To achieve that, one has to resolve the details, even if these cannot be observed, as that provides a much simpler possibility of analysis. In modelling stochastic processes the key role is played by time; in fact, the stochastic model is a tool for predicting probability distributions of potential outcomes by allowing a random variation in its inputs over time. A longer term consequence of loss of genetic variability is a reduced ability of a population to adapt to environmental changes. Then, we have the concept of ergodicity. Inbreeding expression can be expressed in particular environmental conditions such as harsh winters. 2. Morphological defects in threatened species such as the Florida panther (Felis concolor coryi) and lack of breeding success in the Puerto Rican parrot (Amazona vittata) appear to be a result of inbreeding depression. The relevance of noise and stochastic modelling to state-of-the-art molecular and cell biology is thus unquestionable. Each random variable in the collection takes values from the same mathematical space known as the state space. It means that a stochastic model predicts a set of possible outcomes weighted by their likelihoods, or probabilities. Some information is available for rupture lives and minimum creep rates and both normal and Weibull distributions have been suggested. In a Markov Chain of zero order, the current state (or nucleotide) is totally independent of the previous state, so it’s no memory and every state is untied. This means that, at each observation at a certain time, there is a certain probability to get a certain outcome. Most of the processes we describe can be assumed to be of this type. Monica Franzese, Antonella Iuliano, in Encyclopedia of Bioinformatics and Computational Biology, 2019. One of the main application of Machine Learning is modelling stochastic processes. This implies in particular that both the mean and autocovariance functions are independent of the reference time point. However, such a general situation becomes very cumbersome, and is almost hopeless to treat by any manageable formalism. As it leads to relatively simple, well-defined formalisms, one usually keeps to such processes. The basic idea of ergodicity is that a system, in whatever state it starts, will pass close to any other state and this motivates a basic rule that all states are equally probable, the basics for statistical mechanics. Such stochastic processes are said to have various types of stationary properties. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL:, URL:, URL:, URL:, URL:, URL:, URL:, URL:, URL:, URL:, International Encyclopedia of Education (Third Edition), A stochastic process is any process describing the evolution in time of a random phenomenon. Subsequently, the model could be also used to discover properties of the process, or to predict future events on the basis of the past history. Hugh P. Possingham, ... Michael A. McCarthy, in Encyclopedia of Biodiversity, 2001. (18.1). Note that the right hand side of this equation is independent of t and this implies that CV is symmetric, i.e., CV(τ)=CV(−τ) (Exercise 1). A stochastic process is any process describing the evolution in time of a random phenomenon. Inbreeding depression results in the selective removal of inbred animals and the genes carried by such animals (Lacy, 1993). In the following discussions, the indexing variable a is either a 2D spatial coordinate, α = (x,y)T, or a 2D frequency coordinate, α= (νx,νy)T. The statistical properties of a real stochastic process u(α) are completely determined in terms of its ensemble joint cdf given by, for m = 1, 2, …, ∞. I Discrete I Continuous I State space.