meridian.model.prior_distribution.PriorDistribution

Contains prior distributions for each model parameter.

meridian.model.prior_distribution.PriorDistribution(
    *,
    knot_values: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Normal(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(5.0), name=constants.\n    KNOT_VALUES)),
    tau_g_excl_baseline: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Normal(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(5.0), name=constants.\n    TAU_G_EXCL_BASELINE)),
    beta_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.BETA_M)),
    beta_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.BETA_RF)),
    beta_om: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.BETA_OM)),
    beta_orf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.BETA_ORF)),
    eta_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(1.0), name=constants.ETA_M)),
    eta_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(1.0), name=constants.ETA_RF)),
    eta_om: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(1.0), name=constants.ETA_OM)),
    eta_orf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(1.0), name=constants.ETA_ORF)),
    gamma_c: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Normal(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(5.0), name=constants.GAMMA_C)),
    gamma_n: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Normal(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(5.0), name=constants.GAMMA_N)),
    xi_c: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.XI_C)),
    xi_n: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.XI_N)),
    alpha_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Uniform(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(1.0), name=constants.ALPHA_M)),
    alpha_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Uniform(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(1.0), name=constants.ALPHA_RF)),
    alpha_om: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Uniform(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(1.0), name=constants.ALPHA_OM)),
    alpha_orf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Uniform(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(1.0), name=constants.ALPHA_ORF)\n    ),
    ec_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.TruncatedNormal(\n    backend.np_float_dtype(0.8), backend.np_float_dtype(0.8), backend.\n    np_float_dtype(0.1), backend.np_float_dtype(10.0), name=constants.EC_M)),
    ec_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.\n    TransformedDistribution(backend.tfd.LogNormal(backend.np_float_dtype(\n    0.7), backend.np_float_dtype(0.4)), backend.bijectors.Shift(backend.\n    np_float_dtype(0.1)), name=constants.EC_RF)),
    ec_om: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.TruncatedNormal(\n    backend.np_float_dtype(0.8), backend.np_float_dtype(0.8), backend.\n    np_float_dtype(0.1), backend.np_float_dtype(10.0), name=constants.EC_OM)),
    ec_orf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.\n    TransformedDistribution(backend.tfd.LogNormal(backend.np_float_dtype(\n    0.7), backend.np_float_dtype(0.4)), backend.bijectors.Shift(backend.\n    np_float_dtype(0.1)), name=constants.EC_ORF)),
    slope_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Deterministic(\n    backend.np_float_dtype(1.0), name=constants.SLOPE_M)),
    slope_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.LogNormal(backend.\n    np_float_dtype(0.7), backend.np_float_dtype(0.4), name=constants.SLOPE_RF)),
    slope_om: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Deterministic(\n    backend.np_float_dtype(1.0), name=constants.SLOPE_OM)),
    slope_orf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.LogNormal(backend.\n    np_float_dtype(0.7), backend.np_float_dtype(0.4), name=constants.SLOPE_ORF)\n    ),
    sigma: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.HalfNormal(backend.\n    np_float_dtype(5.0), name=constants.SIGMA)),
    roi_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.LogNormal(backend.\n    np_float_dtype(0.2), backend.np_float_dtype(0.9), name=constants.ROI_M)),
    roi_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.LogNormal(backend.\n    np_float_dtype(0.2), backend.np_float_dtype(0.9), name=constants.ROI_RF)),
    mroi_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.LogNormal(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(0.5), name=constants.MROI_M)),
    mroi_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.LogNormal(backend.\n    np_float_dtype(0.0), backend.np_float_dtype(0.5), name=constants.MROI_RF)),
    contribution_m: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Beta(backend.\n    np_float_dtype(1.0), backend.np_float_dtype(99.0), name=constants.\n    CONTRIBUTION_M)),
    contribution_rf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Beta(backend.\n    np_float_dtype(1.0), backend.np_float_dtype(99.0), name=constants.\n    CONTRIBUTION_RF)),
    contribution_om: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Beta(backend.\n    np_float_dtype(1.0), backend.np_float_dtype(99.0), name=constants.\n    CONTRIBUTION_OM)),
    contribution_orf: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.Beta(backend.\n    np_float_dtype(1.0), backend.np_float_dtype(99.0), name=constants.\n    CONTRIBUTION_ORF)),
    contribution_n: backend.tfd.Distribution = dataclasses.field(default_factory=lambda : backend.tfd.TruncatedNormal(loc=\n    backend.np_float_dtype(0.0), scale=backend.np_float_dtype(0.1), low=-\n    backend.np_float_dtype(1.0), high=backend.np_float_dtype(1.0), name=\n    constants.CONTRIBUTION_N))
)

PriorDistribution is a utility class for Meridian. The required shapes of the arguments to PriorDistribution depend on the modeling options and data shapes passed to Meridian. For example, ec_m is a parameter that represents the half-saturation for each media channel. The ec_m argument must have either batch_shape=[] or batch_shape equal to the number of media channels. In the case of the former, each media channel gets the same prior.

