Testing maximum entropy models with e-values | Paper Citation Record

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This paper cites For the sake of this example, we put independent, dis- crete uniform priors on the alternative parametersna 1 and nb 1: W1(na 1, nb.

Testing maximum entropy models with e-values For the sake of this example, we put independent, dis- crete uniform priors on the alternative parametersna 1 and nb 1: W1(na 1, nb

Reference 1

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This paper cites (34) In this case, Condition A (30) holds, as the null sufficient statistics can be written as a function of the alternative one: n1 = na 1 + nb.

Testing maximum entropy models with e-values (34) In this case, Condition A (30) holds, as the null sufficient statistics can be written as a function of the alternative one: n1 = na 1 + nb

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Testing maximum entropy models with e-values Unresolved cited work

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Observation 420b3602-de0a-4c1c-b226-c82c46a476d0 · outbound

This paper cites To build it, we first transform the canonical universal distribution into a microcanonical one, by finding Wcan,1 as in (39).

Testing maximum entropy models with e-values To build it, we first transform the canonical universal distribution into a microcanonical one, by finding Wcan,1 as in (39)

Reference 5

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Observation 245d1a4d-7c1f-4fae-8959-4b539f9f1721 · outbound

This paper cites (49) where Wpseudo,0(c0(x)) is defined as in (39).

Testing maximum entropy models with e-values (49) where Wpseudo,0(c0(x)) is defined as in (39)

Reference 6

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Observation 6842d2e5-6ba3-4762-822f-c8c0c9170feb · outbound

This paper cites Thus, we can compute the microcanonical approximation SGRO mic by us- ing the results of Example A.

Testing maximum entropy models with e-values Thus, we can compute the microcanonical approximation SGRO mic by us- ing the results of Example A

Reference 7

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Observation b88c9b52-7b5e-4e1b-94cd-cde19b8717d4 · outbound

This paper cites suggest” rather than “prove.

Testing maximum entropy models with e-values suggest” rather than “prove

Reference 8

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Testing maximum entropy models with e-values Unresolved cited work

Reference 9

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Observation ec6ceef1-a436-4faf-9081-7201ed01d7cc · outbound

This paper cites The key question is whether the probability of observing x = 1 differs between the two groups.

Testing maximum entropy models with e-values The key question is whether the probability of observing x = 1 differs between the two groups

Reference 10

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Testing maximum entropy models with e-values Unresolved cited work

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Reference 12

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Reference 13

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Observation 47e21779-4a84-4429-bd1f-83f67b696c13 · outbound

This paper cites For any given prior W1 on the alternative sufficient statistics, SGRO mic is found exactly by computing W ∗ 0 and applying (32).

Testing maximum entropy models with e-values For any given prior W1 on the alternative sufficient statistics, SGRO mic is found exactly by computing W ∗ 0 and applying (32)

Reference 14

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Observation 75d96205-b363-4c45-8646-c04eeaa954e1 · outbound

This paper cites If na 1 and nb 1 are independently distributed: W1(na 1, nb.

Testing maximum entropy models with e-values If na 1 and nb 1 are independently distributed: W1(na 1, nb

Reference 15

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Reference 16

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Reference 17

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Testing maximum entropy models with e-values Unresolved cited work

Reference 18

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Testing maximum entropy models with e-values Unresolved cited work

Reference 19

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Observation e9be9782-1f71-413b-8eca-6d42171949ba · outbound

This paper cites (79) Given that na 1 and nb 1 are independently distributed, W ∗ 0 (n1) is the convolution of W a can,1(na.

Testing maximum entropy models with e-values (79) Given that na 1 and nb 1 are independently distributed, W ∗ 0 (n1) is the convolution of W a can,1(na

Reference 20

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Observation ccc1413e-b7d1-4f14-a707-cd04cf8d16db · outbound

This paper cites Example 3: Independent beta priors.

Testing maximum entropy models with e-values Example 3: Independent beta priors

Reference 21

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Reference 22

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Reference 23

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This paper cites (85) With this choice, W a 1 and W b 1 are beta-binomial distributions.

Testing maximum entropy models with e-values (85) With this choice, W a 1 and W b 1 are beta-binomial distributions

Reference 24

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This paper cites Whether this expression can 15 be written in closed form depends on the specific values of the beta parameters chosen.

