Optimal generalized truncated sequential Monte Carlo test

Silva, Ivair R.; Assunção, Renato M.

doi:10.1016/j.jmva.2013.06.003

Cited by 15 publications

(12 citation statements)

References 12 publications

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“…In order to save computational effort in sequential Monte Carlo tests without power losses with respect to the conventional Monte Carlo test, Silva and Assunçȃo (2013) introduced an optimal generalized truncated sequential Monte Carlo test. Their proposal provided a theoretical expected number of simulations considerably smaller than the predecessors proposals, but the investigations were not devoted to treat the Monte Carlo power losses with respect to the exact test.…”

Section: Sequential Monte Carlo Test Designs: Current Proposals and Their Limitationsmentioning

confidence: 99%

Truncated sequential Monte Carlo test with exact power

Silva¹,

Assunção²

2018

Braz. J. Probab. Stat.

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Monte Carlo hypothesis testing is extensively used for statistical inference. Surprisingly, despite the many theoretical advances in the field, statistical power performance of Monte Carlo tests remains an open question. Because the last assertion may sound questionable for some, the first goal in this paper is to show that the power performance of truncated Monte Carlo tests is still an unsolved question. The second goal here is to present a solution for this issue, that is, we introduce a truncated sequential Monte Carlo procedure with statistical power arbitrarily close to the power of the theoretical exact test. The most significant contribution of this work is the validity of our method for the general case of any test statistic.

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Section: Sequential Monte Carlo Test Designs: Current Proposals and Their Limitationsmentioning

confidence: 99%

Truncated sequential Monte Carlo test with exact power

Silva¹,

Assunção²

2018

Braz. J. Probab. Stat.

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“…With a sequential procedure, the simulations are interrupted as soon as an evidence about accepting/rejecting H 0 is identified, and then a considerable amount of time can be saved in the simulation process. An optimal design for performing sequential Monte Carlo tests was introduced by Silva and Assunção . Their proposal, denoted here by M C o , minimizes the expected number of simulations for any alternative hypothesis.…”

Section: Overview Of Sequential Analysis and Monte Carlo Testingmentioning

confidence: 99%

“…At the t th simulation, that is, after having simulated U 1 , U 2 ,…, U t , the null hypothesis is not rejected if ψ t =1; it is rejected if ψ t =2, and the simulation process proceeds while ψ t =0, where

ψ_{t} = ({, \begin{matrix} 0, & if R_{u} (t) > δ_{u}, R_{l} (t) > δ_{l} and t < m, \\ 1, & if t > 20 and R_{u} (t) \leq δ_{u} or if t = m, \\ 2, & if R_{l} (t) \leq δ_{l}, \end{matrix})

with δ u = ε / m and δ l =0.001/⌊ α ( m + 1)⌋. This test criterion ensures that the power loss, with respect to the n ‐fixed Monte Carlo test, is not greater than ( ε × 100) % . Also, a valid p ‐value can be calculated for this sequential design.…”

Section: Overview Of Sequential Analysis and Monte Carlo Testingmentioning

confidence: 99%

Composite sequential Monte Carlo test for post‐market vaccine safety surveillance

Silva

2015

Statistics in Medicine

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Group sequential hypothesis testing is now widely used to analyze prospective data. If Monte Carlo simulation is used to construct the signaling threshold, the challenge is how to manage the type I error probability for each one of the multiple tests without losing control on the overall significance level. This paper introduces a valid method for a true management of the alpha spending at each one of a sequence of Monte Carlo tests. The method also enables the use of a sequential simulation strategy for each Monte Carlo test, which is useful for saving computational execution time. Thus, the proposed procedure allows for sequential Monte Carlo test in sequential analysis, and this is the reason that it is called ‘composite sequential’ test. An upper bound for the potential power losses from the proposed method is deduced. The composite sequential design is illustrated through an application for post-market vaccine safety surveillance data.

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“…A variety of procedures for sequential Monte Carlo testing are available in the literature which target different error measures. Silva et al (2009) ;Silva and Assunção (2013) bound the power loss of the test while minimising the expected number of steps. Silva and Assunção (2018, Section 4) construct truncated sequential Monte Carlo algorithms which bound the power loss and the level of significance in comparison to the exact test by arbitrarily small numbers.…”

Section: Introductionmentioning

confidence: 99%

A simple method for implementing Monte Carlo tests

Ding

Hahn

2019

Comput Stat

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We consider a statistical test whose p-value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p-value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.

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Optimal generalized truncated sequential Monte Carlo test

Cited by 15 publications

References 12 publications

Truncated sequential Monte Carlo test with exact power

Truncated sequential Monte Carlo test with exact power

Composite sequential Monte Carlo test for post‐market vaccine safety surveillance

A simple method for implementing Monte Carlo tests

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