docs/vmanomaly: improve FAQ (#6369)

### Describe Your Change
More explicit [vmanomaly
FAQ](https://docs.victoriametrics.com/anomaly-detection/faq/index.html),
based on common Q&A from recent communications with users


### Checklist

The following checks are **mandatory**:

- ✔️ My change adheres [VictoriaMetrics contributing
guidelines](https://docs.victoriametrics.com/contributing/).

docs/anomaly-detection/FAQ.md

@@ -27,6 +27,17 @@ The decision to set the changepoint at `1.0` is made to ensure consistency acros
 
 > Note: `anomaly_score` is a metric itself, which preserves all labels found in input data and (optionally) appends [custom labels, specified in writer](/anomaly-detection/components/writer.html#metrics-formatting) - follow the link for detailed output example.
 
+## How is anomaly score calculated?
+For most of the [univariate models](/anomaly-detection/components/models/#univariate-models) that can generate `yhat`, `yhat_lower`, and `yhat_upper` time series in [their output](/anomaly-detection/components/models/#vmanomaly-output) (such as [Prophet](/anomaly-detection/components/models/#prophet) or [Z-score](/anomaly-detection/components/models/#z-score)), the anomaly score is calculated as follows:
+- If `yhat` (expected series behavior) equals `y` (actual value observed), then the anomaly score is 0.
+- If `y` (actual value observed) falls within the `[yhat_lower, yhat_upper]` confidence interval, the anomaly score will gradually approach 1, the closer `y` is to the boundary.
+- If `y` (actual value observed) strictly exceeds the `[yhat_lower, yhat_upper]` interval, the anomaly score will be greater than 1, increasing as the margin between the actual value and the expected range grows.
+
+Please see example graph illustrating this logic below:
+
+<img alt="anomaly-score-calculation-example" src="vmanomaly-prophet-example.webp">
+
+
 ## How does vmanomaly work?
 `vmanomaly` applies built-in (or custom) [anomaly detection algorithms](/anomaly-detection/components/models.html), specified in a config file. Although a single config file supports one model, running multiple instances of `vmanomaly` with different configs is possible and encouraged for parallel processing or better support for your use case (i.e. simpler model for simple metrics, more sophisticated one for metrics with trends and seasonalities).
 
@@ -45,7 +56,9 @@ Respective config is defined in a [`reader`](/anomaly-detection/components/reade
 `vmanomaly` models generate [metrics](/anomaly-detection/components/models.html#vmanomaly-output) like `anomaly_score`, `yhat`, `yhat_lower`, `yhat_upper`, and `y`. These metrics provide a comprehensive view of the detected anomalies. The service also produces [health check metrics](/anomaly-detection/components/monitoring.html#metrics-generated-by-vmanomaly) for monitoring its performance.
 
 ## Choosing the right model for vmanomaly
-Selecting the best model for `vmanomaly` depends on the data's nature and the types of anomalies to detect. For instance, [Z-score](anomaly-detection/components/models.html#z-score) is suitable for data without trends or seasonality, while more complex patterns might require models like [Prophet](anomaly-detection/components/models.html#prophet).
+Selecting the best model for `vmanomaly` depends on the data's nature and the [types of anomalies](https://victoriametrics.com/blog/victoriametrics-anomaly-detection-handbook-chapter-2/#categories-of-anomalies) to detect. For instance, [Z-score](anomaly-detection/components/models.html#z-score) is suitable for data without trends or seasonality, while more complex patterns might require models like [Prophet](anomaly-detection/components/models.html#prophet).
+
+Also, starting from [v1.12.0](/anomaly-detection/changelog/#v1120) it's possible to auto-tune the most important params of selected model class, find [the details here](https://docs.victoriametrics.com/anomaly-detection/components/models/#autotuned).
 
 Please refer to [respective blogpost on anomaly types and alerting heuristics](https://victoriametrics.com/blog/victoriametrics-anomaly-detection-handbook-chapter-2/) for more details.
 
@@ -57,8 +70,86 @@ While `vmanomaly` detects anomalies and produces scores, it *does not directly g
 ## Preventing alert fatigue
 Produced anomaly scores are designed in such a way that values from 0.0 to 1.0 indicate non-anomalous data, while a value greater than 1.0 is generally classified as an anomaly. However, there are no perfect models for anomaly detection, that's why reasonable defaults expressions like `anomaly_score > 1` may not work 100% of the time. However, anomaly scores, produced by `vmanomaly` are written back as metrics to VictoriaMetrics, where tools like [`vmalert`](/vmalert.html) can use [MetricsQL](https://docs.victoriametrics.com/metricsql/) expressions to fine-tune alerting thresholds and conditions, balancing between avoiding [false negatives](https://victoriametrics.com/blog/victoriametrics-anomaly-detection-handbook-chapter-1/#false-negative) and reducing [false positives](https://victoriametrics.com/blog/victoriametrics-anomaly-detection-handbook-chapter-1/#false-positive).
 