Testing maximum entropy models with e-values Whether this expression can 15 be written in closed form depends on the specific values of the beta parameters chosen

Reference 25

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Observation f9ee54ed-db83-403e-a6c5-b2dffaaf4dfb · outbound

This paper cites The key question remains whether the probability of observing x = 1 differs between groups.

Testing maximum entropy models with e-values The key question remains whether the probability of observing x = 1 differs between groups

Reference 26

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Testing maximum entropy models with e-values Unresolved cited work

Reference 27

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Observation b6927132-784f-48b5-8f45-31c7dac731ed · outbound

This paper cites k} (−1)|S| n1 + k − 1 − P j∈S(nj − n) n1 − 1 × " kY i=1 ni + 1 #−1 , (97) where the sum runs over all possible subsets of {1,.

Testing maximum entropy models with e-values k} (−1)|S| n1 + k − 1 − P j∈S(nj − n) n1 − 1 × " kY i=1 ni + 1 #−1 , (97) where the sum runs over all possible subsets of {1,

Reference 28

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Testing maximum entropy models with e-values Unresolved cited work

Reference 29

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Observation aad129e5-81c7-40b2-aeb3-21987dd948af · outbound

This paper cites (104) W ∗ 0 is then the convolution of all W i can,1(ni 1), which again can be computed numerically or by resorting to the Gaussian approximation (95).

Testing maximum entropy models with e-values (104) W ∗ 0 is then the convolution of all W i can,1(ni 1), which again can be computed numerically or by resorting to the Gaussian approximation (95)

Reference 30

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Reference 31

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Testing maximum entropy models with e-values Unresolved cited work

Reference 32

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Reference 33

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Reference 34

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Observation 7e09ccdf-ced1-4549-b19f-42789b8e2360 · outbound

This paper cites thermodynamic limit.

Testing maximum entropy models with e-values thermodynamic limit

Reference 35

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Reference 36

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Reference 37

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Reference 38

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This paper cites Game-theoretic statistics and safe anytime-valid inference.

Testing maximum entropy models with e-values Game-theoretic statistics and safe anytime-valid inference

Reference 39

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Observation 01bc27bd-8640-4d17-b14c-924fb44bd805 · outbound

This paper cites Hypothesis test- ing with e-values.

Testing maximum entropy models with e-values Hypothesis test- ing with e-values

Reference 40

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Observation 095ef989-8f80-4485-8b77-6a8b6ecca0bf · outbound

This paper cites Asymptotically optimal data analysis for rejecting local realism.

Testing maximum entropy models with e-values Asymptotically optimal data analysis for rejecting local realism

Reference 41

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Observation 76c15676-9fbd-4ed0-9afb-0e248f286d08 · outbound

This paper cites Gr¨ unwald, R.

Testing maximum entropy models with e-values Gr¨ unwald, R

Reference 42

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Observation 9ee9790d-6d24-461e-9186-d0180bd8e6da · outbound

This paper cites Wasserman, A.

Testing maximum entropy models with e-values Wasserman, A

Reference 43

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Observation f3b40253-4dab-4b21-8514-411c2adf3721 · outbound

This paper cites Vovk and R.

Testing maximum entropy models with e-values Vovk and R

Reference 44

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Observation 512f7a1c-35bb-4c49-b168-447d2c7d338b · outbound

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Testing maximum entropy models with e-values Unresolved cited work

Reference 45

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Observation 66ca44b2-8a59-4770-b5b1-f0aa99331189 · outbound

This paper cites Re- verse information projections and optimal e-statistics.

Testing maximum entropy models with e-values Re- verse information projections and optimal e-statistics

Reference 46

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Observation 6665f33a-be52-4ac3-b3ca-0f48b8feea22 · outbound

This paper cites The numeraire e-variable and reverse information pro- jection.

Testing maximum entropy models with e-values The numeraire e-variable and reverse information pro- jection

Reference 47

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Reference 48

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Observation 618e586a-c8dd-4509-b19b-8d9d11576251 · outbound

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Testing maximum entropy models with e-values Unresolved cited work

Reference 49

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Observation f44ac3ed-8ba8-4e50-a4b6-efdf374a536b · outbound

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Reference 50

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Observation 4eba72e8-46af-4c6b-92d6-6c05543846f7 · outbound

This paper cites Squartini and D.

