IRIS Toolbox Reference Manual

## prior

Add new prior to system priors object

#### Syntax

    S = prior(S,Expr,PriorFunc,...)
    S = prior(S,Expr,[],...)

#### Input arguments

- `S` [ systempriors ] - System priors object.

- `Expr` [ char ] - Expression that defines a value for which a prior density will be defined; see Description for system properties that can be referred to in the expression.

- `PriorFunc` [ function_handle | empty ] - Function handle returning the log of prior density; empty prior function, `[]`, means a uniform prior.

#### Output arguments

- `S` [ systempriors ] - The system priors object with the new prior added.

#### Options

- `'lowerBound='` [ numeric | `-Inf` ] - Lower bound for the prior.

- `'upperBound='` [ numeric | `Inf` ] - Upper bound for the prior.

#### Description

##### System properties that can be used in `Expr`

- `srf[VarName,ShockName,T]` - Plain shock response function of variables `VarName` to shock `ShockName` in period `T`. Mind the square brackets.

- `ffrf[VarName,MVarName,Freq]` - Filter frequency response function of transition variables `TVarName` to measurement variable `MVarName` at frequency `Freq`. Mind the square brackets.

- `corr[VarName1,VarName2,Lag]` - Correlation between variable `VarName1` and variables `VarName2` lagged by `Lag` periods.

- `spd[VarName1,VarName2,Freq]` - Spectral density between variables `VarName1` and `VarName2` at frequency `Freq`.

If a variable is declared as a `log-variable`, it must be referred to as `log(VarName)` in the above expressions, and the log of that variables is returned, e.g. `srf[log(VarName),ShockName,T]`. or `ffrf[log(TVarName),MVarName,T]`.

##### Expressions involving combinations or functions of parameters

Model parameter names can be referred to in `Expr` preceded by a dot (period), e.g. `.alpha^2 + .beta^2` defines a prior on the sum of squares of the two parameters (`alpha` and `beta`).

#### Example

Create a new, empty systemprios object based on an existing model.

    s = systempriors(m);

Add a prior on minus the shock response function of variable `ygap` to shock `eps_pie` in period 4. The prior density is lognormal with mean 0.3 and std deviation 0.05;

    s = prior(s,'-srf[ygap,eps_pie,4]',logdist.lognormal(0.3,0.05));

Add a prior on the gain of the frequency response function of transition variable `ygap` to measurement variable 'y' at frequency `2*pi/40`. The prior density is normal with mean 0.5 and std deviation 0.01. This prior says that we wish to keep the cut-off periodicity for trend-cycle decomposition close to 40 periods.

    s = prior(s,'abs(ffrf[ygap,y,2*pi/40])',logdist.normal(0.5,0.01));

Add a prior on the sum of parameters `alpha1` and `alpha2`. The prior is normal with mean 0.9 and std deviation 0.1, but the sum is forced to be between 0 and 1 by imposing lower and upper bounds.

    s = prior('s,'alpha1+alpha2',logdist.normal(0.9,0.1), ...
        'lowerBound=',0,'upperBound=',1);

IRIS Toolbox. Copyright © 2007—2013 Jaromir Benes.