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Towards Reliable Inference for Precision Medicine
www.statslab.cam.ac.uk/~qz280/talk/jsm-2021/slides.pdf3 Jun 2024: I Strengths: Free of selection bias; scientifically rigorous.I Limitations: Cannot test too many; no flexibility. ... Selecting positive ITRs. I Simply needs to test the hypotheses H0i : r0 6Γ ri, i = 1,. -
47 A1/12 B1/15 Principles of Statistics (i) Explain in ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2002.pdf28 Apr 2023: Show that we may construct a different, randomised, size α test with the samepower function for θ > θ0. ... f(x; θ) = h(x)g(θ) exp{θt(x)} , x R. Explain in detail how you would test. -
26 1/I/3H Statistics State the factorization criterion for sufficient …
www.statslab.cam.ac.uk/~lab85/resources/Stats2002.pdf28 Apr 2023: What is the result of applying this test at the 0.01 level? [ ... tostrength tests, the number out of the six blocks failing the test being recorded in thefollowing table:. -
PRINCIPLES OF STATISTICS – EXAMPLES 2/4 Part II, Michaelmas ...
www.statslab.cam.ac.uk/~lab85/resources/PoSM23b.pdf31 Oct 2023: From this limiting result: (i) derive a test for the hypothesis H0 : θ = θ0 vs. ... For all these models, derive explicit expressions for the likelihood ratio test statistic ofa simple hypothesis test of H0 : θ = θ0, θ0 Θ, vs. -
STATISTICS Part IBExample Sheet 2 (of 3) Lent 2022 ...
www.statslab.cam.ac.uk/~lab85/resources/StatsL23b.pdf27 Apr 2023: By first deriving the MLEs under each hypothesis, show that the likelihood ratio andPearson’s chi-squared tests are identical to those for the independence test. ... Is the test uniformly most powerfulfor testing H0 : θ = θ0 against H1 : θ > θ0? -
59 1/II/27I Principles of Statistics An angler starts fishing ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2008.pdf28 Apr 2023: What arethe size and power of the test in terms of α and β? ... Is φkadmissible as a test of H0 against Hθ for every θ (0, 1)? -
44 Paper 1, Section I 7H StatisticsSuppose that X1, ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2019.pdf27 Apr 2023: test to test the hypothesis H1 : σ2 > σ̃2 against the hypothesis H0 : σ. ... 2 = σ̃2. Does the F-test depend on whether µ, µ̃ are known? -
CAUSAL INFERENCE - Example Sheet 1 Solutions J. Hera ...
www.statslab.cam.ac.uk/~qz280/teaching/causal-2023/S1.pdf3 Jun 2024: that the sharp null hypothesis is true. For a level-alpha test against the alternative that. ... 1. (2.11). This can then be used to construct asymptotic tests and confidence intervals ofn. -
53 1/II/27I Principles of Statistics State Wilks’ Theorem on ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2005.pdf28 Apr 2023: Explain why for large n thelikelihood-ratio test and the t-test are nearly the same. ... Howcould you use this to make a test of H0 against H1 : µ Θ1? -
Fisher, Statistics, and Randomization
www.statslab.cam.ac.uk/~qz280/talk/fisher-2022/slides.pdf3 Jun 2024: Outline. 1 Fisher and randomizationRole 1: Avoid hidden biasRole 2: Justification of experimental inferenceRole 3: Randomization tests. ... 3 Provide a basis for exact tests of significance and related interval estimates. -
28 1/I/7C Statistics Let X1, . . . ,Xn ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2007.pdf28 Apr 2023: Explain carefully how the test should be implemented. 1/II/18C Statistics. Let X1,. ... yθ1eydy and θ > 1 is unknown. Find the most powerful test of size α,. -
The Randomization Principle in Causal Inference: A Modern Look ...