Testing maximum entropy models with e-values Squartini and D

Reference 51

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Observation 22fb06ba-cbfd-4810-b938-fece61be8839 · outbound

This paper cites Squartini, G.

Testing maximum entropy models with e-values Squartini, G

Reference 52

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Observation c738be8a-a422-48d3-aa9b-ca931e3c76ec · outbound

This paper cites Cimini, T.

Testing maximum entropy models with e-values Cimini, T

Reference 53

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Observation 869b22bd-312e-4a85-b9cc-ac8ecd1e255b · outbound

This paper cites Marcaccioli and G.

Testing maximum entropy models with e-values Marcaccioli and G

Reference 54

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Observation c4ec6b99-5b88-4f31-8546-69ab9df2c796 · outbound

This paper cites Marcaccioli and G.

Testing maximum entropy models with e-values Marcaccioli and G

Reference 55

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Observation dc47892c-4c81-4b7b-9bd9-234e7cbee1b0 · outbound

This paper cites Anytime-valid confidence intervals for contingency tables and beyond.

Testing maximum entropy models with e-values Anytime-valid confidence intervals for contingency tables and beyond

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.953371Z

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Observation f9249b13-01d2-49df-b8ec-eb43984efc99 · outbound

This paper cites Generic e-variables for exact sequential k-sample tests that allow for optional stopping.

Testing maximum entropy models with e-values Generic e-variables for exact sequential k-sample tests that allow for optional stopping

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.946767Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7c108ba8-2198-4338-ad29-b785202947df · outbound

This paper cites E-Values for Exponential Families: the General Case.

Testing maximum entropy models with e-values E-Values for Exponential Families: the General Case

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-05T13:02:09.027078Z

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Unavailable: canonical work link unavailable.

Observation 23af4833-8c8c-4f6c-8350-f8cc7d4c3cc1 · outbound

This paper cites Optimal E-Values for Exponential Families: the Simple Case.

Testing maximum entropy models with e-values Optimal E-Values for Exponential Families: the Simple Case

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-05T13:02:09.216132Z

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Observation be498198-c2cd-4156-be6a-0a4ac501f7f2 · outbound

This paper cites Gr¨ unwald.

Testing maximum entropy models with e-values Gr¨ unwald

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.940705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 177a58cf-4463-4534-a703-4f80a3f3f32b · outbound

This paper cites On the existence of powerful p-values and e-values for composite hypotheses.

Testing maximum entropy models with e-values On the existence of powerful p-values and e-values for composite hypotheses

Reference 61

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:02:09.752429Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d16d384-ed48-4f7c-a024-dde344180662 · outbound

This paper cites E-backtesting.

Testing maximum entropy models with e-values E-backtesting

Reference 62

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:02:09.738831Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0ec4346a-931f-4453-aa60-ea1643129b8f · outbound

This paper cites Efficiency of nonparametric e-tests.

Testing maximum entropy models with e-values Efficiency of nonparametric e-tests

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-05T13:02:09.557141Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f305bb4-44bd-445e-9d73-a622a95e4cea · outbound

This paper cites The philosophy of Bayes factors and the quan- tification of statistical evidence.

Testing maximum entropy models with e-values The philosophy of Bayes factors and the quan- tification of statistical evidence

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.934588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ac3f50ca-9f18-4917-9449-3671195e9316 · outbound

This paper cites Gr¨ unwald.The minimum description length principle.

Testing maximum entropy models with e-values Gr¨ unwald.The minimum description length principle

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.928610Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 275a4308-be67-49eb-9a46-54bd3c4aa387 · outbound

This paper cites Gr¨ unwald and T.

Testing maximum entropy models with e-values Gr¨ unwald and T

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.922077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f823f237-d7e9-46f2-9982-8ec804668913 · outbound

This paper cites Yamanishi.

Testing maximum entropy models with e-values Yamanishi

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.915190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 46c6f95b-adc7-4fd9-b501-607186c17a4d · outbound

This paper cites Li and P.

