Week 9 Flashcards

1
Q

Relate a sufficient statistic to the NP lemma

A

It is trivial to prove that if the test statistic inequality holds, so to does the one above

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2
Q

Can you use a sufficient statistic for composite hypothesis testing

A

Yes if the suff stat has a monotone likelihood ratio

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3
Q

Def monotone likelihood ratio

A
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4
Q

Karlin Rubin theorem

A
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5
Q

finding c for LRT

A
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6
Q

Intuitive interpretation of LRT

A
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7
Q

Lecture 27

A

Tests of significance

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8
Q

Purpose of test of significance

A

To measure the strength of the evidence provided by experimental data AGAINST NULL

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9
Q

Test of significance requires

A

Discrepancy measure or test criterion D(x) >= 0

P dist of D under Null

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10
Q

Define significance level or p value

A

= 1 - F0(d)

= 1 - CDF under null hypothesis at discrepancy value d

= area under curve P( D | H0)

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11
Q

Interpretation of p value

A

Smaller the p value, the larger the evidence against null by observed x

Lack of evidence against null CANT be interpreted as evidence in favour of null

p values do not provide evidence in favour of hypothesis

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12
Q

Interpretation of discrepancy measure

A

D(•) ranks samples x according to their strength of evidence against null

If x’ contains stronger evidence against null than x’’ then D(x’) > D(x’’)

Observed discrepancy D = d is regarded as large if the P of getting a larger value is small

That is to say d is an outlier in the dist of D

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13
Q

Distribution of p value

A
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14
Q

Prove dist of p value

A
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15
Q

Choosing discrepancy test

A

Generally

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