###### Markov Chains

###### Monte Carlo Method

In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)

###### Bayes Theorem

A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result.

###### Algorithms

###### Models, Genetic

###### Models, Statistical

###### Computer Simulation

###### Likelihood Functions

###### Stochastic Processes

###### Software

###### Models, Biological

###### Evolution, Molecular

###### Computational Biology

A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.

###### Chromosome Mapping

###### Sequence Analysis, DNA

###### Sequence Alignment

The arrangement of two or more amino acid or base sequences from an organism or organisms in such a way as to align areas of the sequences sharing common properties. The degree of relatedness or homology between the sequences is predicted computationally or statistically based on weights assigned to the elements aligned between the sequences. This in turn can serve as a potential indicator of the genetic relatedness between the organisms.

###### Data Interpretation, Statistical

###### Models, Theoretical

###### Pattern Recognition, Automated

###### Biometry

###### Biostatistics

###### Genetics, Population

###### Polymerase Chain Reaction

In vitro method for producing large amounts of specific DNA or RNA fragments of defined length and sequence from small amounts of short oligonucleotide flanking sequences (primers). The essential steps include thermal denaturation of the double-stranded target molecules, annealing of the primers to their complementary sequences, and extension of the annealed primers by enzymatic synthesis with DNA polymerase. The reaction is efficient, specific, and extremely sensitive. Uses for the reaction include disease diagnosis, detection of difficult-to-isolate pathogens, mutation analysis, genetic testing, DNA sequencing, and analyzing evolutionary relationships.

###### Quantitative Trait, Heritable

###### Molecular Sequence Data

Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.

###### Genetic Markers

###### Quality-Adjusted Life Years

###### Cost-Benefit Analysis

A method of comparing the cost of a program with its expected benefits in dollars (or other currency). The benefit-to-cost ratio is a measure of total return expected per unit of money spent. This analysis generally excludes consideration of factors that are not measured ultimately in economic terms. Cost effectiveness compares alternative ways to achieve a specific set of results.

###### Population Dynamics

###### Sequence Analysis, Protein

###### Base Sequence

###### Genetic Linkage

###### Classification

###### Reproducibility of Results

The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.

###### Multifactorial Inheritance

###### Probability Learning

###### Artificial Intelligence

###### Cluster Analysis

A set of statistical methods used to group variables or observations into strongly inter-related subgroups. In epidemiology, it may be used to analyze a closely grouped series of events or cases of disease or other health-related phenomenon with well-defined distribution patterns in relation to time or place or both.

###### Normal Distribution

###### Pedigree

###### Genotype

## Genome-wide bioinformatic and molecular analysis of introns in Saccharomyces cerevisiae. (1/3175)

Introns have typically been discovered in an ad hoc fashion: introns are found as a gene is characterized for other reasons. As complete eukaryotic genome sequences become available, better methods for predicting RNA processing signals in raw sequence will be necessary in order to discover genes and predict their expression. Here we present a catalog of 228 yeast introns, arrived at through a combination of bioinformatic and molecular analysis. Introns annotated in the Saccharomyces Genome Database (SGD) were evaluated, questionable introns were removed after failing a test for splicing in vivo, and known introns absent from the SGD annotation were added. A novel branchpoint sequence, AAUUAAC, was identified within an annotated intron that lacks a six-of-seven match to the highly conserved branchpoint consensus UACUAAC. Analysis of the database corroborates many conclusions about pre-mRNA substrate requirements for splicing derived from experimental studies, but indicates that splicing in yeast may not be as rigidly determined by splice-site conservation as had previously been thought. Using this database and a molecular technique that directly displays the lariat intron products of spliced transcripts (intron display), we suggest that the current set of 228 introns is still not complete, and that additional intron-containing genes remain to be discovered in yeast. The database can be accessed at http://www.cse.ucsc.edu/research/compbi o/yeast_introns.html. (+info)## Economic consequences of the progression of rheumatoid arthritis in Sweden. (2/3175)

OBJECTIVE: To develop a simulation model for analysis of the cost-effectiveness of treatments that affect the progression of rheumatoid arthritis (RA). METHODS: The Markov model was developed on the basis of a Swedish cohort of 116 patients with early RA who were followed up for 5 years. The majority of patients had American College of Rheumatology (ACR) functional class II disease, and Markov states indicating disease severity were defined based on Health Assessment Questionnaire (HAQ) scores. Costs were calculated from data on resource utilization and patients' work capacity. Utilities (preference weights for health states) were assessed using the EQ-5D (EuroQol) questionnaire. Hypothetical treatment interventions were simulated to illustrate the model. RESULTS: The cohort distribution among the 6 Markov states clearly showed the progression of the disease over 5 years of followup. Costs increased with increasing severity of the Markov states, and total costs over 5 years were higher for patients who were in more severe Markov states at diagnosis. Utilities correlated well with the Markov states, and the EQ-5D was able to discriminate between patients with different HAQ scores within ACR functional class II. CONCLUSION: The Markov model was able to assess disease progression and costs in RA. The model can therefore be a useful tool in calculating the cost-effectiveness of different interventions aimed at changing the progression of the disease. (+info)## Multipoint oligogenic analysis of age-at-onset data with applications to Alzheimer disease pedigrees. (3/3175)

It is usually difficult to localize genes that cause diseases with late ages at onset. These diseases frequently exhibit complex modes of inheritance, and only recent generations are available to be genotyped and phenotyped. In this situation, multipoint analysis using traditional exact linkage analysis methods, with many markers and full pedigree information, is a computationally intractable problem. Fortunately, Monte Carlo Markov chain sampling provides a tool to address this issue. By treating age at onset as a right-censored quantitative trait, we expand the methods used by Heath (1997) and illustrate them using an Alzheimer disease (AD) data set. This approach estimates the number, sizes, allele frequencies, and positions of quantitative trait loci (QTLs). In this simultaneous multipoint linkage and segregation analysis method, the QTLs are assumed to be diallelic and to interact additively. In the AD data set, we were able to localize correctly, quickly, and accurately two known genes, despite the existence of substantial genetic heterogeneity, thus demonstrating the great promise of these methods for the dissection of late-onset oligogenic diseases. (+info)## Machine learning approaches for the prediction of signal peptides and other protein sorting signals. (4/3175)

Prediction of protein sorting signals from the sequence of amino acids has great importance in the field of proteomics today. Recently, the growth of protein databases, combined with machine learning approaches, such as neural networks and hidden Markov models, have made it possible to achieve a level of reliability where practical use in, for example automatic database annotation is feasible. In this review, we concentrate on the present status and future perspectives of SignalP, our neural network-based method for prediction of the most well-known sorting signal: the secretory signal peptide. We discuss the problems associated with the use of SignalP on genomic sequences, showing that signal peptide prediction will improve further if integrated with predictions of start codons and transmembrane helices. As a step towards this goal, a hidden Markov model version of SignalP has been developed, making it possible to discriminate between cleaved signal peptides and uncleaved signal anchors. Furthermore, we show how SignalP can be used to characterize putative signal peptides from an archaeon, Methanococcus jannaschii. Finally, we briefly review a few methods for predicting other protein sorting signals and discuss the future of protein sorting prediction in general. (+info)## Genome-wide linkage analyses of systolic blood pressure using highly discordant siblings. (5/3175)

