A likelihood function measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters.
In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation. There are several versions of Taylor's theorem, some giving explicit estimates of the approximation error of the function by its Taylor polynomial.
In statistics, G-tests are likelihood-ratio or maximum likelihood statistical significance tests that are increasingly being used in situations where chi-squared tests were previously recommended.
Trip generation is the first step in the conventional four-step transportation forecasting process used for forecasting travel demands. It predicts the number of trips originating in or destined for a particular traffic analysis zone (TAZ). Trip generation analysis focuses on residences and residential trip generation is thought of as a function of the social and economic attributes of households. At the level of the traffic analysis zone, residential land uses "produce" or generate trips. Traffic analysis zones are also destinations of trips, trip attractors. The analysis of attractors focuses on non-residential land uses.
Trip distribution is the second component in the traditional four-step transportation forecasting model. This step matches tripmakers’ origins and destinations to develop a “trip table”, a matrix that displays the number of trips going from each origin to each destination. Historically, this component has been the least developed component of the transportation planning model.
Mode choice analysis is the third step in the conventional four-step transportation forecasting model of transportation planning, following trip distribution and preceding route assignment. From origin-destination table inputs provided by trip distribution, mode choice analysis allows the modeler to determine probabilities that travelers will use a certain mode of transport. These probabilities are called the modal share, and can be used to produce an estimate of the amount of trips taken using each feasible mode.
Cohen's kappa coefficient is a statistic that is used to measure inter-rater reliability for qualitative (categorical) items. It is generally thought to be a more robust measure than simple percent agreement calculation, as κ takes into account the possibility of the agreement occurring by chance. There is controversy surrounding Cohen's kappa due to the difficulty in interpreting indices of agreement. Some researchers have suggested that it is conceptually simpler to evaluate disagreement between items.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is often used for analysis of time-series data.
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions, or whether outcome frequencies follow a specified distribution. In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares.
Annual average daily traffic (AADT) is a measure used primarily in transportation planning, transportation engineering and retail location selection. Traditionally, it is the total volume of vehicle traffic of a highway or road for a year divided by 365 days. AADT is a simple, but useful, measurement of how busy the road is.
Microsimulation is the use of computerized analytical tools to perform analysis of activities such as highway traffic flowing through an intersection, financial transactions, or pathogens spreading disease through a population on the granularity level of individuals. Synonyms include microanalytic simulation and microscopic simulation. Microsimulation, with its emphasis on stochastic or rule-based structures, should not be confused with the similar complementary technique of multi-agent simulation, which focuses more on the behaviour of individuals.
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula:
An ice road or ice bridge is a human-made structure that runs on a frozen water surface. Ice roads are typically part of a winter road, but they can also be simple stand-alone structures, connecting two shorelines. Ice roads may be planned, built and maintained so as to remain safe and effective, and a number of guidelines have been published with information in these regards. An ice road may be constructed year after year, for instance to service community needs during the winter. It could also be for a single year or two, so as to supply particular operations, such as a hydroelectric project or offshore drill sites.
TRANSIMS is an integrated set of tools developed to conduct regional transportation system analyses. With the goal of establishing TRANSIMS as an ongoing public resource available to the transportation community, TRANSIMS is made available under the NASA Open Source Agreement Version 1.3
The Highway Capacity Manual (HCM) is a publication of the Transportation Research Board (TRB) of the National Academies of Sciences, Engineering, and Medicine in the United States. It contains concepts, guidelines, and computational procedures for computing the capacity and quality of service of various highway facilities, including freeways, highways, arterial roads, roundabouts, signalized and unsignalized intersections, interchanges, rural highways, and the effects of mass transit, pedestrians, and bicycles on the performance of these systems.
In statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.
A traffic count is a count of vehicular or pedestrian traffic, which is conducted along a particular road, path, or intersection. A traffic count is commonly undertaken either automatically, or manually by observers who visually count and record traffic on a hand-held electronic device or tally sheet. Traffic counts can be used by local councils to identify which routes are used most, and to either improve that road or provide an alternative if there is an excessive amount of traffic. Also, some geography fieldwork involves a traffic count. Traffic counts provide the source data used to calculate the Annual Average Daily Traffic (AADT), which is the common indicator used to represent traffic volume. Traffic counts are useful for comparing two or more roads, and can also be used alongside other methods to find out where the central business district (CBD) of a settlement is located. Traffic counts that include speeds are used in speed limit enforcement efforts, highlighting peak speeding periods to optimise speed camera use and educational efforts.
Traffic simulation or the simulation of transportation systems is the mathematical modeling of transportation systems through the application of computer software to better help plan, design, and operate transportation systems. Simulation of transportation systems started in the 1950s, and is an important area of discipline in traffic engineering and transportation planning today. Various national and local transportation agencies, academic institutions and consulting firms use simulation to aid in their management of transportation networks.
Pavement performance modeling or pavement deterioration modeling is the study of pavement deterioration throughout its life-cycle. The health of pavement is assessed using different performance indicators. Some of the most well-known performance indicators are Pavement Condition Index (PCI), International Roughness Index (IRI) and Present Serviceability Index (PSI), but sometimes a single distress such as rutting or the extent of crack is used. Among the most frequently used methods for pavement performance modeling are mechanistic models, mechanistic-empirical models, survival curves and Markov models. Recently, machine learning algorithms have been used for this purpose as well. Most studies on pavement performance modeling are based on IRI.
Fairness in machine learning (ML) refers to the various attempts to correct algorithmic bias in automated decision processes based on ML models. Decisions made by such models after a learning process may be considered unfair if they were based on variables considered sensitive.
