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# Stochastic Models - Science topic

Explore the latest questions and answers in Stochastic Models, and find Stochastic Models experts.

Questions related to Stochastic Models

In robust optimization, random variables are modeled as uncertain parameters belonging to a convex uncertainty set and the decision-maker protects the system against the worst case within that set.

In the context of nonlinear multi-stage max-min robust optimization problems:

What are the best robustness models such as Strict robustness, Cardinality constrained robustness, Adjustable robustness, Light robustness, Regret robustness, and Recoverable robustness?

How to solve max-min robust optimization problems without linearization/approximations efficiently? Algorithms?

How to approach nested robust optimization problems?

For example, the problem can be security-constrained AC optimal power flow.

To start a collaborative Project:

Conference Paper ESSAY ON BIG DATA AND STOCHASTIC MODEL copyright@Amin ELSALEH

The target is to participate to the meeting INNOVATE 2022 Conference at MERLOT University

I am familiar with the concept of stochastic ordering for two random variables and how we can say if a markov matrix is stochastically monotone. What I'm interested in is if there is a concept for ranking two separate markov matrices.

To illustrate suppose we have two stochastically monotone markov matrices A and B which preserve the ordering of x≿y. Under what circumstances can we say (if any) that matrix A is preferred to matrix B in stochastic order?

*Note: The definitions I am using are from this slide deck:*http://polaris.imag.fr/jean-marc.vincent/index.html/Slides/asmta09.pdf

My essay is an attempt to answer the following : « Is the data economy, then, destined to benefit only a few elite firms? » Apparently that would be the issue till now. What are available tools to avoid this false target ? Reference to my essay on Stochastic Models in particular the section « Handling human social technical dimension; in particular man-system interface including positioning technology at man services » you may find guidelines to produce these tools and make BIG DATA exploitable by large majority of users : 1. Engine should trace “player” behaviour, evaluate its capabilities and quickly meet its needs. 2. Immersion generated by simulation enables training and experimentation of behaviour strategies, in particular learning “by doing”. 3. Engine should use following resources : 3.1. Tools to be customized by trainers. 3.2. Applied standards. 3.3. New learning approaches discovery through obtained results, whether these approaches are positive or negative, in the sense of improving technology performance of assembled prototypes. 4. How SPDF (Standard Process Description Format) may produce a universal engine to run the stochastic model ? 4.1. SPDF consists of two parts : 4.1.1. Message structured-data part (including semantics) and, 4.1.2. Process description part (with higher level of semantics). 4.2. Two key outputs of the SPDF research will be a process description specification and framework for the extraction of semantics from legacy systems. 4.2.3. Note that : a)The more we may have semantic rules the more unpredictable events are controlled. b) Acquired knowledge to elaborate semantic rules for unpredictable events requires many occurrences of the stochastic model. c) Convergence shall not be reached until getting more qualitative semantic rules. d) Performing dynamically a given scenario is the goal of the proposed messaging system.

I have computed the basic reproduction number for deterministic system by second generation matrix described in the paper . But in this paper with stochastic model , basic reproduction number have been shown for stochastic counterpart. I am totally confused how they computed it. Please put some light on it.

Which one is best in modeling deterministic model, stochastic model or fractional differential equation model?

Stochastic Modelling with Optimal Control

Chemical reaction systems can be modeled through a deterministic or stochastic approach. However, it is common to introduce new variables in order to perform dynamic analysis in deterministic systems. Could these reduced forms be directly used to derive stochastic equations or is it necessary to start from the original expressions? It is common for many concentrations to be normalized after these procedures.Does this affect the construction of stochastic models?

It is known that the FPE gives the time evolution of the probability density function of the stochastic differential equation.

I could not see any reference that relates the PDF obtain by the FPE with trajectories of the SDE.

for instance, consider the solution of corresponding FPE of an SDE converges to pdf=\delta{x0} asymptotically in time.

does it mean that all the trajectories of the SDE will converge to x0 asymptotically in time?

Few days earlier on a project presentation on Stochastic Programming Real life applications, i constructed 3 real life scenario based Stochastic Models:

**A Farmer's Problem, Container Allotment Problem and another on Stochastic Arc Routing**. Also solved them for particular scenario.As stochastic linear programs are lengthy programs with a lot of constraints, it is long-time process to solve a stochastic linear program. And therefore i used LINDO solver to solve the problem. I have a L-shaped algorithm based example too.