BACKGROUND: Elevated blood pressure is a risk factor for cardiovascular, cerebrovascular, and renal diseases. Complex mechanisms of blood pressure regulation pose a challenge to identifying genetic factors that influence interindividual blood pressure variation in the population at large. METHODS AND RESULTS: We performed a genome-wide linkage analysis of systolic blood pressure in humans using an efficient, highly discordant, full-sibling design. We identified 4 regions of the human genome that show statistical significant linkage to genes that influence interindividual systolic blood pressure variation (2p22.1 to 2p21, 5q33.3 to 5q34, 6q23.1 to 6q24.1, and 15q25.1 to 15q26.1). These regions contain a number of candidate genes that are involved in physiological mechanisms of blood pressure regulation. CONCLUSIONS: These results provide both novel information about genome regions in humans that influence interindividual blood pressure variation and a basis for identifying the contributing genes. Identification of the functional mutations in these genes may uncover novel mechanisms for blood pressure regulation and suggest new therapies and prevention strategies. (+info)## FORESST: fold recognition from secondary structure predictions of proteins. (6/3175)

MOTIVATION: A method for recognizing the three-dimensional fold from the protein amino acid sequence based on a combination of hidden Markov models (HMMs) and secondary structure prediction was recently developed for proteins in the Mainly-Alpha structural class. Here, this methodology is extended to Mainly-Beta and Alpha-Beta class proteins. Compared to other fold recognition methods based on HMMs, this approach is novel in that only secondary structure information is used. Each HMM is trained from known secondary structure sequences of proteins having a similar fold. Secondary structure prediction is performed for the amino acid sequence of a query protein. The predicted fold of a query protein is the fold described by the model fitting the predicted sequence the best. RESULTS: After model cross-validation, the success rate on 44 test proteins covering the three structural classes was found to be 59%. On seven fold predictions performed prior to the publication of experimental structure, the success rate was 71%. In conclusion, this approach manages to capture important information about the fold of a protein embedded in the length and arrangement of the predicted helices, strands and coils along the polypeptide chain. When a more extensive library of HMMs representing the universe of known structural families is available (work in progress), the program will allow rapid screening of genomic databases and sequence annotation when fold similarity is not detectable from the amino acid sequence. AVAILABILITY: FORESST web server at http://absalpha.dcrt.nih.gov:8008/ for the library of HMMs of structural families used in this paper. FORESST web server at http://www.tigr.org/ for a more extensive library of HMMs (work in progress). CONTACT: vale[email protected]; [email protected]; [email protected] (+info)## Age estimates of two common mutations causing factor XI deficiency: recent genetic drift is not necessary for elevated disease incidence among Ashkenazi Jews. (7/3175)

The type II and type III mutations at the FXI locus, which cause coagulation factor XI deficiency, have high frequencies in Jewish populations. The type III mutation is largely restricted to Ashkenazi Jews, but the type II mutation is observed at high frequency in both Ashkenazi and Iraqi Jews, suggesting the possibility that the mutation appeared before the separation of these communities. Here we report estimates of the ages of the type II and type III mutations, based on the observed distribution of allelic variants at a flanking microsatellite marker (D4S171). The results are consistent with a recent origin for the type III mutation but suggest that the type II mutation appeared >120 generations ago. This finding demonstrates that the high frequency of the type II mutation among Jews is independent of the demographic upheavals among Ashkenazi Jews in the 16th and 17th centuries. (+info)## Does over-the-counter nicotine replacement therapy improve smokers' life expectancy? (8/3175)

OBJECTIVE: To determine the public health benefits of making nicotine replacement therapy available without prescription, in terms of number of quitters and life expectancy. DESIGN: A decision-analytic model was developed to compare the policy of over-the-counter (OTC) availability of nicotine replacement therapy with that of prescription ([symbol: see text]) availability for the adult smoking population in the United States. MAIN OUTCOME MEASURES: Long-term (six-month) quit rates, life expectancy, and smoking attributable mortality (SAM) rates. RESULTS: OTC availability of nicotine replacement therapy would result in 91,151 additional successful quitters over a six-month period, and a cumulative total of approximately 1.7 million additional quitters over 25 years. All-cause SAM would decrease by 348 deaths per year and 2940 deaths per year at six months and five years, respectively. Relative to [symbol: see text] nicotine replacement therapy availability, OTC availability would result in an average gain in life expectancy across the entire adult smoking population of 0.196 years per smoker. In sensitivity analyses, the benefits of OTC availability were evident across a wide range of changes in baseline parameters. CONCLUSIONS: Compared with [symbol: see text] availability of nicotine replacement therapy, OTC availability would result in more successful quitters, fewer smoking-attributable deaths, and increased life expectancy for current smokers. (+info)###### Examples of **Markov** **chains**

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**Markov** **Chains** and Mixing Times

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**Markov****chain**on sets of states of the given**chain**),**Markov****chains**with infinitely many states, and**Markov****chains**that ...**Markov****Chains**and Mixing Times is a book on**Markov****chain**mixing times. The second edition was written by David A. Levin, and ... "Review of**Markov****Chains**and Mixing Times (1st ed.)", Mathematical Reviews, MR 2466937 Mai, H. M., "Review of**Markov****Chains**and ... "Review of**Markov****Chains**and Mixing Times (2nd ed.)", zbMATH, Zbl 1390.60001 Aldous, David (March 2019), "Review of**Markov**...**Markov** **chain**

Gauss-

**Markov**process**Markov****chain**approximation method**Markov****chain**geostatistics**Markov****chain**mixing time**Markov****chain**tree ... is a stationary distribution of the**Markov****chain**. A**Markov****chain**with memory (or a**Markov****chain**of order m) where m is finite, ...**Markov****chains**also play an important role in reinforcement learning.**Markov****chains**are also the basis for hidden**Markov**models ...**Markov**decision process**Markov**information source**Markov**odometer**Markov**random field Master equation Quantum**Markov****chain**Semi ...###### Kolmogorov equations (continuous-time **Markov** **chains**)

... focuses on the scenario where we have a continuous-time

**Markov****chain**(so the state space Ω {\displaystyle \Omega } is countable ... for many continuous-time**Markov****chains**appearing in physics and chemistry. Kolmogoroff, A. (1931). "Über die analytischen ... In mathematics and statistics, in the context of**Markov**processes, the Kolmogorov equations, including Kolmogorov forward ... Feller derives the equations under slightly different conditions, starting with the concept of purely discontinuous**Markov**...###### Telescoping **Markov** **chain**

In probability theory, a telescoping

**Markov****chain**(TMC) is a vector-valued stochastic process that satisfies a**Markov**property ... is a**Markov****chain**with transition probability matrix Λ 1 {\displaystyle \Lambda ^{1}} P ( θ k 1 = s ∣ θ k − 1 1 = r ) = Λ 1 ( s ... satisfies a**Markov**property with a transition kernel that can be written in terms of the Λ {\displaystyle \Lambda } 's, P ( θ k ...###### Quantum **Markov** **chain**

In mathematics, the quantum

**Markov****chain**is a reformulation of the ideas of a classical**Markov****chain**, replacing the classical ... More precisely, a quantum**Markov****chain**is a pair ( E , ρ ) {\displaystyle (E,\rho )} with ρ {\displaystyle \rho } a density ... Very roughly, the theory of a quantum**Markov****chain**resembles that of a measure-many automaton, with some important ... "Quantum**Markov****chains**." Journal of Mathematical Physics 49.7 (2008): 072105. (Exotic probabilities, Quantum information science ...###### Additive **Markov** **chain**

In probability theory, an additive

**Markov****chain**is a**Markov****chain**with an additive conditional probability function. Here the ... A binary additive**Markov****chain**is where the state space of the**chain**consists on two values only, Xn ∈ { x1, x2 }. For example ... Examples of**Markov****chains**S.S. Melnyk, O.V. Usatenko, and V.A. Yampol'skii. (2006) "Memory functions of the additive**Markov**... An additive**Markov****chain**of order m is a sequence of random variables X1, X2, X3, ..., possessing the following property: the ...###### Absorbing **Markov** **chain**

