采样频率对使用连续时间模型估计的AR过程动态的影响
Rohit Batra1, Simran K Johal1, Meng Chen1
1Department of Psychology, University of California, Davis.
Psychological methods
|July 10, 2023
概括
连续时间自回归 (CT-AR) 模型有效地恢复潜在的心理动态,当数据采样比生成过程更快时. 较慢的采样需要更强大的效应来准确的恢复,强调频繁的数据收集的重要性.
科学领域:
- 心理建模 心理建模
- 纵向数据分析的数据分析.
- 统计方法 统计方法
背景情况:
- 连续时间 (CT) 模型为分析纵向心理数据提供了灵活的框架.
- CT模型允许单个底层连续函数假设,克服离散时间 (DT) 模型的局限性.
- CT模型通过将参数重新调整到共同的时间尺度来促进跨间隔比较 (例如,每日,每周,每月).
研究的目的:
- 评估连续时间自回归 (CT-AR) 模型在恢复真实过程动态中的准确性.
- 调查不同采样间隔对CT-AR模型参数恢复的影响.
- 评估自回归 (AR) 参数的不同强度如何影响不同采样频率的模型恢复.
主要方法:
- 使用蒙特卡洛模拟来测试CT-AR模型的性能.
- 模拟了两个生成时间间隔 (每日和每周),具有不同的AR参数强度.
- 模型的恢复被评估在三个采样间隔:每日,每周和每月.
主要成果:
- 在比生成过程更快的间隔采样通常允许准确恢复AR效应.
- 当采样速度比生成过程慢时,更强的潜在AR效应是满足参数恢复的必要条件.
- 采样频率不足导致偏差估计和真实参数覆盖率低.
结论:
- 对于可靠的CT-AR模型估计,建议采用频繁的数据采样,理想情况下比基础过程动态更快.
- 研究人员应将抽样间隔与研究中的心理构造的理论知识保持一致.
- CT-AR模型准确地表示纵向数据的能力取决于适当的采样频率.
相关概念视频
01:11Sampling Continuous Time Signal
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
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01:15Sampling Theorem
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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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01:18Aliasing
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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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01:22Upsampling
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01:17Bandpass Sampling
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In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....
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01:15Discrete Fourier Transform
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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