Murtaza -

I'd say that statistical models are a subset of mathematical models that are generally more applied in nature, deal with measurement in some way, and often with error or residuals/random variables.

Cheers - Jim

Thanks James,

Is it possible to use both statistical and mathematical model too prove a point or concept.  if some example exist. ?

Murtaza -

When I hear the word "model," I usually think "regression," which would generally indicate statistics, which is a part of mathematics.  So by that reasoning, any regression used to estimate relationships between data sets would qualify.  For example, showing a relationship between heating fuel consumption and temperature in a region; or hydroelectric generation given rainfall and snowmelt; or lung cancer and smoking.   

But there are other kinds of models.  Consider physical sciences.  That might be closer to what you had in mind.  Descriptions of planetary orbits might just be considered mathematical, but because they involve measurement, I guess one could argue statistics as well.  And in partical physics and chemistry, there are models of physical realities that are mathematical and considered statistical.  See "Bose-Einstein," and "Fermi-Dirac" statistics. 

- Jim

A mathematical model is based on facts, despite their measurability and quantifiability, while statistical models use actual data. Statistical models are derived from mathematical models. There is an issue of realistic.

Hi Murtaza,

Mathematical Models are grow out of equations that determine by the following,

• How a system changes from one state to the next (differential equations)
• How one variable depends on the value or state of other variables (state equations)
• These can also be divided into either numerical models or analytical models.

Statistical Models are Include issues such as,

• Statistical characterization of numerical data,
• Estimating the probabilistic future behavior of a system based on past behavior
• Extrapolation or interpolation of data based on some best-fit
• Error estimates of observations (or) spectral analysis of data (or) model generated output.

Hello Murtaza;

I agree with Jim and Manoj; Statistical approaches are based on mathematical calculations in order to prepare ANOVA (Analysis of Variance) tables, sum of squares, mean of squares, residual amount and so on) and finally will supply you with predicting model for example (Y=a1X1+a2X2+a3X4+…. and thereafter you can compare YRealand YPredicted by least square difference (LSD) approach and finally you can say that you have a above model with correlation coefficient of (R2=0.95 for example)! But when you say mathematical model you should obey from special laws (rules) in chemistry, physics and other sciences; let me tell you example of mathematical model: In engineering we have kinetic models and in our work (mineral processing especially we have flotation process; we know that flotation obeys from first order kinetic law therefore prediction of recovery for flotation should obey from following equation:

R=Rin*(1-e-kt)

[where R= cumulative recovery, Rin= infinity cumulative recovery K= kinetic constant, t= frothing time (second)]; This is mathematical model. We have 5-6 pairs of data for cumulative recovery “R”  versus frothing time “t” but you are now allowed to use linear regression which it is statistical model (R=a + B*t +C*t^2+..) even R2 of statistical model is higher than mathematical model (first order kinetic).

I hope this comment could be satisfying for your desire about distinction of statistical model and mathematical model.

Regards,

Hamed

Hello Mr Murtaza Mohiuddin

all friends answered truly

but main difference between Mathematical model and statistical model is the modelling condition

mathematical model is valid in all condition. for example F=ma. it's true in all mass and acceleration.

but in statistical model the response is valid in modelling conditions. for example we measured relation between height and weight of people and got to H=aW+b formula that a is a coefficient and b is constant value. this formula is valid in your statistical society. if you measured at one city your formula were changed in other city. but if you measured F=ma at on city, its constant everywhere.

regards

I am not trying to insult statisticians here, but is statistics not  a part of mathematics. Even the Normal Distribution was first studied by the great mathematician Gauss and is named after him. Hence we could say that all statistical models are mathematical models, but not all mathematical models are statistical models.

(Mind you I am neither a trained mathematician nor a trained statistician, but I use these tools from time to time.)