Wolfram Demonstration Project: Absorbing

**Markov****Chain**Monopoly as a**Markov****chain**(**Markov**processes,**Markov**models). ... In an absorbing**Markov****chain**, a state that is not absorbing is called transient. Let an absorbing**Markov****chain**with transition ... 3: Absorbing**Markov****Chains**". In Gehring, F. W.; Halmos, P. R. (eds.). Finite**Markov****Chains**(Second ed.). New York Berlin ... Like general**Markov****chains**, there can be continuous-time absorbing**Markov****chains**with an infinite state space. However, this ...**Markov** **chain** geostatistics

A

**Markov****chain**random field is still a single spatial**Markov****chain**. The spatial**Markov****chain**moves or jumps in a space and ...**Markov****chain**geostatistics uses**Markov****chain**spatial models, simulation algorithms and associated spatial correlation measures ... e.g., transiogram) based on the**Markov****chain**random field theory, which extends a single**Markov****chain**into a multi-dimensional ... is proposed as the accompanying spatial measure of**Markov****chain**random fields. Li, W. 2007.**Markov****chain**random fields for ...**Markov** **chains** on a measurable state space

A

**Markov****chain**on a measurable state space is a discrete-time-homogeneous**Markov****chain**with a measurable space as state space. ... The definition of**Markov****chains**has evolved during the 20th century. In 1953 the term**Markov****chain**was used for stochastic ... Sean Meyn and Richard L. Tweedie:**Markov****Chains**and Stochastic Stability. 2nd edition, 2009. Daniel Revuz:**Markov****Chains**. 2nd ... denotes the**Markov****chain**according to a**Markov**kernel p {\displaystyle p} with stationary measure μ {\displaystyle \mu } , and ...**Markov** **chain** Monte Carlo

These interacting

**Markov****chain**Monte Carlo samplers can be interpreted as a way to run in parallel a sequence of**Markov****chain**... In principle, any**Markov****chain**Monte Carlo sampler can be turned into an interacting**Markov****chain**Monte Carlo sampler. ... In contrast to traditional**Markov****chain**Monte Carlo methods, the precision parameter of this class of interacting**Markov****chain**... assess convergence is to run several independent simulated**Markov****chains**and check that the ratio of inter-**chain**to intra-**chain**...###### Continuous-time **Markov** **chain**

cf Chapter 6 Finite

**Markov****Chains**pp. 384ff. John G. Kemeny & J. Laurie Snell (1960) Finite**Markov****Chains**, D. van Nostrand ... of an ergodic continuous-time**Markov****chain**, Q, is by first finding its embedded**Markov****chain**(EMC). Strictly speaking, the EMC ... thus we are not defining continuous-time**Markov****chains**in general but only non-explosive continuous-time**Markov****chains**.) Let P ... "Continuous-time**Markov****chains**II".**Markov****Chains**. pp. 108-127. doi:10.1017/CBO9780511810633.005. ISBN 9780511810633. Anderson, ...**Markov** **chain** approximation method

In case of need, one must as well approximate the cost function for one that matches up the

**Markov****chain**chosen to approximate ... F. B. Hanson, "**Markov****Chain**Approximation", in C. T. Leondes, ed., Stochastic Digital Control System Techniques, Academic Press ... In numerical methods for stochastic differential equations, the**Markov****chain**approximation method (MCAM) belongs to the several ... The basic idea of the MCAM is to approximate the original controlled process by a chosen controlled**markov**process on a finite ...**Markov** **chain** tree theorem

The

**Markov****chain**tree theorem considers spanning trees for the states of the**Markov****chain**, defined to be trees, directed toward ... It sums up terms for the rooted spanning trees of the**Markov****chain**, with a positive combination for each tree. The**Markov****chain**... In the mathematical theory of**Markov****chains**, the**Markov****chain**tree theorem is an expression for the stationary distribution of ... A finite**Markov****chain**consists of a finite set of states, and a transition probability p i , j {\displaystyle p_{i,j}} for ...###### Discrete-time **Markov** **chain**

A continuous-time

**Markov****chain**is like a discrete-time**Markov****chain**, but it moves states continuously through time rather than ... cf Chapter 6 Finite**Markov****Chains**pp. 384ff. John G. Kemeny & J. Laurie Snell (1960) Finite**Markov****Chains**, D. van Nostrand ... A**Markov****chain**with memory (or a**Markov****chain**of order m) where m is finite, is a process satisfying Pr ( X n = x n ∣ X n − 1 ... Time-homogeneous**Markov****chains**(or stationary**Markov****chains**) are processes where Pr ( X n + 1 = x ∣ X n = y ) = Pr ( X n = x ∣ ...**Markov** **chain** mixing time

In probability theory, the mixing time of a

**Markov****chain**is the time until the**Markov****chain**is "close" to its steady state ... More precisely, a fundamental result about**Markov****chains**is that a finite state irreducible aperiodic**chain**has a unique ... Such problems can, for sufficiently large number of colors, be answered using the**Markov****chain**Monte Carlo method and showing ... Mixing (mathematics) for a formal definition of mixing Aldous, David; Fill, Jim, Reversible**Markov****Chains**and Random Walks on ...###### Nearly completely decomposable **Markov** **chain**

In probability theory, a nearly completely decomposable (NCD)

**Markov****chain**is a**Markov****chain**where the state-space can be ...**Markov****chains**, Multi- level, Numerical solution. (**Markov**processes). ... A**Markov****chain**with transition matrix P = ( 1 2 1 2 0 0 1 2 1 2 0 0 0 0 1 2 1 2 0 0 1 2 1 2 ) + ϵ ( − 1 2 0 1 2 0 0 − 1 2 0 1 2 ... Example 1.1 from Yin, George; Zhang, Qing (2005). Discrete-time**Markov****chains**: two-time-scale methods and applications. ...###### Lempel-Ziv-**Markov** **chain** algorithm

LZMA uses

**Markov****chains**, as implied by "M" in its name. The binary tree approach follows the hash**chain**approach, except that ... The Lempel-Ziv-**Markov****chain**algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been under ... the search stop after a pre-defined number of hash**chain**nodes has been traversed, or when the hash**chains**"wraps around", ...**Chaining**is achieved by an additional array which stores, for every dictionary position, the last seen previous position whose ...###### Reversible-jump **Markov** **chain** Monte Carlo

In computational statistics, reversible-jump

**Markov****chain**Monte Carlo is an extension to standard**Markov****chain**Monte Carlo ( ... Green, P.J. (1995). "Reversible Jump**Markov****Chain**Monte Carlo Computation and Bayesian Model Determination". Biometrika. 82 (4 ... Articles with short description, Short description matches Wikidata, Computational statistics,**Markov****chain**Monte Carlo). ...###### Construction of an irreducible **Markov** **chain** in the Ising model

**Markov**

**Chain**in the Ising model is the first step in overcoming a computational obstruction encountered when a

**Markov**

**chain**... So we an get the irreducibility of the

**Markov**

**Chain**based on simple swaps for the 1-dimension Ising model. Even though we just ... Thus in the following we will show how to modify the algorithm mentioned in the paper to get the irreducible

**Markov**

**chain**in ... Then using the Metropolis-Hastings algorithm, we can get an aperiodic, reversible and irreducible

**Markov**

**Chain**. The paper ...

###### Essential range

Freedman, David (1971).

