transition probability

简明释义

跃迁几率

英英释义

例句

1.The transition probability 转移概率 matrix is essential for predicting future states in stochastic processes.

在随机过程中，transition probability 转移概率 矩阵对于预测未来状态至关重要。

2.In finance, the transition probability 转移概率 can indicate the likelihood of credit rating changes.

在金融领域，transition probability 转移概率 可以指示信用评级变化的可能性。

3.Understanding the transition probability 转移概率 helps in developing better predictive models for weather forecasting.

理解 transition probability 转移概率 有助于开发更好的天气预测模型。

4.Researchers used historical data to estimate the transition probability 转移概率 of customer behavior in retail.

研究人员利用历史数据来估计零售中客户行为的 transition probability 转移概率。

5.In a Markov chain, the transition probability 转移概率 determines the likelihood of moving from one state to another.

在马尔可夫链中，transition probability 转移概率 决定了从一个状态转移到另一个状态的可能性。

作文

In the field of statistics and probability theory, the concept of transition probability plays a crucial role, particularly in the study of Markov chains. A Markov chain is a mathematical system that transitions from one state to another within a finite or countable number of possible states. The transition probability refers to the likelihood of moving from one specific state to another in this system. Understanding these probabilities is essential for predicting future states based on current conditions.For example, consider a simple weather model where the states represent different weather conditions: sunny, cloudy, and rainy. The transition probability could be defined as the chance of it being sunny tomorrow given that it is sunny today. If historical data shows that when it is sunny today, there is a 70% chance that it will be sunny tomorrow, we can express this as a transition probability of 0.7.The calculation of transition probabilities often involves analyzing historical data to determine how frequently transitions between states occur. This analysis not only helps in understanding the dynamics of the system but also aids in making informed predictions about future events. In our weather example, by compiling data over several years, meteorologists can establish a matrix of transition probabilities that reflects the likelihood of various weather patterns.One of the fascinating aspects of transition probabilities is their application beyond simple systems. They are widely used in various fields, including economics, genetics, and even artificial intelligence. For instance, in finance, transition probabilities can help analysts predict stock price movements based on previous trends. Similarly, in genetics, they can be used to model the inheritance of traits from one generation to the next.Moreover, the concept of transition probability is not limited to discrete states; it can also be applied to continuous systems. In such cases, the probabilities may be represented as functions, leading to more complex models. This versatility makes transition probabilities a powerful tool in both theoretical research and practical applications.To further illustrate the importance of transition probabilities, consider a scenario in a board game where players move between different locations based on dice rolls. Each possible move can be considered a transition, and the transition probabilities would determine the likelihood of landing on each location after a certain number of moves. Understanding these probabilities can significantly influence a player's strategy, highlighting how knowledge of transition probabilities can lead to better decision-making.In conclusion, the concept of transition probability is fundamental in understanding systems that evolve over time. Whether in predicting weather patterns, analyzing financial markets, or developing strategies in games, transition probabilities provide valuable insights into the dynamics of change. By mastering this concept, individuals can enhance their analytical skills and apply them across various domains, ultimately leading to more informed decisions and predictions.

在统计学和概率论领域，转移概率的概念起着至关重要的作用，尤其是在马尔可夫链的研究中。马尔可夫链是一种数学系统，它在有限或可数的可能状态之间进行转移。转移概率指的是在该系统中从一个特定状态转移到另一个状态的可能性。理解这些概率对于根据当前条件预测未来状态至关重要。例如，考虑一个简单的天气模型，其中状态代表不同的天气条件：晴天、多云和雨天。转移概率可以定义为在今天是晴天的情况下，明天仍然是晴天的机会。如果历史数据显示，当今天是晴天时，明天有70%的机会仍然是晴天，我们可以将其表示为转移概率为0.7。转移概率的计算通常涉及分析历史数据，以确定状态之间转移发生的频率。这种分析不仅有助于理解系统的动态，还能帮助做出关于未来事件的明智预测。在我们的天气示例中，通过汇编数年的数据，气象学家可以建立一个转移概率矩阵，反映各种天气模式的可能性。转移概率的一个迷人之处在于它们超越简单系统的应用。它们被广泛应用于经济学、遗传学，甚至人工智能等各个领域。例如，在金融领域，转移概率可以帮助分析师基于历史趋势预测股票价格的变化。同样，在遗传学中，它们可以用来模拟特征从一代到下一代的遗传。此外，转移概率的概念不仅限于离散状态；它也可以应用于连续系统。在这种情况下，概率可能被表示为函数，从而导致更复杂的模型。这种多样性使得转移概率成为理论研究和实际应用中的强大工具。为了进一步说明转移概率的重要性，考虑一个棋盘游戏的场景，在这个游戏中，玩家根据掷骰子的结果在不同位置之间移动。每一个可能的移动都可以视为一次转移，而转移概率将决定在一定次数的移动后落在每个位置的可能性。理解这些概率可以显著影响玩家的策略，突显了掌握转移概率如何能够导致更好的决策。总之，转移概率的概念是在理解随时间演变的系统中至关重要的。无论是在预测天气模式、分析金融市场，还是在游戏中制定策略，转移概率都提供了关于变化动态的宝贵见解。通过掌握这一概念，个人可以增强他们的分析技能，并将其应用于各个领域，最终导致更明智的决策和预测。