Bayesian Trend Filter Pass Node

Bayesian Trend Probability Filter — Series Input

AdvancedStatisticalPass

Overview

The Bayesian Trend Filter Pass Node applies the Bayesian Trend Filter algorithm to a series input. It uses a Bayesian smoothing approach (controlled by the lambda parameter) to separate the underlying trend signal from noise — computing a probability-weighted smoothed output from any numeric series.

As a Pass node, it accepts any { values, timestamps } series rather than raw OHLCV data. This allows the filter to be chained after other indicators — smoothing RSI, volume, or custom composites — making it a versatile denoising and trend extraction tool within a node graph pipeline.

Algorithm

BayesianFilter(x, λ):

Initialize: smooth[0] = x[0]

For each bar i:

likelihood_trend = exp(−|x[i] − smooth[i−1]| / λ)

smooth[i] = smooth[i−1] + likelihood_trend × (x[i] − smooth[i−1])

Output: smoothed values aligned with input timestamps. No fixed warm-up — recursive from bar 0.

Higher lambda = more smoothing (slower to react); lower lambda = less smoothing (faster to react).

Parameters

Parameter	Default	Description
lambda	50	Smoothing sensitivity. Higher values produce more smoothing and slower trend tracking.

Inputs & Outputs

Slot	Direction	Type	Description
input	Input	{ values, timestamps }	Any numeric series to filter
values	Output	(number \| null)[]	Bayesian-smoothed values aligned to input
timestamps	Output	number[]	Unix timestamps aligned to input

Use Cases

Noise-Filtered Trend Line

Apply to close price to extract a smooth trend line that reacts to large moves (genuine trend changes) while ignoring small fluctuations. The Bayesian weighting adapts the filter strength to the magnitude of each price change.

Pre-Processing for Other Nodes

Chain this node before oscillators (RSI, MACD) to pre-smooth noisy inputs. Applying RSI Pass to a Bayesian-filtered price series rather than raw price produces a more stable oscillator output with fewer whipsaws.

Regime Boundary Detection

Compare the raw input to the Bayesian-filtered output: when price diverges significantly from the filter, it signals a potential trend change or spike. Use the difference as a regime transition signal.

Tips & Best Practices

Tuning Lambda

For price series: lambda=10–30 gives responsive filtering; lambda=50–100 gives heavy smoothing close to a moving average. For indicator series (like RSI 0–100), use smaller lambda values (5–20) as the data range is compressed.

No Fixed Warm-Up

The Bayesian filter is recursive and initializes from bar 0 (smooth[0] = x[0]). There is no formal warm-up period, but the first few bars may have higher estimation uncertainty as the filter settles.

vs. Kalman Smoother

Bayesian Trend Filter and Kalman Smoother are both adaptive filters. The Bayesian approach is more robust to outliers (large spikes reduce their own influence via the likelihood term), while Kalman is optimal under Gaussian assumptions without outliers.