prior

Syntax

S = prior(S,Expr,PriorFn,...)
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.

• PriorFn [ 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 in period 4. The prior density is lognormal with mean 0.3 and std deviation 0.05;

s = prior(s,'-srf[ygap,eps,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);

Add a prior saying that the first 16 periods account for at least 90% of total variability (cyclicality) in a 40-period response of ygap to shock eps. This prior is meant to suppress secondary cycles in shock response functions.

s = prior(s, ...
   'sum(abs(srf[ygap,eps,1:16])) / sum(abs(srf[ygap,eps,1:40]))', ...
   [],'lowerBound=',0.9);