Markov Models

Markov models have a wide range of interdisciplinary applications. They are used for modelling and forecasting consumer behaviour, mobility patterns, formations, networks, voting patterns, environmental management (e.g. patient movement between hospital stations), in particular wide applications have been found in medicine and biotechnology. Markov Models - social, economic and economic analyses Markov Models of the first order are suitable for the analysis of social systems, when the examined individual (person, system, individual) may be characterized as being in one of (say) clearly identifiable states, and when the probability of transition from one state to another depends only on the present state (and not on any of the previous states; for which this dependence is based on the most recent states).

Discrete time models give rise to Markov's chains. Some basic properties are presented for time-homogeneous (stationary) and time-homogeneous chains along with the inference procedures (maximum probability and Bayes's empirical estimation). Also the continuous Markov chains and the Markov processes are taken into account. Some results for linear birth and death models (probability, survival time) are presented. Markov's models in DNA analysis Markov's models can be fixed or variable order models as well as non-homogeneous or homogeneous. In a Markov model with a constant order, the latest state is predicted on the basis of a constant number of the previous state, and this constant number of the previous state is called the order of the Markov model.

For example, the Mark's first order model predicts that the state of a unit at a specific position in a sequence depends on the state of one unit at the previous position (e.g. in various cis-regulatory elements in DNA and motifs in proteins). The second order Markov Model predicts that the state of an entity at a given position in a sequence depends on the state of two entities at the two previous positions (e.g. in codons in DNA). Similarly, the Mark 5th order model predicts the state of the 6th entity in a sequence based on the previous five entities (e.g. hexamers in a coding sequence).

It has been observed that the probability of occurrence of codon pairs (hexamers) in a coding sequence is much higher than in a noncoding sequence. The fifth order Markov model calculates the sixth base probability from the previous five bases in the sequence. In addition to the sequence, if the probability of a state occurring also depends on the position in the sequence, the model is called a heterogeneous Markov model. In contrast, in a homogeneous Mark model, all positions in a sequence are described by the same set of conditional probabilities. Most simple abutment-effect models are models with simple correspondence between the output and the state. Many systems require models with more distinct computing power. We can formally extend the simple Markov model so that each state can produce one of many possible results, each with a different probability of emission.

Our more comprehensive model M is {S, T, s, O, E}, where S is a set of all states in the cardinational model (size) N T is the probability matrix N×N for the transition between pairs of states s is the initial state. We can see our earlier Markov models as special cases of a more complex model in which for each row and matrix E the value Ei,j=1 is the value Ei,j=1. (In other words, each row has a single output, whose probability of emission is a unity.) Because in practice, these more comprehensive models are applied to problem areas where only partial state information and output sequences are available, this more comprehensive model is usually called (HMM).

Usually a sequence of output values is available and the corresponding sequence of states is hidden. This is the scenario to which we will refer here. Additional bioinformatic analyses Markov models can be ordered permanently or in different ways, as well as heterogeneous or homogeneous. In the Markov model with a constant order, the newest state is predicted on the basis of a constant number of the previous state(s), and this constant number of the previous state(s) is called the order of the Markov model. For example, the Markov Model of the first order predicts that the state of a unit at a specific position in a sequence depends on the state of one unit at the previous position (e.g. in various cis-regulatory elements in DNA and motifs in proteins).

The second order Markov Model predicts that the state of an entity at a given position in a sequence depends on the state of two entities at the two preceding positions (e.g. in codons in DNA). Similarly, the Mark 5th order model predicts the state of the 6th entity in the sequence based on the previous five entities (e.g. hexamers in the coding sequence). It has been observed that the probability of occurrence of codon pairs (hexamers) in a coding sequence is much higher than in a noncoding sequence.

The fifth order Markov model calculates the sixth base probability from the previous five bases in the sequence. In addition to the sequence, if the probability of a state occurring also depends on the position in the sequence, the model is called a heterogeneous Markov model. In contrast, in a homogeneous Mark model, all positions in a sequence are described by the same set of conditional probabilities. Markov models are a commonly used tool in evolutionary biology to infer different evolutionary processes. Models for sequence analysis, models exist in three state spaces: DNA, codons and amino acids.

Those models of sequential evolution that describe the probability of transition between states include both empirical models that are initially calculated from large datasets and sequential contexts, and models with free parameters that are to be estimated from the dataset under analysis. In this review, we discuss a number of Markov models, how they are applied and how well they reflect the underlying biology. Markov models - quality of life studies Markov models represent disease processes that evolve over time and are adapted to the development of chronic disease; this type of model can handle relapse and estimate long-term costs and Quality of Life. The Markov Model is built around states of health and movements between them. Therefore, natural medical history becomes very important in the design of the model.

Within the model, health is divided into different categories (or health states) which must be mutually exclusive and include all persons in the model (i.e. all persons must fit into the health state at any time). The unit can be in only one state at a time and will remain in that state for a specified or fixed period of time, i.e. a cycle. At the end of each cycle, the individual/patient may either remain in the same state of health (i.e. cycle) or move to a different state of health.

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