www.statslab.cam.ac.uk/~qz280/talk/imperial-2022/slides.pdf3 Jun 2024: Pitman (1937).“Significance Tests Which May Be Applied To Samples From Any Populations”. ... What is randomization test? Below: a precise description of conditional randomization tests that is a folklore among a small group ofcausal inference -
32 1/I/7D Statistics The fast-food chain McGonagles have three ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2005.pdf28 Apr 2023: It is desiredto test the hypothesis. H0 : f = f0 against H1 : f = f1,. ... You should state, but need not derive, the distribution of the test statistic.]. -
42 Paper 1, Section I 7H StatisticsDescribe the generalised ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2012.pdf28 Apr 2023: It is desired to test the hypothesis H0 : λ = µ against H1 : λ 6= µ. ... Let w(θ) denote the power function of this test at θ (> 1). -
STATISTICAL MODELLING Part IIC / Michaelmas 2022Example Sheet 3 ...
www.statslab.cam.ac.uk/~qz280/teaching/modelling-2022/E3.pdf3 Jun 2024: Pick a college (possibly your own) and test whether it is an outlier. ... What is the issue withusing your test to now determine whether this college is an outlier? -
48 Paper 1, Section I7H Statistics What does it ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2009.pdf28 Apr 2023: What is the critical region C of a test of the null hypothesis H0 : θ Θ0 against. ... the alternative H1 : θ Θ1? What is the size of a test with critical region C? -
SISCER Module 15 Practice 2: Matching/Weighting and Sensitivity…
www.statslab.cam.ac.uk/~qz280/teaching/siscer-2023/S2.pdf3 Jun 2024: mean (SD)) "0.35 (0.48)" "0.27 (0.45)"## dietary.adequacy.missingind (mean (SD)) "0.32 (0.47)" "0.23 (0.42)"## Stratified by physically.inactive## p test## n "" ""## sex (%) ... Wilcoxon signed rank test, a randomization test.# This is only appliable to -
93 1 TELE1RAFFIC AND DATA1RAFFIC in a Period of ...
www.statslab.cam.ac.uk/~frank/PAPERS/cin.pdf8 May 2009: In Arrow K J and Intriligator M D, editors, Handbook of Mathematical Economics, Vol 1, pages 285330, North Holland, 1981. -
Peter Whittle, 1927-2021 (Peter Whittle in 1985, by Peter ...
www.statslab.cam.ac.uk/~frank/PW/whittle_rss.pdf6 Sep 2021: later awarded the Nobel Prize in Economics for empirical research on cause and effect in the. ... economic phenomena. His book Probability via Expectation (1970, expanded in 2000) is an exposition of probability. -
Draft Memorial Tribute for the National Academy of Engineering ...
www.statslab.cam.ac.uk/~frank/PW/whittle_nae.pdf18 Aug 2021: later awarded the Nobel Prize in Economics for empirical research on cause and effect in the. ... economic phenomena. His book Probability via Expectation (1970, expanded in 2000) is an exposition of probability. -
Practical: Mendelian randomization
www.statslab.cam.ac.uk/~qz280/teaching/siscer-2023/P3.pdf3 Jun 2024: 7. Perform the default Mendelian randomisation tests using the function mr. -
41 Paper 1, Section I 7H StatisticsLet x1, . ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2013.pdf28 Apr 2023: It. is desired to test H0 : f(x) = 1 against H1 : f(x) = 2x. ... Let δ : [0, 1] {0, 1} define a test by δ(x1) = i ‘accept Hi’. -
39 Paper 1, Section I6H Statistics State the Rao-Blackwell ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2022.pdf27 Apr 2023: d) Describe a test of size α for the null hypothesis H0 : σ21 = σ. ... Suppose thereexists a likelihood ratio test of size α for H0 against H1. -
25 1/I/3D Statistics Let X1, . . . ,Xn ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2001.pdf28 Apr 2023: Define the terms size and power for a test of onesimple hypothesis against another. ... Part IB. 26. 2/II/12D Statistics. What is meant by a generalized likelihood ratio test? -
STATISTICAL MODELLING Part IIC, Michaelmas 2019Practical 5: ANOVA and …
www.statslab.cam.ac.uk/~qz280/teaching/modelling-2022/P5S.pdf3 Jun 2024: fit. Would it be possible to compare EssayMarksLM2 and EssayMarksLM5 through an F-test? ... We can check that theanova function does not perform a test:anova(EssayMarksLM2,EssayMarksLM4). -
46 A1/12 B1/15 Principles of Statistics (i) A public ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2003.pdf28 Apr 2023: How might the parametric bootstrapbe used to obtain a test of H0 of exact size α? ... Your account should include a discussion of natural statistics andtheir properties and of various conditional tests on natural parameters. -
29 1/I/7C Statistics A random sample X1, . . ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2006.pdf28 Apr 2023: It is desired to test the hypothesis H0 : θ 0 against thealternative H1 : θ > 0. ... Show that there is a uniformly most powerful test of size α = 1/20and identify a critical region for such a test in the case n = 9. -
IB Statistics Michael TehranchiExample sheet 2 of 3 Lent ...
