---
url: >-
  https://jer-k.github.io/effect-prophet/benchmarks/linear/mcmc-linear-regressor-model.md
---

# A regressor forecast by its own model

 [← All linear growth benchmarks](/benchmarks/linear)

256 daily rows and four regressors, one forecast by its own default model. That model is fit by optimizing in both libraries, as `mcmc_samples` doesn't reach it in Python, and each of the 1,200 futures takes the next of its 1,000 draws in turn. Python doesn't save regressor models, so there are no save and load timings.

## Input

[`benchmark/inputs/v1/map-regressors-medium.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v1/map-regressors-medium.json): 256 history rows and 64 forecast rows.

## Output

Largest difference: **0.018** (0.019% of the input's range).

Every forecast row from both libraries.

| Date | Effect Prophet | Python Prophet | Difference |
| --- | ---: | ---: | ---: |
| 2020-09-13 | 107.1988 | 107.1947 | 0.0041 |
| 2020-09-14 | 107.6487 | 107.6433 | 0.0054 |
| 2020-09-15 | 108.0970 | 108.0904 | 0.0066 |
| 2020-09-16 | 108.5453 | 108.5374 | 0.0079 |
| 2020-09-17 | 107.9487 | 107.9411 | 0.0076 |
| 2020-09-18 | 110.1974 | 110.1895 | 0.0079 |
| 2020-09-19 | 110.6471 | 110.6380 | 0.0091 |
| 2020-09-20 | 111.0968 | 111.0865 | 0.010 |
| 2020-09-21 | 110.1079 | 110.0977 | 0.010 |
| 2020-09-22 | 110.5647 | 110.5532 | 0.011 |
| 2020-09-23 | 111.0258 | 111.0132 | 0.013 |
| 2020-09-24 | 111.4912 | 111.4774 | 0.014 |
| 2020-09-25 | 112.3190 | 112.3064 | 0.013 |
| 2020-09-26 | 112.7944 | 112.7807 | 0.014 |
| 2020-09-27 | 115.0738 | 115.0600 | 0.014 |
| 2020-09-28 | 115.5605 | 115.5458 | 0.015 |
| 2020-09-29 | 116.4115 | 116.3980 | 0.013 |
| 2020-09-30 | 113.7098 | 113.6937 | 0.016 |
| 2020-10-01 | 114.2174 | 114.2005 | 0.017 |
| 2020-10-02 | 114.7323 | 114.7145 | 0.018 |
| 2020-10-03 | 115.6121 | 115.5958 | 0.016 |
| 2020-10-04 | 116.1397 | 116.1226 | 0.017 |
| 2020-10-05 | 116.6760 | 116.6583 | 0.018 |
| 2020-10-06 | 119.0198 | 119.0024 | 0.017 |
| 2020-10-07 | 119.9291 | 119.9134 | 0.016 |
| 2020-10-08 | 120.4876 | 120.4713 | 0.016 |
| 2020-10-09 | 119.2526 | 119.2349 | 0.018 |
| 2020-10-10 | 119.8242 | 119.8060 | 0.018 |
| 2020-10-11 | 120.7578 | 120.7413 | 0.016 |
| 2020-10-12 | 121.3407 | 121.3239 | 0.017 |
| 2020-10-13 | 120.5265 | 120.5086 | 0.018 |
| 2020-10-14 | 121.1202 | 121.1020 | 0.018 |
| 2020-10-15 | 123.8759 | 123.8606 | 0.015 |
| 2020-10-16 | 124.4774 | 124.4618 | 0.016 |
| 2020-10-17 | 125.0819 | 125.0660 | 0.016 |
| 2020-10-18 | 123.8868 | 123.8697 | 0.017 |
| 2020-10-19 | 124.8528 | 124.8377 | 0.015 |
| 2020-10-20 | 125.4622 | 125.4469 | 0.015 |
| 2020-10-21 | 126.0729 | 126.0573 | 0.016 |
| 2020-10-22 | 126.6832 | 126.6675 | 0.016 |
| 2020-10-23 | 127.6504 | 127.6367 | 0.014 |
| 2020-10-24 | 130.0585 | 130.0455 | 0.013 |
| 2020-10-25 | 130.6623 | 130.6491 | 0.013 |
| 2020-10-26 | 129.8624 | 129.8482 | 0.014 |
| 2020-10-27 | 129.0191 | 129.0058 | 0.013 |
| 2020-10-28 | 129.6148 | 129.6013 | 0.014 |
| 2020-10-29 | 130.2060 | 130.1921 | 0.014 |
| 2020-10-30 | 130.7921 | 130.7778 | 0.014 |
| 2020-10-31 | 131.7303 | 131.7178 | 0.012 |
| 2020-11-01 | 132.3030 | 132.2900 | 0.013 |
| 2020-11-02 | 134.6709 | 134.6584 | 0.012 |
| 2020-11-03 | 135.2320 | 135.2190 | 0.013 |
| 2020-11-04 | 136.1446 | 136.1333 | 0.011 |
| 2020-11-05 | 134.8922 | 134.8793 | 0.013 |
| 2020-11-06 | 135.4327 | 135.4191 | 0.014 |
| 2020-11-07 | 135.9657 | 135.9514 | 0.014 |
| 2020-11-08 | 135.4447 | 135.4312 | 0.014 |
| 2020-11-09 | 135.9625 | 135.9482 | 0.014 |
| 2020-11-10 | 136.4730 | 136.4578 | 0.015 |
| 2020-11-11 | 138.7772 | 138.7621 | 0.015 |
| 2020-11-12 | 139.6320 | 139.6182 | 0.014 |
| 2020-11-13 | 140.1224 | 140.1077 | 0.015 |
| 2020-11-14 | 138.8063 | 138.7895 | 0.017 |
| 2020-11-15 | 139.2825 | 139.2647 | 0.018 |

