Abstract:
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While there was a time when inference based on the likelihood function was too difficult to implement, advances in computing soon overcame this, and the likelihood function has long provided a reliable foundation for Bayesian and non-Bayesian analyses in a wide range of applications. The formal justification is largely through asymptotic arguments, under “the usual regularity conditions”. With the increase in complexity of models and size of data, computational and theoretical problems arise anew, and many extensions to the likelihood function and asymptotic theory have been developed in response. This talk gives an overview of likelihood inference, including some recent developments that seem to me both interesting and challenging for statistical theory and practice.
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