Jekyll2018-10-16T16:45:27+01:00http://personal.soton.ac.uk/heo1u16//Helen OgdenPersonal website for Helen Ogden, Lecturer in Statistics, University of Southampton, UK
On the error in Laplace approximations of high-dimensional integrals2018-08-21T00:00:00+01:002018-08-21T00:00:00+01:00http://personal.soton.ac.uk/heo1u16/preprints/2018/08/21/laplaceHelen Ogden“On asymptotic validity of naive inference with an approximate likelihood” published in Biometrika2017-02-18T00:00:00+00:002017-02-18T00:00:00+00:00http://personal.soton.ac.uk/heo1u16/news/2017/02/18/new_paper<p>My paper “On asymptotic validity of naive inference with an approximate likelihood” has been published in Biometrika. It is available
<a href="https://academic.oup.com//biomet/article/104/1/153/3003356/On-asymptotic-validity-of-naive-inference-with-an?guestAccessKey=19b0b41d-02b4-450f-9a15-532c845f2c17">here</a>.</p>Helen OgdenMy paper “On asymptotic validity of naive inference with an approximate likelihood” has been published in Biometrika. It is available
here.On asymptotic validity of naive inference with an approximate likelihood2017-02-18T00:00:00+00:002017-02-18T00:00:00+00:00http://personal.soton.ac.uk/heo1u16/papers/2017/02/18/approximate_likelihoods_bka<p>by H.E. Ogden</p>
<p>Biometrika (2017) 104 (1): 153-164.</p>
<h3 id="link-to-paperhttpsacademicoupcombiometarticle10411533003356on-asymptotic-validity-of-naive-inference-with-anguestaccesskey19b0b41d-02b4-450f-9a15-532c845f2c17"><a href="https://academic.oup.com//biomet/article/104/1/153/3003356/On-asymptotic-validity-of-naive-inference-with-an?guestAccessKey=19b0b41d-02b4-450f-9a15-532c845f2c17">Link to paper</a></h3>
<h3 id="summary">Summary</h3>
<p>Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the true likelihood. In this paper, we describe conditions which guarantee that such naive inference with an approximate likelihood has the same first-order asymptotic properties as inference with the true likelihood. We investigate the implications of these results for inference using a Laplace approximation to the likelihood in a simple two-level latent variable model and using reduced dependence approximations to the likelihood in an Ising model.Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, it is common to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the exact likelihood. In this paper, we describe conditions on the approximate likelihood which guarantee that inference with the approximate likelihood has the same first-order asymptotic properties as exact likelihood inference. We investigate the implications of these results in a simple two-level latent variable model, determining the number of repeated observations on each item required for the Laplace approximation to give asymptotically correct inference.</p>Helen Ogdenby H.E. OgdenA caveat on the robustness of composite likelihood estimators: The case of a mis-specified random effect distribution2016-08-01T00:00:00+01:002016-08-01T00:00:00+01:00http://personal.soton.ac.uk/heo1u16/papers/2016/08/01/robustness_CLHelen OgdenA sequential reduction method for inference in generalized linear mixed models2015-10-24T00:00:00+01:002015-10-24T00:00:00+01:00http://personal.soton.ac.uk/heo1u16/papers/2015/10/24/sequential_reduction<p><a href="http://projecteuclid.org/euclid.ejs/1423229753">http://projecteuclid.org/euclid.ejs/1423229753</a></p>
<h3 id="abstract">Abstract</h3>
<p>The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information available on each random effect. The sequential reduction method described in this paper exploits the dependence structure of the posterior distribution of the random effects to reduce substantially the cost of finding an accurate approximation to the likelihood in models with sparse structure.</p>
<h3 id="related-work">Related work</h3>
<p>I have written an R package <a href="https://github.com/heogden/glmmsr">glmmsr</a>, which
may be used to fit Generalized Linear Mixed Models, with a choice of which
method to use to approximate the likelihood, including the sequential
reduction method described in this paper.</p>Helen Ogdenhttp://projecteuclid.org/euclid.ejs/1423229753A sequential reduction method for inference in generalized linear mixed models2014-02-01T00:00:00+00:002014-02-01T00:00:00+00:00http://personal.soton.ac.uk/heo1u16/theses/2014/02/01/PhDHelen Ogden