A deterministic model is a model where:
1 - the material properties are well known, i.e. deterministic. none of them is random
2 - The applied load are also deterministic
A Stochastic model has on the other hand:
1 - random properties, e.g. the Young's modulus is a random variable with uniform distribution [E1, E2]; or normal distribution (of a given mean or standard deviation)
2 - The applied load is random variable, e.g. Wind Load, earthquake (vibration of random amplitude and displacement)
The Hybrid model is a "mixture" of both Deterministic and Stochastic. Its treatment is quite similar to the Stochastic model. The presence of a single random variable in the model necessitates the consideration of the stochastic treatment.
A deterministic model is a model where:
1 - the material properties are well known, i.e. deterministic. none of them is random
2 - The applied load are also deterministic
A Stochastic model has on the other hand:
1 - random properties, e.g. the Young's modulus is a random variable with uniform distribution [E1, E2]; or normal distribution (of a given mean or standard deviation)
2 - The applied load is random variable, e.g. Wind Load, earthquake (vibration of random amplitude and displacement)
The Hybrid model is a "mixture" of both Deterministic and Stochastic. Its treatment is quite similar to the Stochastic model. The presence of a single random variable in the model necessitates the consideration of the stochastic treatment.
Hady has given a good definition of the different model types. I have heard people say that "a stocahstic model handles uncertainty, a deterministic model doesn't". This is not strictly correct. The correct statement should be:
a stochastic model has the capacity to handle then uncertainty in the inputs built into it, for a deterministic model, the uncertainties are extenal to the model. The uncertainties in the inputs to a deterministic model can be handled through use of a Monte Carlo simulation (note that this does not make it a stochastic model). This is computationally inefficient however.
In terms of building a hybrid model, you need to consider how well things are known, and how the uncertainties in the inputs affect the output of the model. Ideally, the components that contribute strongest to the uncertainty in the output should be treated stochastically, the components that do not contribute significant can be treated deterministically. This will result in a hybrid model.
The alternative is the brute force approach of building a deterministic model and using a Monte Carlo simulation. Needs a lot of computer time if there are a significant number of contributors to the output uncertainty.
A Deterministic Model corresponds to a Design (Analytical Decision) in the Certainty State. The Stochastic Model in a Random Analysis Corresponds to a Design in a Risk State which uses Probabilistic Definitions.
A Deterministic model is developed applying first principals equations, that is, mass balance, energy balances, kinetic rates, calculating phisico-chemical parameters and so on. It is also called white box model.
A Stochastic model is sometimes called black box modelling. You know the input and output values and a non-deterministic model is applied to correlate the variables.
Hybrid model mixes both, that is, some parameter(s) of the deterministic model are ramdonly defined, according to the experimental observations.
G'day Luciane,
Your definition of a deterministic and stochastic model are not correct. Deterministic models can be black box models. Also, a stochastic model can be generated by first principles (e.g. if the underlying processes are random), while a deterministic model can be generated by a conceptual understanding of the processes (an approach widely used in Hydrology).
A deterministic model is one that uses numbers as inputs, and produces numbers as outputs. A stochastic model includes a random component that uses a distribution as one of the inputs, and results in a distribution for the output. These distributions may reflect the uncertainty in what the input should be (e.g. a deterministic input plus noise), or may reflect a random process (i.e. a stochastic input).
I agree with Barry....except that I would add that in many if not most situations, the "Known" first principles and necessary "Known" parameters are less well understood than one would like and in nearly all nontrivial situations at least one parameter is free requiring estimation from data and therefore an uncertain "stochastic" setting. For example, we commonly use deterministic models for groundwater flow but almost never know the distribution of the hydraulic conductivity field. When this uncertainty is ignored, a deterministic approach results, and when efforts to account for this uncertainty are used, a stochastic model results.
In my experience, the primary reason that deterministic models are used in these incompletely specified situations has to do with the difficulty of developing rigorous inference for complex computational models. For example in the field of climate change circulation models are enormously computationally intensive....so it is difficult to iterate in the parameter space to identify maximum likelihood parameter estimates...So models are "calibrated" essentially by hand with a small number of model runs....Optimal parameter sets are virtually never found by hand calibration.
This stumbling block has led to the area of Model Emulation, where statistical models are fit to deterministic model inputs and outputs resulting in a computationally efficient version of the original model which can be used to develop statistical inference through Monte-Carlo simulation or other approaches.
According to what I know deterministic events are not subject to chance and two realizations of the model using the same parameters will give the same results whereas stochastic incorporates chance by using the Monte Carlo simulation where the set of possible next events is defined with a probability attached to each.
Deterministic model is composed of trend and/or periodic components, whether they vary in mean and/or variance. Stochastic model is compossed of periodic correlation structure (ARMA model) and/or probabilistic random component.
