WishartMoments: means, inverse means and expected log-determinant
of the Wishart or inverse-Wishart distribution. PartitionedCovariance:
Bartlett decomposition of a partitioned covariance and Gaussian
conditioning. SeparablePrewhiten: temporal prewhitening of a
separable matrix-normal field. NormalGammaDlm: West-Harrison
normal-gamma dynamic linear model filter with unknown observation variance.
HarmonicOzoneDlm: Huerta et al. multi-site harmonic DLM (Kalman
filter). CarrollStCorrelation: Carroll et al. space-time correlation
with its smallest eigenvalue. ProcessConvolutionCovariance: Higdon
process-convolution covariance with location-specific Gaussian kernels.
ArmaAcf: theoretical ARMA autocorrelation function. Identical to the
Python arm morie.fn.stblocks.
Usage
WishartMoments(scale, df, inverse_wishart = FALSE)
PartitionedCovariance(sigma, k, x2 = NULL, mean = NULL)
SeparablePrewhiten(z, rho_t)
NormalGammaDlm(y, F, G, W, m0, C0, n0, S0)
HarmonicOzoneDlm(y, times, coords, a, lam, sigma2, w, m0 = NULL, c0 = 1e+06)
CarrollStCorrelation(coords, times, a, b)
ProcessConvolutionCovariance(coords, kernels, sigma2 = 1, normalize = FALSE)
ArmaAcf(ar = numeric(0), ma = numeric(0), lag_max = NULL)Arguments
- scale
Scale matrix.
- df
Degrees of freedom.
- inverse_wishart
Moments of the inverse Wishart instead.
- sigma
Covariance matrix.
- k
Size of the first block.
- x2
Optional values of the second block.
- mean
Optional mean vector.
- z
Sites by times data matrix.
- rho_t
Temporal correlation matrix.
- y
Observations (vector, or times by sites matrix).
- F
Observation vector.
- G
Evolution matrix.
- W
Scale-free evolution covariance.
- m0, C0, n0, S0
Prior mean, scale-free covariance, degrees of freedom and variance estimate.
- times
Times (hours for the ozone model).
- coords
Site coordinates, one row per site or point.
- a
Harmonic coefficients (ozone model) or the three log-psi coefficients (Carroll).
- lam
Range of the exponential measurement-error correlation.
- sigma2
Variance.
- w
Evolution variances of the level and the two amplitude sets.
- c0
Prior variance of the state.
- b
The three log-phi coefficients.
- kernels
One kernel covariance matrix per location (array) or one matrix.
- normalize
Return correlations.
- ar, ma
AR and MA coefficients.
- lag_max
Largest lag.
References
Shaddick, G., Zidek, J. V. and Schmidt, A. M. (2023). Spatio-Temporal Methods in Environmental Epidemiology with R, 2nd edn. CRC Press.
West, M. and Harrison, J. (1997). Bayesian Forecasting and Dynamic Models, 2nd edn. Springer.
Huerta, G., Sanso, B. and Stroud, J. R. (2004). A spatiotemporal model for Mexico City ozone levels. Applied Statistics 53, 231-248.
Higdon, D., Swall, J. and Kern, J. (1999). Non-stationary spatial modeling. Bayesian Statistics 6, 761-768.