**Markov****Chains**. Holden-Day. p. 1. Cf. Chung, Kai Lai (1967).**Markov****Chains**with Stationary Transition ...###### Fork-join queue

Serfozo, R. (2009). "

**Markov****Chains**". Basics of Applied Stochastic Processes. Probability and Its Applications. pp. 1-98. doi: ...###### Stochastic matrix

Krumbein, W. C.; Dacey, Michael F. (1 March 1969). "

**Markov****chains**and embedded**Markov****chains**in geology". Journal of the ... The stochastic matrix was developed alongside the**Markov****chain**by Andrey**Markov**, a Russian mathematician and professor at St. ... The**Markov****chain**that represents this game contains the following five states specified by the combination of positions (cat, ... In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a**Markov****chain**. Each of its entries ...###### Birth process

Norris, J.R. (1997).

**Markov****Chains**. Cambridge University Press. ISBN 9780511810633. Ross, Sheldon M. (2010). Introduction to ... In probability theory, a birth process or a pure birth process is a special case of a continuous-time**Markov**process and a ... Articles with short description, Short description matches Wikidata,**Markov**processes, Poisson point processes). ...###### Transition rate matrix

The vertices of the graph correspond to the

**Markov****chain's**states. The transition rate matrix has following properties: There ... Norris, J. R. (1997).**Markov****Chains**. doi:10.1017/CBO9780511810633. ISBN 9780511810633. Keizer, Joel (1972-11-01). "On the ... Passage Times for**Markov****Chains**. IOS Press. doi:10.3233/978-1-60750-950-9-i. ISBN 90-5199-060-X. Asmussen, S. R. (2003). " ... is an array of numbers describing the instantaneous rate at which a continuous time**Markov****chain**transitions between states. In ...###### Time reversibility

Kolmogorov's criterion defines the condition for a

**Markov****chain**or continuous-time**Markov****chain**to be time-reversible. Time ...**Markov****chains**, and piecewise deterministic**Markov**processes. Time reversal method works based on the linear reciprocity of the ... Norris, J. R. (1998).**Markov****Chains**. Cambridge University Press. ISBN 978-0521633963. Löpker, A.; Palmowski, Z. (2013). "On ...**Markov**processes can only be reversible if their stationary distributions have the property of detailed balance: p ( x t = i , ...###### James R. Norris

Norris, J. R. (28 February 1997).

**Markov****Chains**. Cambridge University Press. doi:10.1017/cbo9780511810633. ISBN 978-0-521-48181 ...###### Foster's theorem

It uses the fact that positive recurrent

**Markov****chains**exhibit a notion of "Lyapunov stability" in terms of returning to any ... Consider an irreducible discrete-time**Markov****chain**on a countable state space S having a transition probability matrix P with ... Brémaud, P. (1999). "Lyapunov Functions and Martingales".**Markov****Chains**. pp. 167. doi:10.1007/978-1-4757-3124-8_5. ISBN 978-1- ... Foster's theorem states that the**Markov****chain**is positive recurrent if and only if there exists a Lyapunov function V : S → R ...###### Probability

In 1906, Andrey

**Markov**introduced the notion of**Markov****chains**, which played an important role in stochastic processes theory ... "**Markov****Chains**" (PDF). Statistical Laboratory. University of Cambridge. Vitanyi, Paul M.B. (1988). "Andrei Nikolaevich ...###### Andrey **Markov**

Gauss-

**Markov**theorem Gauss-**Markov**process Hidden**Markov**model**Markov**blanket**Markov****chain****Markov**decision process**Markov's**... inequality**Markov**brothers' inequality**Markov**information source**Markov**network**Markov**number**Markov**property**Markov**process ... "Centennial of**Markov****Chains**". Wolfram Blog. Wikimedia Commons has media related to Andrey**Markov**. Andrei Andreyevich**Markov**at ... A primary subject of his research later became known as the**Markov****chain**.**Markov**and his younger brother Vladimir Andreevich ...###### Uncertainty quantification

**Markov**

**chain**Monte Carlo (MCMC) is often used for integration; however it is computationally expensive. The fully Bayesian ...

###### Mie scattering

Ye Z, Jiang X, Wang Z (Oct 2012). "Measurements of Particle Size Distribution Based on Mie Scattering Theory and

**Markov****Chain**...###### Baum-Welch algorithm

... of

**Markov**processes and to a model for ecology Statistical Inference for Probabilistic Functions of Finite State**Markov****Chains**... Thus we can describe a hidden**Markov****chain**by θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} . The Baum-Welch algorithm ... A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of**Markov****Chains**An inequality with ... A hidden**Markov**model describes the joint probability of a collection of "hidden" and observed discrete random variables. It ...###### Sequence motif

The E. coli lactose operon repressor LacI (PDB: 1lcc

**chain**A) and E. coli catabolite gene activator (PDB: 3gap**chain**A) both ... In 2018, a**Markov**random field approach has been proposed to infer DNA motifs from DNA-binding domains of proteins. ... Sometimes patterns are defined in terms of a probabilistic model such as a hidden**Markov**model. The notation [XYZ] means X or Y ... devised a code they called the "three-dimensional**chain**code" for representing the protein structure as a string of letters. ...###### Length of stay

This has usually been done with regression models, but

**Markov****chain**methods have also been applied. Within regression ... "A continuous time**Markov**model for the length of stay of elderly people in institutional long-term care". Journal of the Royal ...###### Automated planning and scheduling

forward

**chaining**state space search, possibly enhanced with heuristics backward**chaining**search, possibly enhanced by the use ... Discrete-time**Markov**decision processes (MDP) are planning problems with: durationless actions, nondeterministic actions with ... When full observability is replaced by partial observability, planning corresponds to partially observable**Markov**decision ...**Markov** decision process

... a

**Markov**decision process reduces to a**Markov****chain**. A**Markov**decision process is a 4-tuple ( S , A , P a , R a ) {\ ... the state transitions of an MDP satisfy the**Markov**property.**Markov**decision processes are an extension of**Markov****chains**; the ... The name of MDPs comes from the Russian mathematician Andrey**Markov**as they are an extension of**Markov****chains**. At each time ... Like the discrete-time**Markov**decision processes, in continuous-time**Markov**decision processes we want to find the optimal ...###### Comparison of Gaussian process software

... gradient descent or

**Markov****chain**Monte Carlo. These columns are about the possibility of fitting datapoints simultaneously to a ...**Markov**: algorithms for kernels which represent (or can be formulated as) a**Markov**process. Approximate: whether generic or ...###### March 1929

Born: Georgi

**Markov**, Bulgarian dissident writer, in Sofia (d. 1978) Died: Royal H. Weller, 47, American politician Coal miners ... Wales, Henry (March 29, 1929). "I.T. & T. Buys a World Wide Radio**Chain**". Chicago Daily Tribune. p. 1. "New $7,000,000 Stadium ... William Fox of the Fox Film Corporation announced a merger with the Loew's theatre**chain**. Mexican rebels seized Nogales and ...###### Austrian colonization of the Nicobar Islands

**Markov**, Walter, "L'expansion autrichienne outre-mer et les intérêts portugaises 1777-81", Congresso Internacional de História ... In February 1858, Novara reached the island of Car Nicobar, the northernmost island of the

**chain**. The Austrian team sailed ... pp.45-49

**Markov**, Walter, "La Compagnia Asiatica di Trieste", Studi Storici, vol.2, no.1, 1961, p.14. Von Pollack-Parnau, Franz ...

