Question

What is the fundamental assumption behind a Markov model?

• A. The probability of transitioning from one state to another in a sequence depends only on the current state, not the past state.
• B. The model is used to optimize decision-making processes under uncertainty.
• C. The model represents a system as a series of interconnected states with defined transition probabilities.
• D. The model uses statistical methods to predict future events based on observed patterns in data.

Hint:

Remember the Markov property with the phrase: "The future depends only on the present, not the past." Think of a simple weather model: if today is sunny (the current state), the probability of it being rainy tomorrow might be 10%, regardless of whether yesterday was sunny or rainy.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A Markov model (or Markov chain/process) is a type of stochastic model used to describe sequences of events. The question asks for its most fundamental, defining assumption.
Step 2: Detailed Explanation:
Let's analyze the options:
1. The probability of transitioning...depends only on the current state, not the past state: This is the precise definition of the Markov property. It is the core assumption that makes a process "Markovian." It implies that the system is "memoryless"—to predict the future, you only need to know the present state; the history of how it got there is irrelevant. This is the fundamental assumption.
2. The model is used to optimize decision-making processes...: This describes an application of Markov models, specifically Markov Decision Processes (MDPs), which are used in reinforcement learning and operations research. It is a use case, not the core assumption of the model itself.
3. The model represents a system as a series of interconnected states...: This is a true description of the structure of a Markov model, but it is not the underlying assumption. The assumption is about *how* the system moves between those states.
4. The model uses statistical methods to predict future events...: This is a very general statement that applies to almost any predictive statistical model (e.g., regression, time series analysis, etc.), not just Markov models. It is not specific enough to be the fundamental assumption.
Step 3: Final Answer:
The defining characteristic and fundamental assumption of a Markov model is the Markov property: the future is conditionally independent of the past, given the present.