www.statslab.cam.ac.uk/~mike/stats/Example2.pdf27 Feb 2019: 8. Let X1,. ,Xniid Exp(θ). Find the likelihood ratio test of size α of H0 : θ = θ0 against. ... the size α likelihood ratio test.11. Statisticians A and B obtain independent samples X1,. -
Goodness of fit tests for high-dimensional linear models Rajen ...
www.statslab.cam.ac.uk/~rds37/papers/RPtests8 Apr 2017: In Section 3 we explain how several RP tests can beaggregated into a single test that combines the powers of each of the tests. ... We also compare the power of RP tests to the global test procedure of Goeman et al. -
45 Paper 1, Section I 7H StatisticsLet X1, . ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2016.pdf28 Apr 2023: Find the criticalregion of the most powerful test of size α for the hypotheses H0 : λ = 1 versus H1 : λ = 2.Determine whether or not this test is uniformly most powerful ... Prove that the power function of this test is of theform w(α,β,σ2) = -
BETS: The dangers of selection bias in early analyses ...
www.statslab.cam.ac.uk/~qz280/talk/ido-2021/slides.pdf3 Jun 2024: False negative test: Her first test was negative. A few days later she wastested again and the result came back positive. ... The principle is to only include cases as Wuhan-exported that pass a “beyond areasonable doubt” test. -
57 1/II/27I Principles of Statistics Suppose that X has ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2007.pdf28 Apr 2023: If it is, how (according to the conditionalityprinciple) do we test hypotheses on ψ? ... Explain when this test may be used. (ii) Independent identically-distributed observations X1,. -
BETS: The dangers of selection bias in early analyses ...
www.statslab.cam.ac.uk/~qz280/talk/osu-2020/slides.pdf3 Jun 2024: False negative test: Her first test was negative. A few days later she wastested again and the result came back positive. ... The principle is to only include cases as Wuhan-exported that pass a “beyond areasonable doubt” test. -
The Cycle of Statistical Research Qingyuan Zhao Statistical…
www.statslab.cam.ac.uk/~qz280/talk/ccimi-2020/slides.pdf3 Jun 2024: History. Three movements:. Around 1900: Standard deviation, correlation, regression analysis, method ofmoments, χ2-test, student’s t-test,. ... 1930s – 1940s: Confidence intervals, power of a statistical test, stratifiedsampling, decision theory -
31 1/I/3H Statistics Derive the least squares estimators α̂ ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2003.pdf28 Apr 2023: Derive carefully the test of homogeneity and test the hypothesis that the distributions ofscores among students in the two cities are the same. ... Conduct a goodness-of-fit test at the 0.05 level for the null hypothesis that the coins areall fair. -
41 Paper 1, Section I 7H StatisticsSuppose that X1, ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2015.pdf28 Apr 2023: For 0 < α < 1, derive the test that is most powerful among all tests of size atmost α. ... x6. Explain how to obtain anapproximate size 0.05 test using the value of T. -
83 Paper 1, Section II29J Principles of Statistics Let ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2021.pdf28 Apr 2023: b) Suppose you do not have access to the quantiles of the sampling distribution ofthe Kolmogorov–Smirnov test statistic. ... Describe a test of H0 : F = F0 with size exactly 1/(m 1). -
35 1/I/7H Statistics A Bayesian statistician observes a random ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2008.pdf28 Apr 2023: ii) Find the form of the size-α likelihood–ratio test of the hypothesis. ... The t-test of the null hypothesis that α = 0 against an unrestricted alternativedoes not reject the null hypothesis. -
45 Paper 1, Section I 6H StatisticsLet X1, . ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2021.pdf27 Apr 2023: Conduct a 5% significance level test of the null hypothesis that the medicine andplacebo have the same effect, against the alternative that their effects differ. ... Find a uniformly most powerful test of size α of H0 : θ = 0 againstH1 : θ > 0. -
CAUSAL INFERENCE Part III / Michaelmas 2023Example Sheet 3 ...