###### Memorylessness

"Notes on Memoryless Random Variables" (PDF). "

**Markov****Chains**and Random Walks" (PDF). Bowden, Rory; Keeler, Holger Paul; ... In the context of**Markov**processes, memorylessness refers to the**Markov**property, an even stronger assumption which implies ... The present article describes the use outside the**Markov**property. Most phenomena are not memoryless, which means that ...###### Tree diagram (probability theory)

Decision tree

**Markov****chain**"Tree Diagrams". BBC GCSE Bitesize. BBC. p. 1,3. Retrieved 25 October 2013. Charles Henry Brase, ...###### Kolmogorov's criterion

... aperiodic

**Markov****chain**with transition matrix P is reversible if and only if its stationary**Markov****chain**satisfies p j 1 j 2 p ... The proof for continuous-time**Markov****chains**follows in the same way as the proof for discrete-time**Markov****chains**. Kelly, Frank ... is a theorem giving a necessary and sufficient condition for a**Markov****chain**or continuous-time**Markov****chain**to be ... and S is the state space of the**chain**. Consider this figure depicting a section of a**Markov****chain**with states i, j, k and l and ...###### Gibberish

A statistical gibberish generator based on

**Markov****chains**The Online Dictionary of Language Terminology Gibberish - World Wide ...###### Deterministic system

**Markov**

**chains**and other random walks are not deterministic systems, because their development depends on random choices. A ...

###### Snakes and ladders

Any version of snakes and ladders can be represented exactly as an absorbing

**Markov****chain**, since from any square the odds of ... Snakes & Lattes is a board game café**chain**headquartered in Toronto, Canada, named after snakes and ladders. In the Abby ...**Markov**models, Milton Bradley Company games, Products introduced in 1943). ...###### Éric Moulines

He is interested in the inference of latent variable models and in particular hidden

**Markov****chains**, and non-linear state models ... 1462-1505 R Douc, E Moulines, P Priouret, P Soulier, «**Markov****Chains**», Springer, 2018 A Durmus, E Moulines, « Nonasymptotic ... obtaining fundamental results on the long time behaviour of**Markov****chains**. Since 2005, he has been working on statistical ... coupling estimation and simulation problems with Monte Carlo**Markov****Chain**Methods (MCMC). He has also developed numerous ...###### Discrete event dynamic system

Supervisory control theory Petri net theory Discrete event system specification Boolean differential calculus

**Markov****chain**...###### Munther A. Dahleh

Crescent Technologies (1996-2000): Founder, Supply

**chain**systems for large-scale production. BAE (2009-present): Fast ... learning low dimensional Hidden**Markov**Models. Dahleh has served on multiple panels, boards and visiting committees. He is the ...###### Felix Kübler

... assuming that all exogenous variables follow a

**Markov****chain**, there are also stationary equilibria, which can be characterized ...###### 100 mm anti-tank gun T-12

Hull,

**Markov**& Zaloga 1999, p. VI-13. Широкорад 1997. Dyčka 2017, p. 101. Dyčka 2017, p. 102. Hull,**Markov**& Zaloga 1999, p. VI ... The wheels are rolled up to the runners and fastened with a coupling**chain**. The gun can fire directly from the skis. The ...**Markov**, David R.; Zaloga, Steven J. (1999), Soviet/Russian Armor and Artillery Design Practices 1945 to Present, Darlington ...###### Wang and Landau algorithm

**Markov**

**chain**Monte Carlo, Statistical algorithms, Computational physics, Articles with example Python (programming language) ...

###### Dissociated press

Cut-up technique

**Markov****chain**Mark V. Shaney Racter Word salad Parody generator, generic term for a computer program that ... The generated text is based on another text using the**Markov****chain**technique. The name is a play on "Associated Press" and the ...###### Uniformization (probability theory)

For a continuous-time

**Markov****chain**with transition rate matrix Q, the uniformized discrete-time**Markov****chain**has probability ... This representation shows that a continuous-time**Markov****chain**can be described by a discrete**Markov****chain**with transition ... by approximating the process by a discrete-time**Markov****chain**. The original**chain**is scaled by the fastest transition rate γ, so ... Matlab implementation Stewart, William J. (2009). Probability,**Markov****chains**, queues, and simulation: the mathematical basis of ...###### PageRank

It can be understood as a

**Markov****chain**in which the states are pages, and the transitions are the links between pages - all of ... As a result of**Markov**theory, it can be shown that the PageRank of a page is the probability of arriving at that page after a ...**Markov**models, Link analysis, Articles with example MATLAB/Octave code, Graph algorithms). ...###### List of statistical software

Bayesian analysis using

**Markov****chain**Monte Carlo methods Winpepi - package of statistical programs for epidemiologists Alteryx ... a program for analyzing Bayesian hierarchical models using**Markov****chain**Monte Carlo developed by Martyn Plummer. It is similar ...###### Fine-structure constant

have used

**Markov****chain**Monte Carlo methods to investigate the algorithm used by the UNSW group to determine Δα/ α from the ... King, J.A.; Mortlock, D.J.; Webb, J.K.; Murphy, M.T. (2009). "**Markov****chain**Monte Carlo methods applied to measuring the fine ...###### Multicanonical ensemble

The tunneling time is defined by the number of

**Markov**steps (of the**Markov****chain**) the simulation needs to perform a round-trip ... In statistics and physics, multicanonical ensemble (also called multicanonical sampling or flat histogram) is a**Markov****chain**...###### Total variation distance of probability measures

David A. Levin, Yuval Peres, Elizabeth L. Wilmer,

**Markov****Chains**and Mixing Times, 2nd. rev. ed. (AMS, 2017), Proposition 4.2, p ...###### Representing Sampling Distributions Using **Markov** **Chain** Samplers
- MATLAB & Simulink

**Markov**

**chain**samplers can generate numbers from a sampling distribution that is difficult to represent directly. ...

**Markov**

**chain**with a stationary distribution equal to the target sampling distribution, using the states of the

**chain**to ... Such distributions arise, for example, in Bayesian data analysis and in the large combinatorial problems of

**Markov**

**chain**Monte ... Representing Sampling Distributions Using

**Markov**

**Chain**Samplers. For probability distributions that are complex, or are not in ...

###### rwet/ngrams-and-**markov**-**chains**.ipynb at master · aparrish/rwet · GitHub

###### Probabilistic Model of Cumulative Damage in Pipelines Using **Markov** **Chains**

This paper presents a probabilistic model of cumulative damage based on

**Markov****chains**theory to model propagation of internal ... to represent this probability mass function and, based on**Markovs****chain**theory:. p x = p 0 P x = p x − 1 P ∀ x = 0 , 1 , 2 , ...**Markov****chains**or processes. Andrei Andreyevich**Markov**was a Russian mathematician known for his works on theory of numbers and ... Probabilistic Model of Cumulative Damage in Pipelines Using**Markov****Chains**() Francisco Casanova-del-Angel, Esteban Flores- ...###### Dynamics of Multiple, Interacting and Concurrent **Markov** **Chains** | DYNAMICMARCH Project | Results | H2020 | CORDIS | European...

###### Stochastic Modeling with **Markov** **Chains** | Stochastics Group | Universität des Saarlandes

This course aims to provide an introduction on

**Markov****chains**in discrete time. The main content includes:. ***Markov****chains**; ... O. Häggström, Finite**Markov****Chains**and Algorithmic Applications, Cambridge, 2002. (available online in the IP range of Saarland ... Hitting probabilities and mean hitting times; Birth and death**chains**, in particular M/M/1 model; ...**Markov**-**chain**-params

###### Optimal Tagging with **Markov** **Chain** Optimization

###### RSFgen: use of -nreps with **Markov** **Chain**

RSFgen to optimal stimulus sequences and have restrictions on what conditions can follow which so I am using the

**Markov****chain**... Is -nreps a null option when using -**markov**. I suspect that the -nreps information should be built into the**Markov****chain**... Re: RSFgen: use of -nreps with**Markov****Chain**Vincent Costa. September 18, 2009 10:40AM. ... Re: RSFgen: use of -nreps with**Markov****Chain**Vincent Costa. September 24, 2009 04:34PM. ...###### 2002.01184] tfp.mcmc: Modern **Markov** **Chain** Monte Carlo Tools Built for Modern Hardware