But the examiner said me that, why you didn't used the general solving procedure to solve these LP problems? I explained about the long programs and complexity. In reply, I found complement that

**all credit goes to the LINDO solver, not you**.I am wondering that advances in Science could make our works easier and faster. Shouldn't we take these type of advances in our daily life?

If existing microgrid energy management system is deterministic, how to design it in real time probabilistic or stochastic model?

How to get expertise in this modeling?

(1) What is difference between Fuzzy and Stochastic ?

(2) Fuzzy number converted to Non-Fuzzy. What great advantage is derived in using Fuzzy ?

(3) Can it be Fuzzy and Stochastic model viz. Fuzzy Stochastic TOPSIS ?

I want to improve the specification performance of my MEMS Gyro, As we know, the measurement errors of a MEMS gyroscope usually contain deterministic errors and stochastic errors. I just focus on stochastic part and so we have:

y(t) = w(t)+b(t)+n(t)

where:

{w(t) is "True Angular Rate"}

{b(t) is "Bias Drift"}

{n(t) is "Measurement Noise"}

The bias drift and other noises are usually modeled in a filtering system to compensate for the outputs of gyroscope to improve accuracy. In order to achieve a considerable noise reduction, there's another solution that the true angular rate and bias drift are both modeled to set as the system state vector to design a KF.

Now if I want model the true angular rate, How could I do this? I just have a real dynamic test of gyro that includes above terms and I don't know how can I determine parameters required by the different models (such as Random Walk, 1st Gauss Markov or AR) for modeling ture angular rate from an unknown true angular rate signal!

Please do anybody with an idea on how to estimate linear stochastic models of time series analysis? Be it material or link that might help.

I want to predict 2013 landuse change based on Markovian stochastic model using CA-MARKOV module.It takes long time, sometimes 24hrs to 3 days. What might be wrong?

I have already run MARKOV module to cross tabulate 2000 and 2006 Landuses. I have suitability maps in Raster group file(each stretched 0-255 integer values), i have also the Markov Transition area file. I am now using 2006 Landuse to predict 2013 Landuse change, where i specified 7 as a Number of Cellular automata iterations, 5 x5 filter.

I have also checked the disk space i have 45GB, RAM is 8GB,

Other computer specifications :Windows7 , Core i3.

Software in Use:IDRISI SELVA v17.00

The process runs well and pass from step 1 to 8, then in step 8 when starts "mola" process, it stays there for so long more 24hrs-5 days, before i terminate it.

Anyone with similar experience? Please help.

Any stochastic model is very easy derived from a known deterministic model.

I need help in understanding the role of (random) sampling in implementation of a control system in Simulink. I need a basic, general example to visualize the role of the sampler in a control system, and the way it can be programmed (to be random/event-triggered etc).

Any help in this regard is very much appreciated

Thank you in advance

I have 3 objective function in one GAMS code. I have 3 different state stochastic models that each state includes 1000 scenarios which uses in each objective function. (I mean one stochastic data for one objective function). I want to use scented in my code for all objective functions.

It`s possible to do that? How can I do?

If we train a data model once on a dataset using a machine learning algorithm, save the model, and then train it again using the same algorithm and the same dataset and data ordering, will the first model be the same as the second?

I would propose a classification of ml algorithms based on their "determinism"

in this respect. On the one extreme we would have:

(i) those which always produce an identical model when trained from the same dataset with the records presented in the same order and on the other end we would have:

(ii) those which produce a different model each time with a very high variability.

Two reasons for why a resulting model varies could be (a) in the machine learning algorithm itself there could be a random walk somewhere, or (b) a sampling of a probability distribution to assign a component of an optimization function. More examples would be welcome !

Also, it would be great to do an inventory of the main ML algorithms based on their "stability" with respect to retraining under the same conditions (i.e. same data in same order). E.g. decision tree induction vs support vector vs neural networks. Any suggestions of an initial list and ranking would be great !

for quite a comprehensive list of methods.

In Time Dependent Model, the definition of foreshock, mainshock and aftershock is not necessary. In this model, every event is potentially triggered by all the previous events and every event can trigger subsequent events according to their relative time-space distance. What do you say about Stochastic models of earthquake clustering?

What are Stochastic models of earthquake clustering?.

Several theoretical models have been proposed for the study of the lasing behavior in random media such as "Correlated Random Walk", "diffusion with gain", "disorder induced localization coupled with non-linearity". But it seems that none of them have been able to cover the diverse experimental results. I need a model that predicts both localized and extended modes in two and three dimension.

