Economics - Research Publications

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Author: TAYLOR, GREGORY × End date: 2009 × Start date: 2000 × Type: Preprint × Subject: generalised linear model ×

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    Second order Bayesian revision of a generalised linear model
    Taylor, Greg ( 2005-05)
    It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e. multivariate EDF subject to alink function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second order Bayes estimators of parameters of the posterior.The family of second order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with theacquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case.A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readilyderived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this isobtained (Section 6.3).
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    Loss reserving with GLMs : a case study
    Taylor, Greg ; McGuire, Gráinne ( 2004-05)
    This paper provides a case study in the application of generalised linearmodels (“GLMs”) to loss reserving. The study is motivated by approachingthe exercise from the viewpoint of an actuary with a predisposition to theapplication of the chain ladder (“CL”).The data set under study is seen to violate the conditions for application of theCL in a number of ways. The difficulties of adjusting the CL to allow forthese features of the data are noted (Sections 3).Regression, and particularly GLM regression, is introduced as a structured andrigorous form of data analysis. This enables the investigation and modellingof a number of complex features of the data responsible for the violation of the CL conditions. These include superimposed inflation and changes in the rules governing the payment of claims (Sections 4 to 7).The development of the analysis is traced in some detail, as is the production of a range of diagnostics and tests used to compare candidate models and validate the final one.The benefits of this approach are discussed in Section 8.
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    Modelling mortgage insurance as a multi-state process
    Taylor, Greg ; Mulquiney, Peter ( 2006-02)
    Mortgage insurance claims are considered in Section 2 as an absorbing state in aMarkov chain that involves transitions between the states Healthy, In arrears,Property in Possession, Property sold, Loan discharged, Claim. Section 3considers the representation of this process by a cascade of five frequencyGLMs, and a further GLM for claim size. These models are applied to theforecast of technical liabilities in Section 4, and the estimation of the associatedforecast error in Section 5.