It can be used to specify either a prior distribution for a model parameter or a likelihood function for an observation model.
Gaussian(mu, sigma, ordered = NULL, equal = NULL, bounds = list(NULL, NULL), trunc = list(NULL, NULL), k = NULL, r = NULL, param = NULL, ...)
| mu | Either a fixed value or a prior density for the location parameter. |
|---|---|
| sigma | Either a fixed value or a prior density for the shape parameter. |
| ordered | (optional) A logical setting an increasing ordering constraint on any univariate parameter and any unconstrained parameter vector. Ordered simplices (e.g. |
| equal | (optional) A logical setting whether the parameter takes the same value in every hidden state, i.e. the parameter is shared across states. It defaults to unequal parameters. |
| bounds | (optional) A list with two elements specifying the lower and upper bound for the parameter space. Use either a fixed value for a finite bound or NULL for no bounds. It defaults to an unbounded parameter space. |
| trunc | (optional) A list with two elements specifying the lower and upper bound for the domain of the density function. Use either a fixed value for a finite bound or NULL for no truncation. It defaults to an unbounded domain. |
| k | (optional) The number of the hidden state for which this density should be used. This argument is mostly for internal use: you should not use it unless you are acquainted with the internals of this software. |
| r | (optional) The dimension of the observation vector dimension for which this density should be used. This argument is mostly for internal use: you should not use it unless you are acquainted with the internals of this software. |
| param | (optional) The name of the parameter. This argument is mostly for internal use: you should not use it unless you are acquainted with the internals of this software. |
| ... | Other arguments for the density. |
A Density object.
Betancourt, Michael (2017) Identifying Bayesian Mixture Models Stan Case Studies Volume 4. Link.
Other Density: Bernoulli, Beta,
Binomial, Categorical,
Cauchy, CholeskyLKJCor,
Density, Dirichlet,
Exponential, GammaDensity,
ImproperUniform,
InitialFixed, InitialSoftmax,
InverseWishart,
MVGaussianCholeskyCor,
MVGaussian, MVStudent,
Multinomial,
NegativeBinomialLocation,
NegativeBinomial, Poisson,
RegBernoulliLogit,
RegBinomialLogit,
RegBinomialProbit,
RegCategoricalSoftmax,
RegGaussian, Student,
TransitionFixed,
TransitionSoftmax, Wishart
# With fixed values for the parameters Gaussian(0, 1)#> Variable Density: Gaussian (-infty, infty) #> Fixed parameters: 2 (mu = 0, sigma = 1)# With priors for the parameters Gaussian( mu = Gaussian(mu = 0, sigma = 10), sigma = Cauchy(mu = 0, sigma = 10, bounds = list(0, NULL)) )#> Variable Density: Gaussian (-infty, infty) #> Free parameters: 2 (mu, sigma) #> mu : #> Variable Density: Gaussian (-infty, infty) #> Fixed parameters: 2 (mu = 0, sigma = 10), #> sigma : #> Variable Density: Cauchy [0, infty) #> Fixed parameters: 2 (mu = 0, sigma = 10)