Black Box Model

Examples of Black Box Model in the following topics:

• Lifestyle

  • Lifestyle is also referred to as a buyer characteristic in the Black Box Model, which shows the interaction of stimuli, consumer characteristics, decision process, and consumer responses.
  • The Black Box Model is related to the Black Box Theory of Behaviorism, where the focus is set not on the processes inside a consumer, but the relation between the stimuli and the response of the consumer.
  • The buyer's "black box" contains the buyer characteristics (e.g., attitudes, motivation, perception, lifestyle, personality, and knowledge) and the decision process (e.g., problem recognition, information research, alternative evaluation, purchase decision, and post-purchase behavior) which determine the buyer's response (e.g., product choice, brand choice, dealer choice, purchase timing, and purchase amount).
  • The Black Box Model considers the buyer's response as a result of a conscious, rational decision process, in which it is assumed that the buyer has recognized the problem.

• Making a Box Model

  • A box plot (also called a box-and-whisker diagram) is a simple visual representation of key features of a univariate sample.
  • When we explore relationships between multiple variables, even more statistics arise, such as the coefficient estimates in a regression model or the Cochran-Maentel-Haenszel test statistic in partial contingency tables.
  • A box plot (also called a box and whisker diagram) is a simple visual representation of key features of a univariate sample.
  • Another common extension of the box model is the 'box-and-whisker' plot , which adds vertical lines extending from the top and bottom of the plot to, for example, the maximum and minimum values.
  • Produce a box plot that is representative of a data set.

• Random variables exercises

  • (a) Create a probability model for the amount you win at this game.
  • If you draw 3 black cards, you win $25.
  • (a) Create a probability model and find Andy's expected profit per game.
  • Gamblers can place bets on red or black.
  • (a) An entire box of ice cream, plus 3 scoops from a second box is served at a party.

• Particle in a Box

  • The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically.
  • The wavefunction must vanish everywhere beyond the edges of the box, as the potential outside of the box is infinite.
  • where n = {1,2,3,4...} and L is the size of the box .
  • Inside the box the potential V(x) is zero.
  • Outside the box the potential energy is infinite.

• Black-Scholes Formula

  • The Black-Scholes formula is a way of pricing a European option.
  • The model was originally presented in a 1973 paper by Fischer Black and Myron Scholes who eventually received a Nobel Prize for their work in 1997.
  • The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way, and consequently "eliminate risk".
  • reversible, as the model's original output, price, can be used as an input and one of the other variables solved for; the implied volatility calculated in this way is often used to quote option prices
  • Since this characteristic is true for bonds but not for equity options, the Black-Scholes model cannot be used for bond valuation.

• References

  • Box, G.
  • Applied Linear Statistical Models, McGraw-Hill/Irwin, Homewood, IL.

• Box-Cox Transformations

  • George Box and Sir David Cox collaborated on one paper (Box, 1964).
  • In fact, Professor Box is married to the daughter of Sir Ronald Fisher.
  • Rewriting the Box-Cox formula as
  • For the model
  • Examples of the Box-Cox transformation versus log(x) for −2 < λ< 3.

• Statistical Graphics

  • Statistical graphics allow results to be displayed in some sort of pictorial form and include scatter plots, histograms, and box plots.
  • They include plots such as scatter plots , histograms, probability plots, residual plots, box plots, block plots and bi-plots.
  • They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection.

• Problems

  • A reasonable model for the neutrons and protons in a nucleus is that they are confined to a small region.
  • Let's take a one-dimensional model of this.

• Linear Systems

  • It is useful to have the a mental picture of the bell as a black box.
  • Into the left side of the black box we put the input signal–in this case the hammer strike.
  • Since our mathematical model of an impulsive force is a Dirac delta function, the claim is that if we can solve: