Statistical assumptionStatistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.
Statistical theoryThe theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures.
Global Forecast SystemThe Global Forecast System (GFS) is a global numerical weather prediction system containing a global computer model and variational analysis run by the United States' National Weather Service (NWS). The mathematical model is run four times a day, and produces forecasts for up to 16 days in advance, but with decreased spatial resolution after 10 days. The forecast skill generally decreases with time (as with any numerical weather prediction model) and for longer term forecasts, only the larger scales retain significant accuracy.
Statistical inferenceStatistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.
Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
Data assimilationData assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – for example, to determine the optimal state estimate of a system, to determine initial conditions for a numerical forecast model, to interpolate sparse observation data using (e.g. physical) knowledge of the system being observed, to set numerical parameters based on training a model from observed data.
Vector processorIn computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called vectors. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SWAR Arithmetic Units.
Gather/scatter (vector addressing)Gather/scatter is a type of memory addressing that at once collects (gathers) from, or stores (scatters) data to, multiple, arbitrary indices. Examples of its use include sparse linear algebra operations, sorting algorithms, fast Fourier transforms, and some computational graph theory problems. It is the vector equivalent of register indirect addressing, with gather involving indexed reads, and scatter, indexed writes. Vector processors (and some SIMD units in CPUs) have hardware support for gather and scatter operations.