An error is raised upon Meridian construction if any prior distribution has a shape that cannot be broadcast to the shape designated by the model specification.

The parameter batch shapes are as follows:

Parameter Batch shape
knot_values n_knots
tau_g_excl_baseline n_geos - 1
beta_m n_media_channels
beta_rf n_rf_channels
beta_om n_organic_media_channels
beta_orf n_organic_rf_channels
eta_m n_media_channels
eta_rf n_rf_channels
eta_om n_organic_media_channels
eta_orf n_organic_rf_channels
gamma_c n_controls
gamma_n n_non_media_channels
xi_c n_controls
xi_n n_non_media_channels
alpha_m n_media_channels
alpha_rf n_rf_channels
alpha_om n_organic_media_channels
alpha_orf n_organic_rf_channels
ec_m n_media_channels
ec_rf n_rf_channels
ec_om n_organic_media_channels
ec_orf n_organic_rf_channels
slope_m n_media_channels
slope_rf n_rf_channels
slope_om n_organic_media_channels
slope_orf n_organic_rf_channels
sigma (σ)
roi_m n_media_channels
roi_rf n_rf_channels
mroi_m n_media_channels
mroi_rf n_rf_channels
contribution_m n_media_channels
contribution_rf n_rf_channels
contribution_om n_organic_media_channels
contribution_orf n_organic_f_channels
contribution_n n_non_media_channels