In deterministic models, the output of the model is fully determined by the parameter values and the initial conditions. Stochastic models possess some inherent randomness. The same set of parameter values and initial conditions will lead to an ensemble of different outputs.
Stochastic model: output represented by distribution accounting for the uncertainty
Deterministic model: output are devoid of randomness but presented in single values
Stochastic: Multiple runs are used to estimate probability distribution
Deterministic: Assumes that its outcome is certain if the input of the model is fixed
In addition to all of the above, a deterministic model results in same exact outputs for a fixed set of inputs/conditions, irrespective of how many times the model re-run the calculation. A deterministic model is useful in predictions by allowing for “what if” secenarios where one can try out different inputs/condition to observe their outcomes for decision making.
Deterministic model explains the effects of inputs.
Stochastic model explain the effects of disturbances and sensor noise.
Reference: Tangirala, A. K. (2014). Principles of System Identification: Theory and Practice.
A deterministic models processes which are often described by differential equations, with a unique input leading to unique output for a well defined linear models.
example:
a membrane potential is deterministic
fluctuation caused by opening and closing of ion channels is stochastic
the membrane potential that fluctuating in a non-coherent way is hybrid
Deterministic models are always gives same output for a given set of input variables. Hence the output always falls with in a given specified range.
Stochastic models may not always gives the same output for a given set of input variables, since it incorporates some randomness. This random often introduced by stochastic factor, generally we use different type distribution function mostly skewed distributions to derive these stochastic factors.
The advantage of stochastic models are they can predict the patterns similar to realistic patterns. since most of the real systems often surprises us by different outcome, this may be due we don't know them completely. so using deterministic approach to study the real or complex systems are not advisable for most of the time.
Coming to the hybrid model is mixture of both without any doubt. But it is a subjective question depending on the system under study. For example you have a system "S". Divide system into to manageable pieces, for example "A", "B", "C" and "D". Now you need to check which method is good to model each piece, for example "A", "B" and "C" are deterministic in nature, "D" is some what random in nature, use stochastic factor to model, calibrate it. And identify the relation among them to club to model entire system.
Regards
A model or process is stochastic if it has randomness. For example, if given the same inputs (independent variables, weights/parameters, hyperparameters, etc.), the model might produce different outputs. In deterministic models, the output is fully specified by the inputs to the model (independent variables, weights/parameters, hyperparameters, etc.), such that given the same inputs to the model, the outputs are identical. The origin of the term "stochastic" comes from stochastic processes. As a general rule of thumb, if a model has a random variable, it is stochastic. Stochastic models can even be simple independent random variables.
A stochastic model represents a situation where uncertainty is present. In other words, it’s a model for a process that has some kind of randomness. The word stochastic come from the Greek word stokhazesthai meaning to aim or guess. In the real word, uncertainty is a part of everyday life, so a stochastic model could literally represent anything. The opposite is a deterministic model, which predicts outcomes with 100% certainty. Deterministic models always have a set of equations that describe the system inputs and outputs exactly. On the other hand, stochastic models will likely produce different results every time the model is run.
uncertainty always accompany change with it. there are mathematical models to address uncertainties. these are deterministic and stochastic. 1st one establishes a design factor based on absolute uncertainties of loss of function parameter and a max allowable parameter while stochastic model are based on statistical nature of the design parameters and focuses on probability of survival of the design function.
In my opinion if usnig differnet softwares result in different outputs, the model is stochastic; but if the results are the same through different softwares , the model is deterministic.
I think nowadays very few models could be deterministic because complexity and probability of the problems increase day to day in the present full of uncertainities world.
Thanks for insight on stochastic and determinism model, In simulation can step signal used as deterministic model ? please suggest.
I have the question and I am happy to read many interesting and useful answers, I might come back with ny views but I am afraid I will repeat a number of arguments that so nicely have been out here
You have defined it perfectly already. A deterministic system is a system in which no randomness is involved in the development of future states of the system. A stochastic system has a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely. the hybrid model is mixture of both without any doubt.@
Dear Dr. Chitta Behera
A deterministic system is a system in which no randomness is involved in the development of future states of the system. A stochastic system has a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely. the hybrid model is mixture of both without any doubt.