I have hydraulic conductivity data from pumping wells in the area and I try to use this raw data to generate many realizations to see the uncertainty of flow and transport of pollutants. Please suggest the public model to create the stochastic modeling and can be further used as the input data for visual modflow.

I have question regarding simulating under mentioned 1D Stochastic Differential Equation in R using Sim.DiffProc package:

dx1 = (b1*x1 − d1*x1) dt + Sqrt(b1*x1 + d1*x1) dW1(t)

I have taken this equation from book: Modeling with Ito Stochastic Differential Equations by E. Allen. In the deterministic and diffusion part of equation, b1 and d1 are model parameters representing birth and death rates (for single population approximation of two interacting populations compartment model). Relevant lines of my code are as under (note that i,ve used theta's to represent parameters in my code):

Code (1):

> fx <- expression( theta[1]*x1-theta[2]*x1 ) ## drift part

> gx <- expression( (theta[3]*x1+theta[4]*x1)^0.5 ) ## diffusion part

> fitmod <- fitsde(data=mydata,drift=fx,diffusion=gx,start = list(theta1=1,

+ theta2=1,theta3=1,theta4=1),pmle="euler")

Or should I model it like this

Code (2):

>fx <- expression( theta[1]*x1-theta[2]*x1 )

> gx <- expression( (theta[1]*x1+theta[2]*x1)^0.5 )

> fitmod <- fitsde(data=mydata,drift=fx,diffusion=gx,start = list(theta1=1,

+ theta2=1),pmle="euler")

I am not clear whether to use theta[1], theta[2], theta[3], theta[4] as I have used at first place above or should I code it like only using parameters theta[1] and theta[2] (done at second place above) because in original model the parameters b1 and d1(birth and death rates) appearing in the deterministic part are same as appearing in the diffusion part.

I don’t find a single example in Sim.DiffProc package documentation where there is any repetition of parameters just like I have done at second place.

Thanking in anticipation and best regards.

Saad Sharjeel.

Hello Researchers,

I am trying to model a Noise which is basically difference between Actual and Theoretical Solar radiation. As I am concerned on Long term prediction, models like ARMA is not a suitable option.

Can someone of you suggest models that can be used to model the same. I am looking forward for a stochastic model.

Thanks!

I am looking for a stochastic model in use clearly for extreme rainfall generation.

the rainfall will be used for hydraulic models and drainage system models.

few concepts are developed in past but it seems there is not any toolkit or software with manual about them, like

Neyman-Scott (NS) or Bartlett-Lewis or DRIP MODEL

thanks

Other stochastic modelling processes which can be used to model the data being modelled by dirichlet process

Hello Researchers,

I have a developed a "Stochastic solar model" for the purpose of long term distribution system planning. I am aware about the indices researchers commonly use to validate Solar models like; RMSE, MBE etc.

But I face the challenge to find similar literature's (or Similar Solar prediction models) and the same Solar data set that they had used for validating the models. I'm also confused whether it is logical to use aforementioned indices for validating a "Stochastic model", because indices values are not constant.

Kindly let me know your suggestions in this regard. Thanks in advance!

I have the data and want to find some rule of thumbs to conclude that the data point distribution is either highly, moderately or approximately skewed. I have used Skewness and Kurtosis. I have calculated the mean, median already.

Any idea ... ?

Thanks

when posteriori probabilities are 0 or 1, Stochastic EM is usable?

I attached this complete question.

Any recent research on semi markov processes in reliability?

I am using a birth and death process.

I am considering the scenario as a birth and death process

Suppose we have different candidate models proposed for a time series based on ACF and PACF. Now the basic equation has the white noise term. In MATLAB, u have "randn" command to generate normal random numbers. The parameters can be estimated from "armax" command.

After parameter estimation (calibration), the validation involves comparing the observed data with the predicted values. Now the problem which I m facing is that figuring out whether the white noise should be generated of what length (data length or a bigger population). Secondly, the white noise sequence should be preserved for all candidate model validation or subject to change? If they are changed, then the performance indicators such as RMSE, ML, AIC, BIC will also change.

So what should i do?

Developing models in past to what extent have supported real life situation...

How can one simulate a stationary Gaussian process through its spectral density?

Hello, I am currently working on models where energy can be produced using either a clean or dirty technology and investment (in knowledge) reduces the average cost of the clean technology or backstop. A steady state involves using both the dirty and clean technologies when their marginal costs are equal.

