What is the common method of comparing the two types of importance samplers?

Simulated maximum likelihood based on simple importance sampling is usually prescribed as an iterative method, with new importance samplers with θ0 in equation (2) based on current θ.

What is the mean of the scores for the two types of importance samplers?

The means of the score functions are about 0 for both types of importance sampler, corroborating13that the authors have found the approximate maximum likelihood.

What is the key to a computationally efficient implementation of SML?

The key to computationally efficient implementation of SML is hence importance samplers that give W as defined in equation (6) with low variance.

What is the example of an optimal importance sampler?

A real example of an optimal EPD importance sampler is the EPD Laplace importance sampler as defined below applied to Gaussian linear mixed models.

What is the difference between the two types of EPD importance samplers?

Since g must be a continuous function of θ, accept-reject algorithms and more advanced samplers that use acceptreject sampling as building blocks, such as the Metropolis algorithm, are not compatible with EPD importance sampling.

Open AccessJournal Article10.1007/S00180-011-0230-Z

Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling

Christian N. Brinch

- 01 Mar 2012

- Computational Statistics

- Vol. 27, Iss: 1, pp 13-28

TL;DR: The theoretical points are illustrated by applying Laplace importance sampling in both variants to the classic salamander mating model, and the negative assessment by the coupling of the algorithm with “simple importance samplers”,Samplers that are not explicitly parameter dependent.

Abstract: There exists an overall negative assessment of the performance of the simulated maximum likelihood algorithm in the statistics literature, founded on both theoretical and empirical results At the same time, there also exist a number of highly successful applications This paper explains the negative assessment by the coupling of the algorithm with “simple importance samplers”, samplers that are not explicitly parameter dependent The successful applications in the literature are based on explicitly parameter dependent importance samplers Simple importance samplers may efficiently simulate the likelihood function value, but fail to efficiently simulate the score function, which is the key to efficient simulated maximum likelihood The theoretical points are illustrated by applying Laplace importance sampling in both variants to the classic salamander mating model

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Most frequently asked questions

1. Why should a document of successful application of the method include histograms of replicated?

Because simulated maximum likelihood can produce heavy-tailed distributions of estimates, a documentation of successful application of the method should arguably include histograms of replicated parameter estimates.

2. What is the prerequisite for a powerful simulated maximum likelihood algorithm?

A necessary prerequisite for a powerful simulated maximum likelihood algorithm is that it is based on explicitly parameter dependent importance sampling - otherwise efficient simulation of the score function is not possible.

3. What is the reason for the poor performance of the simple Laplace importance sampling algorithm?

the poor performance of the simple Laplace importance sampling algorithm in this example most likely reflects the drawbacks discussed in Section 2.14Simulated maximum likelihood is a powerful method for approximating the exact maximum likelihood estimates in models where the likelihood function contains moderately difficult integrals.

4. How does the simulated maximum likelihood algorithm work?

The simulated maximum likelihood algorithm proceeds by simulating the likelihood function, and finding the maximum of the simulated function, typically by numerical optimization methods.

Table 1 Mean, median and standard deviation in 1000 replications of simulated maximum likelihood estimation using EPD Laplace importance sampling with importance sample size 1000, corresponding to histograms in Figure 1.

Table 2 Simulated maximum likelihood estimate of salamander mating model based on EPD Laplace importance sampling with importance sample size 100 000.

Table 4 Asymptotic ”simulation errors” derived from simulated score functions and approximated lower bounds based on ”missing information”.

Fig. 1 Histograms of parameter estimates from 1000 replications of simulated maximum likelihood estimation using EPD Laplace importance sampling with importance sample size 1000.

Table 3 Mean and standard deviation in 1000 simulated score functions at approximate maximum likelihood, based on simple and EPD Laplace importance sampling with importance sample size 1000.

Citations

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- 03 Oct 2011

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Monia Ranalli

- 01 Sep 2016

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TL;DR: In this paper, the authors modify existing approaches to account for the unique decision-making process characterizing catcher-processor's production technologies, focusing on sequential decisions regarding what products to produce and the factors that influence productivity once those decisions are made using a multiproduct revenue function.

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References

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Monte Carlo Statistical Methods

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- 01 Jan 1999

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Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling

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AI Agents for this Paper

Most frequently asked questions

1. Why should a document of successful application of the method include histograms of replicated?

2. What is the prerequisite for a powerful simulated maximum likelihood algorithm?

3. What is the reason for the poor performance of the simple Laplace importance sampling algorithm?

4. How does the simulated maximum likelihood algorithm work?

5. What is the common method of comparing the two types of importance samplers?

6. What is the mean of the scores for the two types of importance samplers?

7. What is the key to a computationally efficient implementation of SML?

8. What is the example of an optimal importance sampler?

9. What is the difference between the two types of EPD importance samplers?

Figures

Citations

Maximum likelihood estimation in nonlinear structured fisheries models using survey and catch-at-age data

A simulated maximum likelihood method for estimation of stochastic Wiener systems

Recent Developments in Approximated-Likelihood Inference Methods for Latent Variable Models

Topics in Statistical Models for Network Analysis

Productivity Growth and Product Choice in Fisheries: the Case of the Alaskan Pollock Fishery Revisited

References

Monte Carlo Statistical Methods

Generalized Linear Models

Generalized, Linear, and Mixed Models

Generalized Linear Models

Generalized Linear Models (2nd ed.)

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