Module vickrey.likelihood.likelihood

Functions concerning the computation of the likelihood.

Functions

def likelihood(travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t)

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def likelihood(travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t):
    """Find the likelihood of a single data point.

    Given the parameters, find the likelihood of a point realizing a
    minimum. Beta, gamma and t* are assumed to be normally
    distributed.

    Args:
        travel_time: Instance of the TravelTime class the likelihood
            is computed on
        t_a: Time point of which the likelihood is computed
        mu_b: Mean of the beta parameter, relative to the early
            arrival penalty
        mu_g: Mean of the gamma parameter, relative to the late
            arrival penalty
        mu_t: Mean of the t* parameter, relative to the desired
            arrival time
        sigma: Variance of the beta and gamma distributions, that are
            assumed to share the same variance
        sigma_t: Variance of the t* parameter

    Returns:
        likelihood: float number representing the likelihood of an
            optimal arrival being equal to t_a

    """
    lik_early = _early_lik(travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t)
    lik_late = _late_lik(travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t)
    likelihood_kink = _ot_lik(
        travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t
    )
    likelihood_internal = lik_early + lik_late
    likelihood = likelihood_kink + likelihood_internal
    return jnp.maximum(likelihood, 1e-31)

Find the likelihood of a single data point.

Given the parameters, find the likelihood of a point realizing a minimum. Beta, gamma and t* are assumed to be normally distributed.

Args

travel_time

Instance of the TravelTime class the likelihood is computed on

t_a

Time point of which the likelihood is computed

mu_b

Mean of the beta parameter, relative to the early arrival penalty

mu_g

Mean of the gamma parameter, relative to the late arrival penalty

mu_t

Mean of the t* parameter, relative to the desired arrival time

sigma

Variance of the beta and gamma distributions, that are assumed to share the same variance

sigma_t

Variance of the t* parameter

Returns

likelihood()

float number representing the likelihood of an optimal arrival being equal to t_a

def total_liks(travel_time, t_as)

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def total_liks(travel_time, t_as):
    """Likelihood of each data point in a set of arrival times.

    Args:
        travel_time: Travel time function.
        t_as: Dataset of arrival times.

    Returns:
        mapped_lik: Function mapping a parameter set to the array
            of likelihoods.
    """

    def mapped_lik(mu_b, mu_g, mu_t, sigma, sigma_t):
        @jit
        def lik_restr(t_a):
            return likelihood(
                travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t
            )

        return vmap(lik_restr)(t_as)

    return mapped_lik

Likelihood of each data point in a set of arrival times.

Args

travel_time

Travel time function.

t_as

Dataset of arrival times.

Returns

mapped_lik

Function mapping a parameter set to the array of likelihoods.

def total_log_lik(travel_time, t_as)

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def total_log_lik(travel_time, t_as):
    """Total log likelihood of a set of arrival times.

    Args:
        travel_time: Travel time function.
        t_as: Dataset of arrival times.

    Returns:
        mapped_lik: Function mapping a parameter set to the value
            of the total likelihood.
    """

    def mapped_lik(mu_b, mu_g, mu_t, sigma, sigma_t):
        def lik_restr(t_a):
            return likelihood(
                travel_time, t_a, mu_b, mu_g, mu_t, sigma, sigma_t
            )

        return jnp.sum(jnp.log(vmap(lik_restr)(t_as)), axis=0)

    return mapped_lik

Total log likelihood of a set of arrival times.

Args

travel_time

Travel time function.

t_as

Dataset of arrival times.

Returns

mapped_lik

Function mapping a parameter set to the value of the total likelihood.