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Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.

Backtesting is a kind of retrodiction, and a special type of cross-validation applied to time series data.

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

Their essential idea is using randomness to solve problems that might be deterministic in principle.

They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches.

Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution.

Tactical asset allocation (TAA) is a dynamic investment strategy that actively adjusts a portfolio's asset allocation.

The goal of a TAA strategy is to improve the risk-adjusted returns of passive management investing.

Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk, defined as variance.

Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return.

In statistical modeling, regression analysis is a statistical process for estimating the relationships among variables.

It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors').

More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.

Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed.

Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables.

In all cases, the estimation target is a function of the independent variables called the regression function.

In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.

A related but distinct approach is necessary condition analysis (NCA), which estimates the maximum (rather than average) value of the dependent variable for a given value of the independent variable (ceiling line rather than central line) in order to identify what value of the independent variable is necessary but not sufficient for a given value of the dependent variable.