(σ) n_geos if unique_sigma_for_each_geo, otherwise this is 1

knot_values Prior distribution on knots for time effects. Default distribution is Normal(0.0, 5.0).
tau_g_excl_baseline Prior distribution on geo effects, which represent the average KPI of each geo relative to the baseline geo. This parameter is broadcast to a vector of length n_geos - 1, preserving the geo order and excluding the baseline_geo. After sampling, Meridian.inference_data includes a modified version of this parameter called tau_g, which has length n_geos and contains a zero in the position corresponding to baseline_geo. Meridian ignores this distribution if n_geos = 1. Default distribution is Normal(0.0, 5.0).
beta_m Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for impression media channels (beta_gm). When media_effects_dist is set to 'normal', it is the hierarchical mean. When media_effects_dist is set to 'log_normal', it is the hierarchical parameter for the mean of the underlying, log-transformed, Normal distribution. Meridian ignores this distribution if paid_media_prior_type is 'roi' or 'mroi', and uses the roi_m or mroi_m prior instead. Default distribution is HalfNormal(5.0).
beta_rf Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for reach and frequency media channels (beta_grf). When media_effects_dist is set to 'normal', it is the hierarchical mean. When media_effects_dist is set to 'log_normal', it is the hierarchical parameter for the mean of the underlying, log-transformed, Normal distribution. Meridian ignores this distribution if paid_media_prior_type is 'roi' or 'mroi', and uses the roi_m or mroi_rf prior instead. Default distribution is HalfNormal(5.0).
beta_om Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for organic media channels (beta_gom). When media_effects_dist is set to 'normal', it is the hierarchical mean. When media_effects_dist is set to 'log_normal', it is the hierarchical parameter for the mean of the underlying, log-transformed, Normal distribution. Default distribution is HalfNormal(5.0).
beta_orf Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for organic reach and frequency media channels (beta_gorf). When media_effects_dist is set to 'normal', it is the hierarchical mean. When media_effects_dist is set to 'log_normal', it is the hierarchical parameter for the mean of the underlying, log-transformed, Normal distribution. Default distribution is HalfNormal(5.0).
eta_m Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for impression media channels (beta_gm). When media_effects_dist is set to 'normal', it is the hierarchical standard deviation. When media_effects_dist is set to 'log_normal' it is the hierarchical parameter for the standard deviation of the underlying, log-transformed, Normal distribution. Default distribution is HalfNormal(1.0).
eta_rf Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for RF media channels (beta_grf). When media_effects_dist is set to 'normal', it is the hierarchical standard deviation. When media_effects_dist is set to 'log_normal' it is the hierarchical parameter for the standard deviation of the underlying, log-transformed, Normal distribution. Default distribution is HalfNormal(1.0).
eta_om Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for organic media channels (beta_gom). When media_effects_dist is set to 'normal', it is the hierarchical standard deviation. When media_effects_dist is set to 'log_normal' it is the hierarchical parameter for the standard deviation of the underlying, log-transformed, Normal distribution. Default distribution is HalfNormal(1.0).
eta_orf Prior distribution on a parameter for the hierarchical distribution of geo-level media effects for organic RF media channels (beta_gorf). When media_effects_dist is set to 'normal', it is the hierarchical standard deviation. When media_effects_dist is set to 'log_normal' it is the hierarchical parameter for the standard deviation of the underlying, log-transformed, Normal distribution. Default distribution is HalfNormal(1.0).
gamma_c Prior distribution on the hierarchical mean of gamma_gc which is the coefficient on control c for geo g. Hierarchy is defined over geos. Default distribution is Normal(0.0, 5.0).
gamma_n Prior distribution on the hierarchical mean of gamma_gn which is the coefficient on non-media channel n for geo g. Hierarchy is defined over geos. Default distribution is Normal(0.0, 5.0).
xi_c Prior distribution on the hierarchical standard deviation of gamma_gc which is the coefficient on control c for geo g. Hierarchy is defined over geos. Default distribution is HalfNormal(5.0).
xi_n Prior distribution on the hierarchical standard deviation of gamma_gn which is the coefficient on non-media channel n for geo g. Hierarchy is defined over geos. Default distribution is HalfNormal(5.0).
alpha_m Prior distribution on the Adstock decay parameter for media input. Default distribution is Uniform(0.0, 1.0).
alpha_rf Prior distribution on the Adstock decay parameter for RF input. Default distribution is Uniform(0.0, 1.0).
alpha_om Prior distribution on the Adstock decay parameter for organic media input. Default distribution is Uniform(0.0, 1.0).
alpha_orf Prior distribution on the Adstock decay parameter for organic RF input. Default distribution is Uniform(0.0, 1.0).
ec_m Prior distribution on the half-saturation Hill parameter for media input. Default distribution is TruncatedNormal(0.8, 0.8, 0.1, 10).
ec_rf Prior distribution on the half-saturation Hill parameter for RF input. Default distribution is TransformedDistribution(LogNormal(0.7, 0.4), Shift(0.1)).
ec_om Prior distribution on the half-saturation Hill parameter for organic media input. Default distribution is TruncatedNormal(0.8, 0.8, 0.1, 10).
ec_orf Prior distribution on the half-saturation Hill parameter for organic RF input. Default distribution is TransformedDistribution( LogNormal(0.7, 0.4), Shift(0.1)).
slope_m Prior distribution on the slope Hill parameter for media input. Default distribution is Deterministic(1.0).
slope_rf Prior distribution on the slope Hill parameter for RF input. Default distribution is LogNormal(0.7, 0.4).
slope_om Prior distribution on the slope Hill parameter for organic media input. Default distribution is Deterministic(1.0).
slope_orf Prior distribution on the slope Hill parameter for organic RF input. Default distribution is LogNormal(0.7, 0.4).
sigma Prior distribution on the standard deviation of noise. Default distribution is HalfNormal(5.0).
roi_m Prior distribution on the ROI of each media channel. This parameter is only used when paid_media_prior_type is 'roi', in which case beta_m is calculated as a deterministic function of roi_m, alpha_m, ec_m, slope_m, and the spend associated with each media channel. Default distribution is LogNormal(0.2, 0.9). When kpi_type is 'non_revenue' and revenue_per_kpi is not provided, ROI is interpreted as incremental KPI units per monetary unit spent. In this case, the default value for roi_m and roi_rf will be ignored and a common ROI prior will be assigned to all channels to achieve a target mean and standard deviation on the total media contribution.
roi_rf Prior distribution on the ROI of each Reach & Frequency channel. This parameter is only used when paid_media_prior_type is 'roi', in which case beta_rf is calculated as a deterministic function of roi_rf, alpha_rf, ec_rf, slope_rf, and the spend associated with each RF channel. Default distribution is LogNormal(0.2, 0.9). When kpi_type is 'non_revenue' and revenue_per_kpi is not provided, ROI is interpreted as incremental KPI units per monetary unit spent. In this case, the default value for roi_m and roi_rf will be ignored and a common ROI prior will be assigned to all channels to achieve a target mean and standard deviation on the total media contribution.
mroi_m Prior distribution on the mROI of each media channel. This parameter is only used when paid_media_prior_type is 'mroi', in which case beta_m is calculated as a deterministic function of mroi_m, alpha_m, ec_m, slope_m, and the spend associated with each media channel. Default distribution is LogNormal(0.0, 0.5). When kpi_type is 'non_revenue' and revenue_per_kpi is not provided, mROI is interpreted as the marginal incremental KPI units per monetary unit spent. In this case, a default distribution is not provided, so the user must specify it.
mroi_rf Prior distribution on the mROI of each Reach & Frequency channel. This parameter is only used when paid_media_prior_type is 'mroi', in which case beta_rf is calculated as a deterministic function of mroi_rf, alpha_rf, ec_rf, slope_rf, and the spend associated with each media channel. Default distribution is LogNormal(0.0, 0.5). When kpi_type is 'non_revenue' and revenue_per_kpi is not provided, mROI is interpreted as the marginal incremental KPI units per monetary unit spent. In this case, a default distribution is not provided, so the user must specify it.
contribution_m Prior distribution on the contribution of each media channel as a percentage of total outcome. This parameter is only used when paid_media_prior_type is 'contribution', in which case beta_m is calculated as a deterministic function of contribution_m, alpha_m, ec_m, slope_m, and the total outcome. Default distribution is Beta(1.0, 99.0).
contribution_rf Prior distribution on the contribution of each Reach & Frequency channel as a percentage of total outcome. This parameter is only used when paid_media_prior_type is 'contribution', in which case beta_rf is calculated as a deterministic function of contribution_rf, alpha_rf, ec_rf, slope_rf, and the total outcome. Default distribution is Beta(1.0, 99.0).
contribution_om Prior distribution on the contribution of each organic media channel as a percentage of total outcome. This parameter is only used when organic_media_prior_type is 'contribution', in which case beta_om is calculated as a deterministic function of contribution_om, alpha_om, ec_om, slope_om, and the total outcome. Default distribution is Beta(1.0, 99.0).
contribution_orf Prior distribution on the contribution of each organic Reach & Frequency channel as a percentage of total outcome. This parameter is only used when organic_media_prior_type is 'contribution', in which case beta_orf is calculated as a deterministic function of contribution_orf, alpha_orf, ec_orf, slope_orf, and the total outcome. Default distribution is Beta(1.0, 99.0).
contribution_n Prior distribution on the contribution of each non-media treatment channel as a percentage of total outcome. This parameter is only used when non_media_treatment_prior_type is 'contribution', in which case gamma_n is calculated as a deterministic function of contribution_n and the total outcome. Default distribution is TruncatedNormal(0.0, 0.1, -1.0, 1.0).

