Questions tagged [sequential-analysis]
Hypothesis testing without a fixed sample size.
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Distribution of tuples in chaotic sequences
I study infinite aperiodic sequences like Thue-Morse.
Simple substitution rules allow you to get even more complex.
I'm interested in the distribution of tuples in such sequences.
For example, in Thue-...
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Lower threshold for Sequential Probability Ratio Test on Contingency Table testing
For testing whether a die is fair, we have the log likelihood ratio:
$$
\Lambda = \frac{1}{2} \sum_{i} \mathrm{observed}_i \log\left(\frac{\mathrm{observed}_i}{\mathrm{expected}_i}\right).
$$
Suppose ...
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How to read and use equations for confidence interval from sequential testing
in the book "Group Sequential and Confirmatory Adaptive Designs in Clinical Trials" by Wasmer and Brannath - they explain on p.85 how to calculate a confidence interval.
They consider a ...
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Sequential analysis - adjusting effect size
I am aware that sequential testing is risky, but it makes sense for me to do it anyway. So, I would like to read up, to do it properly.
My idea (which is probably not new):
In my reality, the true ...
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Looking to extract patterns from sequences of codes
I have the following problem: I have a registration of people who enter a building, I have the name, entry date and end date. I also have the times at which events occur inside the building.
I want to ...
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Techniques for Stopping a Diagnostic Study for Safety
I'm working with a group of physicians who are interested in evaluating a new diagnostic tool for detecting colon cancer in older patients. The gold standard to detect colon cancer is with a ...
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How to pick the winner in the "Play the Winner" treatment assignment scheme (Urn model)
"Play the winner" is an intutitive procedure whereby successful treatments in earlier trials have a higher probability of being assigned in later trials. Quoting https://online.stat.psu.edu/...
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Sample size for 2-arm 2-stage trial: R package Trialsize vs rpact vs gsDesign
Which sample size calculation is correct?
Intended design:
Superiority two-arm trial between drug A (intervention) vs drug B (comparator),
outcome is binomial (response or no response to treatment),
...
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prior distribution for iid gaussian, with a known variance
I have been reading Pattern Recognition and Machine Learning by Bishop, and I have a question regarding the prior distribution of an iid Gaussian with known variance.
The relationship $\dfrac{n}{\...
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PRML: Why does the sequential estimation algorithm of normal parameters use $X_N$ but $X_{n-1}$?
I'm reading sequential estimation section 2.3.5 PRML where Bishop introduces Robbins-Monro algorithm to calculate the root of $f(\theta) = E z | \theta = \int zp(z|\theta) dz, (z, \theta) \sim p(z, \...
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Can't reproduce closed form expression from sequential testing
I've been trying to implement and extend some results from the papers "Always Valid Inference" and "Peeking at A/B Tests". The authors provide a closed form expression of the "...
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Identifying synchrony across individual time series
We are working with some time series data that look like the following:
We have three individuals (a1,a2,a3) and then several observations at regular time-intervals. Here, we have 12 time intervals. ...
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Understanding the Sequential Probability Ratio Test
I am trying to understand how to apply SPRT to the following case.
Random variable $X$ is exponentially distributed according to $f(x, \theta)$. Test the following hypotheses
$$
H_0 : \theta \ge \...
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How are group sequential analysis, random walks, and Brownian motion related?
Assume that I am planning a clinical trial comparing two groups using a binary outcome. I will do the $\chi^2$ test after 3 equal enrollment intervals: interim test #1 after $m_1$ enrollments in ...
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Can you use Multilevel Modeling (aka Hierarchical Linear Modeling) with Sequential Linear Modeling?
I have a question regarding the use of Multilevel Modeling (aka Hierarchical Linear Modeling) with Sequential Linear Modeling.
I am trying to perform Sequential Linear Modeling (with a binary outcome) ...
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