Best Regards
Dear Chitta Behera,
Look the link, maybe useful.
https://www.linkedin.com/pulse/understanding-differences-between-deterministic-stochastic-paul-dalen
https://www4.stat.ncsu.edu/~gross/BIO560%20webpage/slides/Jan102013.pdf
Regards, Shafagat
Interesting the above discussion is nice and informative but my question is that from all respected teachers and group members "when we design controller for specific system" then we suggest our model as deterministic or stochastic
Previous answers have covered the specific differences between deterministic and stochastic models. Presume by hybrid, you mean semi-probabilistic? Such concepts are common in structural engineering where safety factors are calibrated and assigned to parameters (that would otherwise be stochastic) in deterministic models to achieve a pre-defined safety target. What’s not commonly discussed is the relationship between safety, determinism and uncertainty. You might this interesting: https://www.sfpe.org/page/Issue7Feature2/Certain-Uncertainty---Demonstrating-Safety-in-Fire-Engineering-Design-.htm
A stochastic model is model that has both an endogenous variable and exogenous variable. Endogenous variable are determined within the model while exogenous variables are determined outside the model.
Thought provoking Conversion relevant to this question:
As I practice and research lower extremity closed chain biomechanics and body movement (body in stance and moving when weighted to the ground at the feet) the only method of research that can study longitudinal, variable issues (prevention, performance enhancement, quality of life upgrading) is Stochastic. Deterministic research in Biomechanics is complaint oriented and eliminates as many variables as possible. For me, cohorts can be developed with inherited, anatomical traits (such as foot type) and then studied over time accepting independent variables such as changes in weight, health, activity, environment, tools and habits of a large cohort in order to produce high level valid, high level and applicable results longitudinally.
In biomechanics, N=1000, quantitative, deterministic study has poor (if any) applicability N=1 (clinical).
My take is that we need new Journals that peer review stochastic study of subjects like biomechanics (currently called non-evidenced or qualitative).
Hi
My research in the past two decades led into the detection and development of a so called, “the state based philosophy (SBP)”, in which a phenomenon is considered as the change of state of the system between the origin and the destination. Via logical reasoning and mathematical logics the connecting functions called the Persian curves are explicitly developed. The SBP is the universal law of nature, then there is no difference between the stochastic and deterministic approaches. The difference In conventional approach is due to lack of understanding the phenomenon. Example, when I have a coin, I put the coin on the table with Head up. Does not matter how many times I repeat the test , always I put Head up. What is the probability of putting coin on the table wit he Head up? My answer is one! But your or any other one answer is one half. The difference is because I underestand the process, but you or others do not, because I know my decision but you and others are not awar of my decision!
if I tell you and others that I put the Head up, then your answer is also one!
For more information regarding the SBP look for it in researchgate.
Hi
Deterministic and stochastic are two methods of approach in analysis of the system behavior. Clearly there is NO stochastic or deterministic SYSTEM. Example: There is a cube with six different color sides. Six person look at the cube from different sides. There is a: 1. green cube; 2. red cube; 3. blue cube; 4. ...
There is one system (cube), but different approaches concluded in different system!
The state based philosophy provides the basis for understanding the actual behavior of natural systems!
Deterministic demand model is a model where the parameter of the model can be obtained without any ambiguity while the parameters of a stochastic model are controlled by a probability distribution function
Hi
As mentioned before deterministic and stochastic are two different approaches of analysis. Both have more or less aleatory and epistemic uncertainties! In spite of the common belief that deterministic methods are accurate, the stochastic methods have more accuracy because usually the stochastic results are calibrated by test results.
Look for the State based philosophy and the Persian curves, as the most reliable , simple, and accurate method for analysis of natural phenomena.
For me, it is important (according to Sackett) to provide researched evidence, of the highest level, that has clinical value and applicability. A study that deterministically eliminates all but young healthy women can only be valid and applicable to young healthy women.
N=1000 cohorts that are deterministic work well, for instance, in pharmacology and dermatology. as they focus on one complaint such as infection or a lesion and test one oral antibiotic or steroid cream for effectiveness, validity and applicability.
This model works poorly for many surgical and biomechanical applications because an N=1000 cohort would contain too many variables (weight, health state, activity level, age, etc) that would render them almost useless when applying to a general population.
In these cases, typing or classification (such as blood typing, foot typing or Salter-Harris Classification) lead to much better application and outcomes in general.
In deterministic models, the output of the model is fully determined by the parameter values and the initial conditions.
Stochastic models possess some inherent randomness. The same set of parameter values and initial conditions will lead to an ensemble of different outputs.
Obviously, the natural world is buffeted by stochastic city. But stochastic models are considerably are considerably more complicated. When do deterministic models provide a useful approximation to truly stochastic processes?
Rajesh:
When you create a hybrid model that eliminates some variables and allows others so that there is a higher clinical applicability.
In biomechanics of the lower extremity, for instance, instead of selecting cohorts with low, high and "normal" arch values, using functional foot typing, selecting for instance, 1000 rigid rearfoot, flexible forefoot foot types when studying plantar fascitis etiology and treatment, produces options that have a greater clinical applicability for that foot type.
Dennis
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