+## How to backtest particular configuration on historical data?
+Starting from [v1.7.2](/anomaly-detection/changelog/#v172) you can produce (and write back to VictoriaMetrics TSDB) anomaly scores for historical (backtesting) period, using `BacktestingScheduler` [component](/anomaly-detection/components/scheduler/#backtesting-scheduler) to imitate consecutive "production runs" of `PeriodicScheduler` [component](/anomaly-detection/components/scheduler/#periodic-scheduler). Please find an example config below:
+
+```yaml
+schedulers:
+  scheduler_alias:
+    class: "scheduler.backtesting.BacktestingScheduler"
+    # define historical period to backtest on
+    # should be bigger than at least (fit_window + fit_every) time range
+    from_iso: '2024-01-01T00:00:00Z'
+    to_iso: '2024-01-15T00:00:00Z'
+    # copy these from your PeriodicScheduler args
+    fit_window: 'P14D'
+    fit_every: 'PT1H'
+
+models:
+  model_alias1:
+    # ...
+    schedulers: ['scheduler_alias']  # if ommited, all the defined schedulers will be attached
+    queries: ['query_alias1']  # if ommited, all the defined queries will be attached
+    # https://docs.victoriametrics.com/anomaly-detection/components/models/#provide-series
+    provide_series: ['anomaly_score']  
+  # ... other models
+
+reader:
+  datasource_url: 'some_url_to_read_data_from'
+  queries:
+    query_alias1: 'some_metricsql_query'
+  sampling_frequency: '1m'  # change to whatever you need in data granularity
+  # other params if needed
+  # https://docs.victoriametrics.com/anomaly-detection/components/reader/#vm-reader
+
+writer:
+  datasource_url: 'some_url_to_write_produced_data_to'
+  # other params if needed
+  # https://docs.victoriametrics.com/anomaly-detection/components/writer/#vm-writer
+
+# optional monitoring section if needed
+# https://docs.victoriametrics.com/anomaly-detection/components/monitoring/
+```
+
+Configuration above will produce N intervals of full length (`fit_window`=14d + `fit_every`=1h) until `to_iso` timestamp is reached to run N consecutive `fit` calls to train models; Then these models will be used to produce `M = [fit_every / sampling_frequency]` infer datapoints for `fit_every` range at the end of each such interval, imitating M consecutive calls of `infer_every` in `PeriodicScheduler` [config](/anomaly-detection/components/scheduler/#periodic-scheduler). These datapoints then will be written back to VictoriaMetrics TSDB, defined in `writer` [section](/anomaly-detection/components/writer/#vm-writer) for further visualization (i.e. in VMUI or Grafana)
+
 ## Resource consumption of vmanomaly
 `vmanomaly` itself is a lightweight service, resource usage is primarily dependent on [scheduling](/anomaly-detection/components/scheduler.html) (how often and on what data to fit/infer your models), [# and size of timeseries returned by your queries](/anomaly-detection/components/reader.html#vm-reader), and the complexity of the employed [models](anomaly-detection/components/models.html). Its resource usage is directly related to these factors, making it adaptable to various operational scales.
 
 ## Scaling vmanomaly
-`vmanomaly` can be scaled horizontally by launching multiple independent instances, each with its own [MetricsQL](https://docs.victoriametrics.com/metricsql/) queries and [configurations](/anomaly-detection/components/). This flexibility allows it to handle varying data volumes and throughput demands efficiently.
+> **Note:** As of latest release we don't support cluster or auto-scaled version yet (though, it's in our roadmap for - better backends, more parallelization, etc.), so proposed workarounds should be addressed manually.
+
+`vmanomaly` can be scaled horizontally by launching multiple independent instances, each with its own [MetricsQL](https://docs.victoriametrics.com/metricsql/) queries and [configurations](/anomaly-detection/components/):
+
+- By splitting **queries**, [defined in reader section](/anomaly-detection/components/reader/?highlight=queries#vm-reader) and spawn separate service around it. Also in case you have *only 1 query returning huge amount of timeseries*, you can further split it by applying MetricsQL filters, i.e. using "extra_filters" [param in reader](/anomaly-detection/components/reader/?highlight=extra_filters#vm-reader)
+
+- or **models** (in case you decide to run several models for each timeseries received i.e. for averaging anomaly scores in your alerting rules of `vmalert` or using a vote approach to reduce false positives) - see `queries` arg in [model config](/anomaly-detection/components/models/#queries)
+
+- or **schedulers** (in case you want the same models to be trained under several schedules) - see `schedulers` arg [model section](/anomaly-detection/components/models/#schedulers) and `scheduler` [component itself](/anomaly-detection/components/scheduler/)
+
+
+```yaml
+# config file #1, for 1st vmanomaly instance
+# ...
+reader:
+  # ...
+  queries:
+    extra_big_query: metricsql_expression_returning_too_many_timeseries
+    extra_filters:
+      # suppose you have a label `region` with values to deterministically define such subsets
+      - '{region="region_name_1"}'
+      # ...
+```
+
+```yaml
+# config file #2, for 2nd vmanomaly instance
+# ...
+reader:
+  # ...
+  queries:
+    extra_big_query: metricsql_expression_returning_too_many_timeseries
+    extra_filters:
+      # suppose you have a label `region` with values to deterministically define such subsets
+      - '{region="region_name_2"}'
+      # ...
+```

docs/anomaly-detection/README.md

@@ -49,7 +49,7 @@ Got questions about VictoriaMetrics Anomaly Detection? Chances are, we've got th
 Dive into [our FAQ section](/anomaly-detection/FAQ) to find responses to common questions.
 
 ## Get in Touch
-We're eager to connect with you and tailor our solutions to your specific needs. Here's how you can engage with us:
+We are eager to connect with you and adapt our solutions to your specific needs. Here's how you can engage with us:
 * [Book a Demo](https://calendly.com/victoriametrics-anomaly-detection) to discover what our product can do.
 * Interested in exploring our [Enterprise features](https://victoriametrics.com/products/enterprise), including [Anomaly Detection](https://victoriametrics.com/products/enterprise/anomaly-detection)? [Request your trial license](https://victoriametrics.com/products/enterprise/trial/) today and take the first step towards advanced system observability.