Barnard's Monte Carlo Tests: How Many Simulations?

Marriott, F. H. C.

doi:10.2307/2346816

Cited by 160 publications

(100 citation statements)

References 3 publications

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“…The probabilities (3.8) and (3.10) may be computed a posteriori to assess the probability of obtaining p-values as low (or as high) asp N (S 0 ) when the result of the corresponding fundamental test is actually not significant (or significant) at level α. Note also that similar (although somewhat different) calculations may be used to determine the number N of simulations that will ensure a given probability of concordance between the fundamental and the Monte Carlo test [see Marriott (1979)]. …”

Section: Power Functions and Concordance Probabilitiesmentioning

confidence: 99%

“…Only the power of the procedure is influenced by the number of replications, but the power gains associated with lengthy simulations are typically rather small. For further discussion of Monte Carlo tests, see Besag and Diggle (1977), Kiviet (1996, 1998), Edgington (1980), Edwards (1985), Edwards and Berry (1987), Foutz (1980), Jöckel (1986), Kiviet and Dufour (1997), Marriott (1979) and Ripley (1981).…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics

Dufour

2006

Journal of Econometrics

235

245

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Section: Power Functions and Concordance Probabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics

Dufour

2006

Journal of Econometrics

235

245

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“…The computer models were run and the outcomes observed at eight (simulated) days and 12 (simulated) days for the three 6 Â 6 con¢gurations (tessellations 1, 2 and 3) using the calibration data from the 2 Â1 experiments. One thousand runs of each tessellation, providing su¤cient output for testing the model against the biological data at the 5% signi¢cance level (Marriott 1979), were undertaken and ranked. The means and central 95% con¢dence intervals for each state-transition category are also shown in tables 1, 2 and 3 (assuming v 1 and w 0).…”

Section: Resultsmentioning

confidence: 99%

Evidence for emergent behaviour in the community-scale dynamics of a fungal microcosm

Bown

Sturrock

Samson

et al. 1999

Proc. R. Soc. Lond. B

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A stochastic cellular automaton for modelling the dynamics of a two-species fungal microcosm is presented. The state of each cell in the automaton depends on the state of a prede¢ned neighbourhood via a set of conditional probabilities derived from experiments conducted on pairwise combinations of species. The model is tested by detailed comparison with larger-scale experimental microcosms. By employing di¡erent hypotheses which relate the pairwise data to the conditional probabilities in the model, the nature of the local and non-local interactions in the community is explored. The hypothesis that the large-scale dynamics are a consequence of independent interactions between species in a local neighbourhood can be excluded at the 5% signi¢cance level. The form of the interdependencies is determined and it is shown that the outcome of the interactions at the local neighbourhood-scale depends on the community-scale patterning of individuals. The dynamics of the microcosm are therefore an emergent property of the system of interacting mycelia that cannot be deduced from a study of the components in isolation.

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“…For larger problems, the MC hypothesis test approximates that distribution by sampling. Algorithms have been developed to extend the exact test to some logistic regressions, for example, (Hirji et al, 1987;Mehta & Patel, 1995), and yet for larger problems, an approximation by simulation is necessary (Zamar et al, 2007 Besag & Diggle, 1977;Ripley, 1977;Marriott, 1979). Random processes are hypothesized to cause things (animals, plants, etc.)…”

Section: The Monte Carlo Hypothesis Test Can Be Thought Of As An Extementioning

confidence: 99%

“…Nevertheless, we can trace the use of this tool back into the 1950s. Efforts to frame out a standard methodology have been offered from time to time (see Hope (1968);Jockel (1986); Besag & Clifford (1989) Besag & Diggle, 1977;Ripley, 1977;Marriott, 1979). Random processes are hypothesized to cause things (animals, plants, etc.…”

Section: Understanding Sampling Distributionsmentioning

confidence: 99%

Monte Carlo Analysis in Academic Research

Johnson

2013

Oxford Handbooks Online

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Monte Carlo analysis is a research strategy that incorporates randomness into the design, implementation or evaluation of theoretical models. It began in the 1940s, when the development of computer hardware and mathematical models made it possible to generate streams of random numbers. These random number streams are combined with mathematical models in order to create models and evaluate theories of random processes. This chapter attempts to tame this diverse, unmanageable collection of concepts and methods by dividing simulation projects into three types. The first, commonly called "Monte Carlo simulation," is used to evaluate statistical estimators. When an estimation procedure is proposed, it is standard procedure to test it against a variety of simulated research problems. A second type of project, referred to as "Markov chain Monte Carlo" (or MCMC), helps researchers to draw conclusions about complicated probability models for which conventional research strategies do not yield insights. The third 1 type of project arises in the study of complex systems, which are characterized by a large number of loosely interconnected, autonomous elements. Commonly known as agent-based models, these simulations have found enthusiastic advocates in environmental and social sciences.Keywords: Monte Carlo, Markov chain Monte Carlo (MCMC), pseudo random number generation (PRNG), Bayesian statistics, agent-based modeling Monte Carlo (MC) analysis is a general term that refers to research that employs random numbers, usually in the form of a computer model (or simulation). Although this research began in the natural sciences, computer science, and mathematics, it is now widely applied in social science as well. This essay attempts to explain the fundamental ideas that spurred the creation of these new procedures as well as their eventual adaptation for use in social science research.This chapter is not a "how to" guide for simulation, but rather it is a "what for" or "why you might want to" guide. Some of the difficulties that arise in MC research projects are considered as well. It begins with some background information on the development of computers and algorithms for random numbers. After that, the chapter takes up applications in the evaluation of proposed statistical estimators, the practice of Bayesian statistics via computer simulation, and investigation of complex systems through agent-based models. Some conclusions about the challenges that face the field are presented, along with a conclusion. A significant part of the presentation is about the exciting developments that have occurred since 1990. Rapid improvements in hardware and software have opened up opportunities for scholars to work with models that were previously prohibited by conceptual and technical barriers. At the current time, we are able to conceptualize and implement models that were simply impossible just 10 years ago. The extremely rapid progress has been driven by a fruitful interaction of substantive researchers in the natural and social science...

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Barnard's Monte Carlo Tests: How Many Simulations?

Cited by 160 publications

References 3 publications

Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics

Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics

Evidence for emergent behaviour in the community-scale dynamics of a fungal microcosm

Monte Carlo Analysis in Academic Research

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