Abstract:

**Markov****chain**Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. Its ... Title:tfp.mcmc: Modern**Markov****Chain**Monte Carlo Tools Built for Modern Hardware. Authors:Junpeng Lao, Christopher Suter, Ian ... Download a PDF of the paper titled tfp.mcmc: Modern**Markov****Chain**Monte Carlo Tools Built for Modern Hardware, by Junpeng Lao ... Download a PDF of the paper titled tfp.mcmc: Modern**Markov****Chain**Monte Carlo Tools Built for Modern Hardware, by Junpeng Lao ...###### Etymologia: **Markov** **Chain** Monte Carlo - Volume 25, Number 12-December 2019 - Emerging Infectious Diseases journal - CDC

**Markov**

**Chain**Monte Carlo. A

**Markov**

**chain**Monte Carlo (MCMC) simulation is a method of estimating an unknown probability ... In a

**Markov**

**chain**(named for Russian mathematician Andrey

**Markov**[Figure]), the probability of the next computed estimated ...

**Markov**

**chain**Monte Carlo: an introduction for epidemiologists. Int J Epidemiol. 2013;42:627-34. DOIPubMedGoogle Scholar ... A simple introduction to

**Markov**

**Chain**Monte-Carlo sampling. Psychon Bull Rev. 2018;25:143-54. DOIPubMedGoogle Scholar ...

###### Efficient Continuous-Time **Markov** **Chain** Estimation | UBC Department of Statistics

**Markov** **chain** Monte Carlo methods in biostatistics - PubMed

**Markov**

**chain**Monte Carlo (MCMC) methods are an important set of tools for such simulations. We give an overvi … ...

**Markov**

**chain**Monte Carlo methods in biostatistics A Gelman et al. Stat Methods Med Res. 1996 Dec. ...

**Markov**

**chain**Monte Carlo methods in biostatistics A Gelman 1 , D B Rubin ... Bayesian models and

**Markov**

**chain**Monte Carlo methods for protein motifs with the secondary characteristics. Xie J, Kim NK. Xie ...

**Markov** **Chain** vs Hidden **Markov** Model - Cross Validated

I am a beginner on using

**Markov**models, but I did some research in the last days regarding**Markov****chain**/hidden**Markov**model. So ... Thank you in advance to everyone, who will take some time to help me on understanding better the**Markov****chain**and HMM. ... A bigram model is essentially a**markov****chain**. You have to either manually specify the parameters like P(brush/line tool) or ... A trigram model is a second order**markov****chain**. Hence you consider two previous interactions to predict the next, like P(brush ...###### probability - Spectral gap of mixture of **Markov** **chains** - Mathematics Stack Exchange

In this example, one of the matrices is a graph laplacian (which could have been written as a

**markov****chain**) and the other is ... This is related to the mixing time of the**Markov****chain**; the bigger the spectral gap, the faster the convergence to the ... Let $P$ be the transition matrix of an irreducible, aperiodic, discrete-time**Markov****chain**. The spectral gap is given by ... Intuitive explanation of the spectral gap in context of**Markov****Chain**Monte Carlo (MCMC) ...###### Quasi 3D transdimensional **Markov**-**chain** Monte Carlo for seismic impedance inversion and uncertainty analysis | Interpretation |...

Quasi 3D transdimensional

**Markov**-**chain**Monte Carlo for seismic impedance inversion and uncertainty analysis Yongchae Cho; ... The**Markov**-**chain**Monte Carlo (MCMC) stochastic approach is widely used to estimate subsurface properties. We have used a ... Yongchae Cho, Richard L. Gibson Jr., Dehan Zhu; Quasi 3D transdimensional**Markov**-**chain**Monte Carlo for seismic impedance ... Joint probabilistic petrophysics-seismic inversion based on Gaussian mixture and**Markov****chain**prior models Geophysics ...###### Modelling spectrum assignment in a two-service flexi-grid optical link with imprecise continuous-time **Markov** **chains** - Alexander...

The obtained imprecise

**Markov****chain**can be used to evaluate the precision of approximate reduced-state models as well as to ... Modelling spectrum assignment in a two-service flexi-grid optical link with imprecise continuous-time**Markov****chains**. Cristina ... Imprecise continuous-time**Markov****chains**: Efficient Computational methods with guaranteed error bounds → ... In addition, we introduce a**Markov**model that uses imprecise probabilities, which allows us to derive upper and lower bounds on ...###### Introduction to the **Markov** **Chain** and **Markov** Decision Process

Using SpiceLogic Rational Will

**Markov**Decision Process tool to model and analyze a Decision Problem ... Modeling**Markov****Chain**and**Markov**Decision Process. SpiceLogic Decision Tree Software lets you model a**Markov****Chain**or**Markov**... A**Markov****Chain**or a**Markov**Decision Process is built with the**Markov**States.**Markov**State is similar to a Decision Tree Chance ... to a**Markov**State or**Markov**Action and perform Utility Analysis or Cost-Effectiveness Analysis for that**Markov****Chain**or**Markov**...###### Bounds on regeneration times and convergence rates for **Markov** **chains**. - Research Portal | Lancaster University

###### Estimation of trace gas fluxes with objectively determined basis functions using reversible jump **Markov** **Chain** Monte Carlo<...

We rely on the well-established reversible-jump

**Markov****chain**Monte Carlo algorithm to use the data to determine the dimension ... We rely on the well-established reversible-jump**Markov****chain**Monte Carlo algorithm to use the data to determine the dimension ... We rely on the well-established reversible-jump**Markov****chain**Monte Carlo algorithm to use the data to determine the dimension ... We rely on the well-established reversible-jump**Markov****chain**Monte Carlo algorithm to use the data to determine the dimension ...**Markov** **Chain** Analysis of Electricity Distribution Networks

... Volchenkov D (2010) In: Advances in Energy Research. Acosta MJ (Ed ...

**Markov****Chain**Analysis of Electricity Distribution Networks. In M. J. Acosta, ed. Advances in Energy Research. Advances in ... "**Markov****Chain**Analysis of Electricity Distribution Networks". In Advances in Energy Research, ed. Morena J. Acosta. Vol. 6. ... Volchenkov D.**Markov****Chain**Analysis of Electricity Distribution Networks. In: Acosta MJ, ed. Advances in Energy Research. ...**Markov** **Chain** Models
- MATLAB & Simulink
- MathWorks Benelux

Discrete-Time

**Markov****Chains**.**Markov****chains**are discrete-state**Markov**processes described by a right-stochastic transition ...**Markov****Chain**Modeling. The dtmc. class provides basic tools for modeling and analysis of discrete-time**Markov****chains**. The class ... Visualize**Markov****Chain**Structure and Evolution. Visualize the structure and evolution of a**Markov****chain**model by using dtmc. ... Create and Modify**Markov****Chain**Model Objects. Create a**Markov****chain**model object from a state transition matrix of ...###### Introduction to **Markov** **Chains**: Prerequisites, Properties & Applications | upGrad blog

Learn more about

**Markov****chains**, its working and properties in this article. ... Did you know that Google ranks pages using the**Markov**model? ... Introduction to**Markov****Chains**.**Markov****chains**get their name ... Properties of**Markov****Chains**. Lets take a look at the fundamental features of**Markov****chains**to understand them better. We wont ... Applications of**Markov****Chains**.**Markov****chains**find applications in many areas. Here are their prominent applications: ...**Markov** **Chain** MOOC and Free Online Courses | MOOC List