I am thinking of including a stochastic process for change in energy prices such that investment in the backstop is feasible only when energy prices are above a certain level (that is to say, investment in knowledge now reduces the future average cost of the backstop but there is also a huge fixed cost in actually using the backstop). Theoretically, I believe that this would involve switching back and forth between clean and dirty technologies. I am looking for any ideas in how to model this. I am attaching my recent publication (basically including stochasticity as I said in my current model).

I am interested in collaborating! any ideas?

Supratim

Should we use just one value for each realization? Or different quartiles? What if one of the quartiles is eliminated in the reduced model?

I am working on a forced stochastic model and needs to simulate a two-parameter plot indicating where synchrony happens. Been searching literatures about simulating Arnold's tongues but not satisfied with my search. Looking forward to your help. :)

I wish to know whether I could the adopt time-varying stochastic frontier model when the values of each cross section are not available for the complete time period selected for the analysis. Could someone help me in this regard?

Thanking you.

I would like to apply the Integer Value Autoregressive model for predicting pest count.

Can anybody help me in estimating the INAR model using R software, or any other software?

For instance, are there some references about the calculation of the invasion speed of a disease using an IBM?

Can we code Lagrangian stochastic dispersion models in Matlab with providing particle emission data?

I am using an individual based stochastic model to explore the impact of environmental changes on speciation. In this model individuals forage in two different habitats with a probability determined by the profitability of the habitat. Apart from the ecological and mating loci, I have a certain number of non-coding neutral loci that are used to follow genetic signatures of evolutionary divergence. The neutral loci act like microsatellites, with high maturation rates. My question is how to calculate Fst in Matlab? Are there any softwares that can be used in Matlab not in R?

I am facing a problem regarding the stationary distribution of mobility models in revising my paper.

In a general sense, my question is like this.

- Given a stochastic process {X
_{t}: t>=0} such that the initial state X_{0 }is uniformly distributed in the state space and for all t > 0, X_{t}= X_{0},namely, the process does not evolve with time. For this specific process, can we say that {X_{t}} has a stationary distribution that is uniformly distributed in the state space?

Could anyone update me about the differences between a chaotic and stochastic system? Suppose for a certain mathematical model, we have the chaotic behaviour. How could do the similar kind of analysis through stochastic modelling? Do I need to find the SDE and just solve it through EM Method? Please do suggest me relevant papers, books and software to perform all these kinds of analysis.

Suppose we have a metric space (X,d) such that the points in this space are distributed by a probability distribution function (for example Poisson d.f). How we can calculate the probability of d(p,q)<t; such that p,q in X and t in R.

In statistical inference our aim is to study the population characteristic that is the parameter. But if it is said that 'T' is an estimator of the function 'Ѱ(ϴ)' (which is of interest) then what is the meaning of it.

A metric can be used to evaluate performance

Could we determine with certainty a species to have reached a point of no recovery?

Normally we have to assume that the service time of the queueing process has an exponential distribution. How do we assume the service time follows heavy tail and what is the situation for adopting heavy tail distribution? Moreover, what is the reason beyond that?

I think the photons generated in SPDC have a stochastic phase to the pump light because they are generated from the vacuum state. Is it true? I have looked up some references but haven't found anything.

More precisely, I want to bound

|P(\sup_{t\in S_1}X(t)\sup_{t\in S_2}X(t)-P((\sup_{t\in S_1}X(t))P((\sup_{t\in S_1}X(t))|

where S_1,S_2 are two compact set and (d(S_1,S_2)=k with k\to\infty

X is a stationary weakly dependent gaussian process

I am doing a research on a Markov chain approach on the behavior of rainfall and am considering first and second order chains. Using the Bayesian Information Criterion I want to determine the optimal model and use the optimal model to determine the expected length of dry (rainy) spell. So for second order models I am not sure of how I calculate the expected length of dry (rainy) spells?

I started my Ph.D. recently and not know much about this topic.

Proteins within the model cytoplasm are represented as spheres, with different masses/sizes. They interact through effective potentials (attractive) containing aspecific interactions and also the effect of the solvent. These potentials further depend on the sizes of the interacting objects.

The solvent is implicit and so I use the Langevin equation with a proper friction for each protein because friction too depends on the size of the protein.

I see anomalous diffusion (above all for big proteins) and I so I was trying to understand the connection of my model with one of the model between CTRW or FLM. How can understand/prove formally what is this connection, if any?