Testing maximum entropy models with e-values Li and P

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.907435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5f269a05-e62c-472a-b82c-8245f5c8ba41 · outbound

This paper cites Tighter pac-bayes bounds through coin-betting.

Testing maximum entropy models with e-values Tighter pac-bayes bounds through coin-betting

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.901204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 28fbbefd-e059-4d76-ba01-8525435566b3 · outbound

This paper cites Barndorff-Nielsen.

Testing maximum entropy models with e-values Barndorff-Nielsen

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.893332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 05bb2907-0e56-4dc2-b99f-3d2d14ba82b7 · outbound

This paper cites Giuffrida, T.

Testing maximum entropy models with e-values Giuffrida, T

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.884908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7c591aec-3332-442d-a02a-46de94da6f9d · outbound

This paper cites Commu- nity detection in interval-weighted networks.

Testing maximum entropy models with e-values Commu- nity detection in interval-weighted networks

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.878745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bb1d00d0-9a52-4b51-a5bc-b51431b177de · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 73

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.872112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3728b69a-c240-4b06-be52-dfed43fb13d6 · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 74

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.865589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation da1ae65d-f65b-44af-b9f7-47efd93c66b7 · outbound

This paper cites Clarke and A.R.

Testing maximum entropy models with e-values Clarke and A.R

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.857437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 75b646e4-573e-4e2e-ac97-06c6c80849e1 · outbound

This paper cites Earnest (user).

Testing maximum entropy models with e-values Earnest (user)

Reference 76

Resolution: verified exact; raw_fallback, observed 2026-08-05T13:02:09.720847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f2c84749-7730-491a-b521-f5003af3a937 · outbound

This paper cites Maximum Entropy Econometrics: Robust Estimation with Limited Data.

Testing maximum entropy models with e-values Maximum Entropy Econometrics: Robust Estimation with Limited Data

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.849529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3f6be80b-353f-4e42-8d6f-e575ecac2012 · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 78

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.842110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d000bd6-092e-437e-82f2-5771af4220ca · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 79

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.834611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d6d8a328-1f24-41cc-b0ff-3282b19e7709 · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 80

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.825729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ecb77576-e205-4e49-a01e-f69d82bd81b8 · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 81

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.819138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8cf6dc87-772c-43f9-a9ab-9cf9666f8790 · outbound

This paper cites Vall` es-Catal` a, T.

Testing maximum entropy models with e-values Vall` es-Catal` a, T

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.812795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 68584243-c07e-457e-83ce-bb63aaf5977a · outbound

This paper cites Strong ensemble nonequivalence in systems with local constraints.

Testing maximum entropy models with e-values Strong ensemble nonequivalence in systems with local constraints

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.804290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c51865d2-5d40-494c-8c75-a8fde20faa0a · outbound

This paper cites Breaking of ensemble equivalence in networks.

Testing maximum entropy models with e-values Breaking of ensemble equivalence in networks

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.797308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0b88ed97-65f7-4053-9d50-f05cffdf269d · outbound

This paper cites Csisz´ ar.

Testing maximum entropy models with e-values Csisz´ ar

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.788719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 096e3d68-0c5b-48c0-8eee-8194d9f41980 · outbound

This paper cites Growth-Optimal E-Variables and an extension to the multivariate Csisz\'ar-Sanov-Chernoff Theorem.

Testing maximum entropy models with e-values Growth-Optimal E-Variables and an extension to the multivariate Csisz\'ar-Sanov-Chernoff Theorem

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-05T13:02:09.610507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9aafba6a-0075-491b-8858-e87770ac6c44 · outbound

This paper cites an unresolved cited work.

Testing maximum entropy models with e-values Unresolved cited work

Reference 87

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:02:09.781782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d45750ea-8e77-440d-bc11-90d4355f4a24 · outbound

This paper cites log P wpseudo,0 0 (x) P ˜w′ 0 0 (x) # + RED1(θ1; P w1 1 ) = Eθ1.

Testing maximum entropy models with e-values log P wpseudo,0 0 (x) P ˜w′ 0 0 (x) # + RED1(θ1; P w1 1 ) = Eθ1

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:02:09.773968Z

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