**Markov** **Chains**

... 2018-08-12. The first time I ever heard of a

**Markov****chain**was overhearing a conversation at work. My coworker ...**Markov****chains**were invented by Andrey**Markov**,a Russian mathematician who lived in St. Petersburg during the end of the Russian ... func main() {**chain**, err := BuildChain(os.Stdin) if err != nil { panic(err) } for _, cc := range AllCharClasses { link :=**chain**... const Vowels = aáàäâæeéèëêiíïîoóôöœuüúý func BuildChain(r io.Reader) (**Chain**, error) { bf := bufio.NewReader(r)**chain**:= make( ...**Markov** **Chain** Monte Carlo: Innovations and Applications - Institute for Mathematical Science

**Markov** **chain**

almost reversed 2-lag

**Markov****chain**. Posted in Kids, R, Statistics with tags combinatorics,**Markov****chain**, mathematical puzzle, R ... Posted in Statistics with tags**Markov****chain**,**Markov****chain**Monte Carlo algorithm, MCMC convergence, particle filter, pseudo- ... Posted in Books, R, Statistics with tags ergodicity, integral priors,**Markov****chain**,**Markov**kernel, MCMC, null recurrence, R, ... Above, the result of an experiment where I simulated a**Markov****chain**as a Normal random walk in dimension one, hence a Harris π- ...###### Arnout's Eclectica » Fun with **Markov** **chains**

**Markov** **Chain** Models
- MATLAB & Simulink
- MathWorks Italia

Discrete-Time

**Markov****Chains**.**Markov****chains**are discrete-state**Markov**processes described by a right-stochastic transition ...**Markov****Chain**Modeling. The dtmc. class provides basic tools for modeling and analysis of discrete-time**Markov****chains**. The class ... Visualize**Markov****Chain**Structure and Evolution. Visualize the structure and evolution of a**Markov****chain**model by using dtmc. ... Create and Modify**Markov****Chain**Model Objects. Create a**Markov****chain**model object from a state transition matrix of ...###### Absorbing **Markov** **Chains** | Brilliant Math & Science Wiki

An absorbing

**Markov****chain**is a**Markov****chain**in which it is impossible to leave some states, and any state could (after some ... It follows that all non-absorbing states in an absorbing**Markov****chain**are transient. An absorbing state is a state ... ... A common type of**Markov****chain**with transient states is an absorbing one. ... An absorbing**Markov****chain**A common type of**Markov****chain**with transient states is an absorbing one. An absorbing**Markov****chain**is ...###### Predicting Future Events with the **Markov** **Chain**

A

**Markov****Chain**is a math concept that is used to describe transitions from one state to another in accordance with a specific ... also known as**Markov**random fields or the**Markov****Chain**Monte Carlo. ... For this reason,**Markov****Chain**Monte Carlo (MCMC) sampling is one method that can be used to randomly generate high dimensional ... A**Markov****Chain**(MC) refers to a mathematical concept that is used to describe transitions from one state to another in ...Monte CarloMCMCAndrey MarkovProbabilityConvergenceProbabilitiesBayesianTransdimensionalStationaryAperiodicIrreducibleDiscrete-stateMathematicianSEQUENCEAlgorithmProcessesOptimizationSimulationFiniteModelTransitionsGenerateGraphBoundsMathematicsProcessTimeIntroductionHidden MarkovBuiltStateRandomSimilarAnalysisTimesStudyQuestionNull

###### Monte Carlo17

- Such distributions arise, for example, in Bayesian data analysis and in the large combinatorial problems of Markov chain Monte Carlo (MCMC) simulations. (mathworks.com)
- A Markov chain Monte Carlo (MCMC) simulation is a method of estimating an unknown probability distribution for the outcome of a complex process (a posterior distribution). (cdc.gov)
- Markov chain Monte Carlo simulations allow researchers to approximate posterior distributions that cannot be directly calculated. (cdc.gov)
- Hamra G , MacLehose R , Richardson D . Markov chain Monte Carlo: an introduction for epidemiologists. (cdc.gov)
- A simple introduction to Markov Chain Monte-Carlo sampling. (cdc.gov)
- Markov chain Monte Carlo (MCMC) methods are an important set of tools for such simulations. (nih.gov)
- Assessing convergence of Markov chain Monte Carlo simulations in hierarchical Bayesian models for population pharmacokinetics. (nih.gov)
- Markov chain Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. (arxiv.org)
- The Markov-chain Monte Carlo (MCMC) stochastic approach is widely used to estimate subsurface properties. (geoscienceworld.org)
- This paper reviews the way statisticians use Markov Chain Monte Carlo (MCMC) methods. (cmu.edu)
- We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. (bris.ac.uk)
- Seeing the Haar measure appearing in the setting of Markov chain Monte Carlo is fun! (wordpress.com)
- On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo. (bvsalud.org)
- Using a Markov chain Monte Carlo (MCMC) algorithm for posterior computation, we found evidence in favor of a previously hypothesized but unproven association between slow growth early in pregnancy and increased risk of future spontaneous abortion. (nih.gov)
- 9. Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. (nih.gov)
- 12. Markov chain Monte Carlo: an introduction for epidemiologists. (nih.gov)
- Respondent-driven sampling as Markov chain Monte Carlo. (bvsalud.org)

###### MCMC1

- Metropolis-Hastings and slice sampling can produce MCMC chains that mix slowly and take a long time to converge to the stationary distribution, especially in medium-dimensional and high-dimensional problems. (mathworks.com)

###### Andrey Markov3

- In a Markov chain (named for Russian mathematician Andrey Markov [ Figure ]), the probability of the next computed estimated outcome depends only on the current estimate and not on prior estimates. (cdc.gov)
- Markov chains get their name from Andrey Markov, who had brought up this concept for the first time in 1906. (upgrad.com)
- Markov chains were invented by Andrey Markov,a Russian mathematician who lived in St. Petersburg during the end of the Russian Empire. (pboyd.io)

###### Probability4

- I suspect that the -nreps information should be built into the Markov chain probability matrix, however, I'm not clear on how this should be done. (nih.gov)
- Markov chains refer to stochastic processes that contain random variables, and those variables transition from a state to another according to probability rules and assumptions. (upgrad.com)
- A more elaborate definition would be: Markov property says that the probability of a stochastic process only depends on its current state and time, and it is independent of the other states it had before. (upgrad.com)
- Items in a Markov chain are technically linked with a probability, not a count. (pboyd.io)

###### Convergence1

- Bounds on regeneration times and convergence rates for Markov chains. (lancs.ac.uk)

###### Probabilities5

- In addition, we introduce a Markov model that uses imprecise probabilities, which allows us to derive upper and lower bounds on blocking probabilities without needing to specify an assignment policy. (ugent.be)
- But, before getting to the Decision Tree diagram view, you will see a Step by Step wizard show up so that you can easily answer questions about what will be the Markov States, their transition probabilities, etc. (spicelogic.com)
- Probably it is better to review and set up your Markov Simulation setting before performing the simulation and setting up transition probabilities. (spicelogic.com)
- Create a Markov chain model object from a state transition matrix of probabilities or observed counts, and create a random Markov chain with a specified structure. (mathworks.com)
- Using a Markov chain model, we calculated probabilities of each outcome based on projected increases in seeking help or availability of professional resources. (cdc.gov)

###### Bayesian1

- 18. Bayesian posterior distributions without Markov chains. (nih.gov)

###### Transdimensional1

- The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. (bris.ac.uk)

###### Stationary2

- An alternative is to construct a Markov chain with a stationary distribution equal to the target sampling distribution, using the states of the chain to generate random numbers after an initial burn-in period in which the state distribution converges to the target. (mathworks.com)
- Compute the stationary distribution of a Markov chain, estimate its mixing time, and determine whether the chain is ergodic and reducible. (mathworks.com)

