertainties if
they focus on how much they
expect to be surprised
themselves.
They will favor resolving scientific
controversies if they focus on
how much the experiment will
change the beliefs of others.
Photo: Carl Bergstrom

59. Implications
Photo: Carl Bergstrom
Funding agencies can steer the outcome by
telling reviewers to consider their own value,
or the value to the community. Grant panel
discussions may help with the latter.

60. http://carlbergstrom.com