measure_joint: Heuristic Joint Distribution for Maximum-a-Posteriori Fit

In timradtke/heuristika: Robust Probabilistic Forecasts to Tinker With

Heuristic Joint Distribution for Maximum-a-Posteriori Fit

Description

Compute the joint density for each combination of actuals, fitted values, range of possible parameter combinations, and their prior distributions. The result is the log joint density for each parameter combination, over which the maximum can be chosen as optimal parameter combination in a maximum-a-posteriori fashion.

Usage

measure_joint(param_grid, priors, family, m, y, y_hat, n_cleaned)

Arguments

param_grid	A matrix of possible parameter values used in grid search
priors	A named list of lists of prior parameters
family	Distribution to be used as likelihood function
m	Scalar indicating the suspected seasonality
y	Input time series against which the model is fitted, used to calculate the errors that are measured via the likelihood; this is a matrix with number of rows equal to the number of observations in the original input time series, and number of columns equal to the number of parameter combinations
y_hat	Fitted values after fitting the states and parameters to y, used to calculate the errors that are measured via the likelihood; this is a matrix with number of rows equal to the number of observations in the original input time series, and number of columns equal to the number of parameter combinations
n_cleaned	Integer number of values treated as outlier, necessary to evaluate the prior on anomalies.

Details

The distributions for the priors are fixed except for their parameters. The user can choose the family of the likelihood, however. Depending on the choice of the likelihood, the standard deviation (or equivalent) will be estimated differently based on the errors between actuals and fitted values.

Missing values are ignored and do not count into the joint density.

Examples

y <- matrix(c(1, 0, 1, -0.05), ncol = 2)
y_hat <- matrix(c(0.9, 0.25, 1.05, 0.05), ncol = 2)

param_grid <- initialize_params_grid()[6:7,]

priors <- add_prior_error(
  priors = list(),
  guess = 1,
  n = 6
) |>
add_prior_level(
  guess = 0.1,
  n = 12
) |>
add_prior_trend(
  prob = 0.1,
  guess = 0.01,
  n = 6
) |>
add_prior_seasonality(
  prob = 0.75,
  guess = 0.9,
  n = 12
) |>
add_prior_anomaly(
  prob = 1/24
)

tulip:::measure_joint(
  param_grid = param_grid,
  priors = priors,
  family = c("norm", "student"),
  m = 12,
  y = y,
  y_hat = y_hat,
  n_cleaned = rep(0, nrow(param_grid))
)

timradtke/heuristika documentation built on April 24, 2023, 1:55 a.m.