# Information Matrix

## Filter Information matrix

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### Functions of a random variable

Assume we have a random variable, \(X\), with expected value \(\eta\) and variance \(\sigma^2\). Often we find ourselves wanting to know the expected value and variance of a function of that random variable, \(f(X)\). Fortunately there are some workable approximations involving only \(\eta\), \(\sigma^2\) and the derivatives of \(f\). In both cases we make use of a Taylor-series expansion of \(f(X)\) around \(\eta\):

\[f(X)=\sum_{n=0}^\infty \frac{f^{(n)}(\eta)}{n!}(X-\eta)^n\]

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: GLM, Filter information matrix by tag: log link, Filter information matrix by tag: logit link

### Mortality by the book

**Written by:**Iain Currie

**Tags:**Filter information matrix by tag: GLM, Filter information matrix by tag: mortality projections, Filter information matrix by tag: R language

### Working with constraints

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: Lee-Carter, Filter information matrix by tag: identifiability constraints, Filter information matrix by tag: GLM

### Out of line

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: GLM, Filter information matrix by tag: linearity, Filter information matrix by tag: survival models

### Groups v. individuals

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: survival models, Filter information matrix by tag: Poisson distribution, Filter information matrix by tag: GLM

### Out for the count

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: survival models, Filter information matrix by tag: force of mortality, Filter information matrix by tag: GLM, Filter information matrix by tag: missing data

### Logistical nightmares

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: GLM, Filter information matrix by tag: logistic regression

### Great Expectations

When fitting statistical models, a number of features are commonly assumed by users. Chief amongst these assumptions is that the expected number of events according to the model will equal the actual number in the data. This strikes most people as a thoroughly reasonable expectation. Reasonable, but often wrong.

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: GLM

### Do we need standard tables any more?

Actuaries are long used to using standard tables. In the UK these are created by the Continuous Mortality Investigation Bureau (CMIB), and the use of certain tables is often prescribed in legislation. As actuaries increasingly move to using statistical models for mortality, it is perhaps natural that they should first consider incorporating standard tables into these models. But are standard tables necessary, or even useful, in such a context?

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: standard table, Filter information matrix by tag: GLM, Filter information matrix by tag: survival models

### Survival models v. GLMs?

At some point you may be challenged to decide whether to use survival models or the older generalised linear models (GLMs). You could be forgiven for thinking that the two were mutually exclusive, especially since some commercial commentators have tried to frame the debate that way.

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: survival models, Filter information matrix by tag: GLM, Filter information matrix by tag: force of mortality