www.statslab.cam.ac.uk/~qz280/teaching/causal-2023/E3.pdf3 Jun 2024: 1. Γ πi/(1 πi)πn1i/(1 πn1i). Γ, i [n1]. For the sign test (see ES1 Q8b), derive a “upper bounding” asymptotic randomization p-value for thismodel. -
Tel 01223 334940 e-mail masters-assistant@christs.cam.ac.uk web:…
www.statslab.cam.ac.uk/~frank/PAPERS/DfTHS2.pdf5 Oct 2015: the calculation of the economic benefits generated by HS2. Using the terminology of. ... Economic Case for HS2 (October 2013) of a distribution of benefit cost ratios, reflecting. -
BETS: The dangers of selection bias in early analyses ...
www.statslab.cam.ac.uk/~qz280/talk/ghent-2021/slides.pdf3 Jun 2024: False negative test: Her first test was negative. A few days later she wastested again and the result came back positive. ... The principle is to only include cases as Wuhan-exported that pass a “beyond areasonable doubt” test. -
PRINCIPLES OF STATISTICS – EXAMPLES 2/4 Part II, Michaelmas ...
www.statslab.cam.ac.uk/~lab85/resources/PoSM22b.pdf27 Apr 2023: From this limiting result: (i) derive a test for the hypothesis H0 : θ = θ0 vs. ... For all these models, derive explicit expressions for the likelihood ratio test statistic ofa simple hypothesis test of H0 : θ = θ0, θ0 Θ, vs. -
42 Paper 1, Section I 7H StatisticsConsider an estimator ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2014.pdf28 Apr 2023: You do not need to derive the test.] What conclusion shouldbe reported to the doctor? ... What is the size of this test? Write down an expression forits power. -
42 Paper 1, Section I 7H StatisticsX1, X2, . ...
www.statslab.cam.ac.uk/~lab85/resources/Stats2018.pdf27 Apr 2023: 8H StatisticsDefine a simple hypothesis. Define the terms size and power for a test of one simple. ... Construct a best test of size 0.05 for the null hypothesis. -
SISCER Module 12 Lecture 6: Negative Controls and…
www.statslab.cam.ac.uk/~qz280/teaching/siscer-2023/L6.pdf3 Jun 2024: 2020). Can labor market policies reduce deaths ofdespair? Journal of health economics, 74:102372. -
CAUSAL INFERENCE Part III / Michaelmas 2023Example Sheet 2 ...
www.statslab.cam.ac.uk/~qz280/teaching/causal-2023/E2.pdf3 Jun 2024: Read the abstract andthe section “Tests of Initial a Priori Model” (page 649–651) in the paper titled “Causal Ordering ofAcademic Self-Concept and Academic Achievement: A Multiwave, Longitudinal Panel Analysis” -
STATISTICS Part IBExample Sheet 2 (of 3) Lent 2020 ...
www.statslab.cam.ac.uk/~sb2116/Statistics_IB/Qu2.pdf17 Feb 2020: By first deriving the MLEs under each hypothesis, show that the likelihood ratio andPearson’s chi-squared tests are identical to those for the independence test. ... Is the test uniformly most powerfulfor testing H0 : θ = θ0 against H1 : θ > θ0? -
STATISTICS Part IBExample Sheet 3 (of 3) Lent 2022 ...
www.statslab.cam.ac.uk/~lab85/resources/StatsL23c.pdf27 Apr 2023: Find thelikelihood ratio test of size α. (b) The scientist repeats the test in part (a) for each characteristic j = 1,. ... ratio test of equality of means rejects H0 if. 1I1. Ii=1 ni(Y i Y )2. -
80 Paper 3, Section II27I Principles of Statistics What ...
www.statslab.cam.ac.uk/~lab85/resources/PoS2009.pdf28 Apr 2023: For a problem with random variable X and real parameter θ, define monotonelikelihood ratio (MLR) and monotone test. ... Let φ be a monotonetest, with power function γ() , and let φ′ be any other test, with power function γ′().
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