###### Aperiodic2

- Let $P$ be the transition matrix of an irreducible, aperiodic, discrete-time Markov chain. (stackexchange.com)
- When all states of a Markov chain are aperiodic, then we can say that the Markov chain is aperiodic. (upgrad.com)

###### Irreducible1

- Markov chains are irreducible. (upgrad.com)

###### Discrete-state3

- A discrete state-space Markov process, or Markov chain , is represented by a directed graph and described by a right-stochastic transition matrix P . The distribution of states at time t + 1 is the distribution of states at time t multiplied by P . The structure of P determines the evolutionary trajectory of the chain, including asymptotics. (mathworks.com)
- Markov chains are discrete-state Markov processes described by a right-stochastic transition matrix and represented by a directed graph. (mathworks.com)
- A homogeneous discrete-time Markov chain is a Marko process that has discrete state space and time. (upgrad.com)

###### Mathematician1

- Markov was outspoken and rebellious throughout his life, which led to a feud with another mathematician, Pavel Nekrasov. (pboyd.io)

###### SEQUENCE1

- The Poisson-based hidden Markov model (PHMM) is used to capture the sequence of read counts. (nih.gov)

###### Algorithm1

- And if you're familiar with that algorithm, you must also know that it uses Markov chains. (upgrad.com)

###### Processes1

- Markov property makes the study of these random processes quite easier. (upgrad.com)

###### Optimization1

- Does maybe exist a review about the optimization of Markov chain orders? (stackexchange.com)

###### Simulation4

- The decision tree software will execute a cohort simulation to solve the Markov Chain or Markov Decision Process. (spicelogic.com)
- You can define the cohort simulation setting by clicking this fly-over menu icon from the Markov Chance node. (spicelogic.com)
- Once you click that button, the Markov Cohort Simulation setting for that chance node will open up as shown below. (spicelogic.com)
- The software uses 100 as default, which is fair enough for any regular Markov simulation but for healthcare applications, you may need to set that based on exactly how many years of prediction you want. (spicelogic.com)

###### Finite1

- The class supports chains with a finite number of states that evolve in discrete time with a time-homogeneous transition structure. (mathworks.com)

###### Model16

- This paper presents a probabilistic model of cumulative damage based on Markov chains theory to model propagation of internal corrosion depth localized in a hydrocarbons transport pipeline. (scirp.org)
- Casanova-del-Angel, F. , Flores-Méndez, E. and Cortes-Yah, K. (2020) Probabilistic Model of Cumulative Damage in Pipelines Using Markov Chains. (scirp.org)
- And for the purpose, I want to use either Markov Model or Hidden Markov model to recommend next interaction. (stackexchange.com)
- I am a beginner on using Markov models, but I did some research in the last days regarding Markov chain/hidden Markov model. (stackexchange.com)
- A bigram model is essentially a markov chain. (stackexchange.com)
- A trigram model is a second order markov chain. (stackexchange.com)
- a bigram model (A first order markov chain) and see how effective it is. (stackexchange.com)
- SpiceLogic Decision Tree Software lets you model a Markov Chain or Markov Decision Process using a special node called Markov Chance Node. (spicelogic.com)
- If you have already created a decision tree, you can attach a Markov model to an action node as shown in the following screenshot. (spicelogic.com)
- Once you click the Markov Chance node button or the Markov Model button, you will be presented with a Wizard for creating your Markov model step by step. (spicelogic.com)
- Once you finish the wizard, a Markov model will be created and you will see a decision tree-like diagram for your model. (spicelogic.com)
- In the following section, you will learn how to modify your Markov Model which is already created by the wizard. (spicelogic.com)
- A Markov chain model for mental health interventions. (cdc.gov)
- We developed a Markov chain model to determine whether decreasing stigma or increasing available resources improves mental health outcomes. (cdc.gov)
- The approach uses a Poisson hidden Markov model (PHMM) to 1) estimate (hidden) states of gene expression levels in terminal exon 3' UTRs, 2) infer shortening of the region and 3) demonstrate alternative polyadenylation. (nih.gov)
- To solve this problem, we propose a Markov chain model in reverse time. (nih.gov)

###### Transitions1

- We formulate the problem by modeling traffic using a Markov chain, and asking how transitions in this chain should be modified to maximize traffic into a certain state of interest. (neurips.cc)

###### Generate2

- So my question boils down to how to use the -markov option and still generate an equal number of stimulus events for each of the 6 conditions? (nih.gov)
- Generate and visualize random walks through a Markov chain. (mathworks.com)

###### Graph2

- In this example, one of the matrices is a graph laplacian (which could have been written as a markov chain) and the other is not. (stackexchange.com)
- If we can represent the chain with a graph, then the graph would be firmly connected. (upgrad.com)

###### Bounds1

- The obtained imprecise Markov chain can be used to evaluate the precision of approximate reduced-state models as well as to provide policy-free performance bounds. (ugent.be)

###### Mathematics1

- Markov was an atheist, and had no intention of leaving Nekrasov's "abuse of mathematics" unchallenged. (pboyd.io)

###### Process3

- You can set reward (or Payoff) to a Markov State or Markov Action and perform Utility Analysis or Cost-Effectiveness Analysis for that Markov Chain or Markov Decision Process. (spicelogic.com)
- A Markov Chain or a Markov Decision Process is built with the Markov States. (spicelogic.com)
- A Markov property states that we wouldn't get more information about the future outcomes of a process by increasing our knowledge about its past if we know its value at a particular time. (upgrad.com)

###### Time4

- This course aims to provide an introduction on Markov chains in discrete time. (uni-saarland.de)
- Thank you in advance to everyone, who will take some time to help me on understanding better the Markov chain and HMM. (stackexchange.com)
- class provides basic tools for modeling and analysis of discrete-time Markov chains. (mathworks.com)
- The first time I ever heard of a Markov chain was overhearing a conversation at work. (pboyd.io)

###### Introduction1

- In our introduction to Markov chains, we'll take a brief look at them and u nderstand what they are. (upgrad.com)

###### Hidden Markov1

- Can Hidden Markov Models be used to predict next observation? (stackexchange.com)

###### Built1

- I don't know how that's built, of course, but it could be a Markov chain. (pboyd.io)

###### State3

- So far, I think the Markov chain is easy usable in my project if a use the interaction as a State? (stackexchange.com)
- Markov State is similar to a Decision Tree Chance node, but unlike a Decision tree chance node, a Markov state can be cyclic. (spicelogic.com)
- Say you added three states under a Markov Chance node and named them 'Healthy', 'Sick', and 'Dead', you will see that all the state nodes are connected to each other in order to complete a Markov transition system. (spicelogic.com)

###### Random1

- They used Markov Random Field (MRF) to sifiers, and class syntax models are all learned from train- represent contextual information to improve feature classi- ing data. (nih.gov)

###### Similar1

- Markov used a similar technique on 20,000 characters from Eugene Onegin , and subsequently analyzed 100,000 characters of a novel . (pboyd.io)

###### Analysis2

- Markov Chain Analysis of Electricity Distribution Networks" in Advances in Energy Research , Acosta, M. J. ed. (uni-bielefeld.de)
- For an overview of the Markov chain analysis tools, see Markov Chain Modeling . (mathworks.com)

###### Times1

- Compare the estimated mixing times of several Markov chains with different structures. (mathworks.com)

###### Study1

- Markov used this chain to study the distribution of vowels and consonants in text. (pboyd.io)

###### Question1

- First Question/issue is about deciding which one to use Markov chain or HMM? (stackexchange.com)

###### Null2

- Is -nreps a null option when using -markov. (nih.gov)
- converges holds for a Harris π-null-recurrent Markov chain for all functions f,g in L¹(π) [ Meyn & Tweedie, 1993 , Theorem 17.3.2] is rather fascinating. (wordpress.com)