## Timing

Median of all measured repetitions.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Fit | 4.67 s | 4.13 s | 1.1× slower |
| Predict | 1.10 ms | 17.6 ms | Not compared: different work |
| Simulate uncertainty | 16.1 ms | 306 ms | Not compared: different work |

Some steps aren't compared, because the two libraries' public calls produce different outputs. Their times show what each call costs, not which library is faster.

* **Predict:** Python's `predict` on a posterior also computes every component's range over the draws, while Effect Prophet's `predict` returns point forecasts and leaves ranges to `predictWithIntervals`.
* **Simulate uncertainty:** Python's `predict(vectorized=False)` also builds the point forecast and every component, while Effect Prophet's `predictUncertainty` returns only the ranges.

## Settings

The case declaration both libraries ran.

```json
{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-posterior",
    "evidenceId": "posterior-nuts-v1"
  },
  "configuration": {
    "growth": "linear",
    "scaling": "absmax",
    "seasonalityMode": "additive",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "auto",
      "count": 25,
      "range": 0.8
    },
    "changepointPriorScale": 0.05,
    "seasonalities": [],
    "events": [],
    "regressors": [
      {
        "name": "binary-auto",
        "priorScale": 10,
        "standardization": "auto"
      },
      {
        "name": "numeric-auto",
        "priorScale": 10,
        "standardization": "auto",
        "predictor": true
      },
      {
        "name": "numeric-always",
        "priorScale": 7,
        "standardization": "always"
      },
      {
        "name": "numeric-never",
        "priorScale": 5,
        "standardization": "never"
      }
    ]
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  },
  "uncertainty": {
    "seed": 19,
    "samples": 1000,
    "intervalWidth": 0.8,
    "output": "intervals",
    "algorithm": "scalar-continuous-time",
    "evidence": "docs/validation/uncertainty.md#evidence-classes",
    "samplerMemoryLimitBytes": 67108864
  },
  "mcmc": {
    "samples": 300,
    "seed": 19,
    "pointWidthFraction": 0.15
  }
}
```