Multivariate kernel density estimationKernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series. Kernel density estimators were first introduced in the scientific literature for univariate data in the 1950s and 1960s and subsequently have been widely adopted.
Estimation theoryEstimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
Density estimationIn statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population. A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization.
Transient stateA system is said to be transient or in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state. The time taken for the circuit to change from one steady state to another steady state is called the transient time. When a chemical reactor is being brought into operation, the concentrations, temperatures, species compositions, and reaction rates are changing with time until operation reaches its nominal process variables.
Plant physiologyPlant physiology is a subdiscipline of botany concerned with the functioning, or physiology, of plants. Closely related fields include plant morphology (structure of plants), plant ecology (interactions with the environment), phytochemistry (biochemistry of plants), cell biology, genetics, biophysics and molecular biology. Fundamental processes such as photosynthesis, respiration, plant nutrition, plant hormone functions, tropisms, nastic movements, photoperiodism, photomorphogenesis, circadian rhythms, environmental stress physiology, seed germination, dormancy and stomata function and transpiration, both parts of plant water relations, are studied by plant physiologists.
Mass balanceIn physics, a mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique. The exact conservation law used in the analysis of the system depends on the context of the problem, but all revolve around mass conservation, i.e., that matter cannot disappear or be created spontaneously.
Steady-state economyA steady-state economy is an economy made up of a constant stock of physical wealth (capital) and a constant population size. In effect, such an economy does not grow in the course of time. The term usually refers to the national economy of a particular country, but it is also applicable to the economic system of a city, a region, or the entire world. Early in the history of economic thought, classical economist Adam Smith of the 18th century developed the concept of a stationary state of an economy: Smith believed that any national economy in the world would sooner or later settle in a final state of stationarity.
Bayes estimatorIn estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation. Suppose an unknown parameter is known to have a prior distribution .
Steady stateIn systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so: In discrete time, it means that the first difference of each property is zero and remains so: The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering.
Plant breedingPlant breeding is the science of changing the traits of plants in order to produce desired characteristics. It has been used to improve the quality of nutrition in products for humans and animals. The goals of plant breeding are to produce crop varieties that boast unique and superior traits for a variety of applications. The most frequently addressed agricultural traits are those related to biotic and abiotic stress tolerance, grain or biomass yield, end-use quality characteristics such as taste or the concentrations of specific biological molecules (proteins, sugars, lipids, vitamins, fibers) and ease of processing (harvesting, milling, baking, malting, blending, etc.