Methods

broadcast

View source

broadcast(
    n_geos: int,
    n_media_channels: int,
    n_rf_channels: int,
    n_organic_media_channels: int,
    n_organic_rf_channels: int,
    n_controls: int,
    n_non_media_channels: int,
    unique_sigma_for_each_geo: bool,
    n_knots: int,
    is_national: bool,
    set_total_media_contribution_prior: bool,
    kpi: float,
    total_spend: np.ndarray
) -> PriorDistribution

Returns a new PriorDistribution with broadcast distribution attributes.

Args
n_geos Number of geos.
n_media_channels Number of media channels used.
n_rf_channels Number of reach and frequency channels used.
n_organic_media_channels Number of organic media channels used.
n_organic_rf_channels Number of organic reach and frequency channels used.
n_controls Number of controls used.
n_non_media_channels Number of non-media channels used.
unique_sigma_for_each_geo A boolean indicator whether to use the same sigma parameter for all geos. Only used if n_geos > 1. For more information, see ModelSpec.
n_knots Number of knots used.
is_national A boolean indicator whether the prior distribution will be adapted for a national model.
set_total_media_contribution_prior A boolean indicator whether the ROI priors should be set to achieve a total media constribution prior with target mean and variance.
kpi Sum of the entire KPI across geos and time. Required if set_total_media_contribution_prior=True.
total_spend Spend per media channel summed across geos and time. Required if set_total_media_contribution_prior=True.

Returns
A new PriorDistribution broadcast from this prior distribution, according to the given data dimensionality.

Raises
ValueError If custom priors are not set for all channels.

has_deterministic_param

View source

has_deterministic_param(
    param: backend.tfd.Distribution
) -> bool

__eq__

__eq__(
    other
)

Return self==value.