Develop Reference

Scipy - adjust National Team means based on sample size

I have a population of National Teams (32), and parameter (mean) that I want to measure for each team, aggregated per match.
For example: I get the mean scouts for all strikers for each team, per match, and then I get the the mean (or median) for all team matches.
Now, one group of teams have played 18 matches and another group has played only 8 matches for the World Cup Qualifying.
I have an hypothesis that, for two teams with equal mean value, the one with larger sample size (18) should be ranked higher.
less_than_8 = all_stats[all_stats['games']<=8]
I get values:
3 0.610759
7 0.579832
14 0.537579
20 0.346510
25 0.403606
27 0.536443
and with:
sns.displot(less_than_8, x="avg_attack",kind='kde',bw_adjust=2)
I plot:
with a mean of 0.5024547681196802
Now, for:
more_than_18 = all_stats[all_stats['games']>=18]
I get values:
0 0.148860
1 0.330585
4 0.097578
6 0.518595
8 0.220798
11 0.200142
12 0.297721
15 0.256037
17 0.195157
18 0.176994
19 0.267094
21 0.295228
22 0.248932
23 0.420940
24 0.148860
28 0.297721
30 0.350516
31 0.205128
and I plot the curve:
with a lower mean, of 0.25982701104003497.
It seems clear that sample size does affect the mean, diminishing it as size increases.
Is there a way I can adjust the means of larger sample size AS IF they were being calculated on a smaller sample size, or vice versa, using prior and posteriori assumptions?
NOTE. I have std for all teams.
There is a proposed solution for a similar matter, using Empirical Bayes estimation and a beta distribution, which can be seen here Understanding empirical Bayes estimation (using baseball statistics), but I'm not sure as to how it could prior means could be extrapolated from successful attempts.

Sample size does affect the mean, but it's not exactly like mean should increase or decrease when sample size is increased. Moreover; sample size will get closer and closer to the population mean μ and standard deviation σ.
I cannot give an exact proposal without more information like; how many datapoints per team, per match, what are the standard deviations in these values. But just looking at the details I have to presume the 6 teams qualified with only 8 matches somehow smashed whatever the stat you have measured. (Probably this is why they only played 8 matches?)
I can make a few simple proposals based on the fact that you would want to rank these teams;
Proposal 1:
Extend these stats and calculate a population mean, std for a season. (If you have prior seasons use them as well)
Use this mean value to rank teams (Without any sample adjustments) - This would likely result in the 6 teams landing on top
Proposal 2:
Calculate per game mean across all teams(call it mean_gt) [ for game 01. mean for game 02.. or mean for game in Week 01, Week 02 ] - I recommend based on week as 6 teams will only have 8 games and this would bias datapoints in the beginning or end.
plot mean_gt and compare each team's given Week's mean with mean_gt [ call this diff diff_gt]
diff_gt gives a better perspective of a team's performance on each week. So you can get a mean of this value to rank teams.
When filling datapoint for 6 teams with 8 matches I suggest using the population mean rather than extrapolating to keep things simple.
But it's possible to get creative; like using the difference of aggregate total for 32 teams also. Like [ 32*mean_gt_of_week_1 - total of [32-x] teams]/x
I do have another idea. But rather wait for a feedback as I am way off the simple solution for adjusting a sample mean. :)

Identifying outliers in an event sequence using a Python Dataframe

I'm experimenting with Machine Learning and LSTM models for river level prediction based on the current level and rainfall within the upstream catchment. I'm currently using TensorFlow and a Keras LSTM model.
I have a hourly rainfall data in mm from eight sites within the catchment, and the river stage (level) in meters at a site downstream from the catchment area. The problem I face is that every now and then the rainfall sites are tested by pouring water into them. This creates a significant spike in the data that I would like to filter out.
Here's an example of what a typical rainfall event looks like within the dataframe:
DataFrame showing typical seqeunce rainfall and river stage data
And here is an example of what it looks like when two sites have been tested
DataFrame showing abnormal rainfall data due to two sites being tested
I've come across several ways to statistically cluster data and identify outliers however none of these really worked on a timed sequence of events. Also, the rainfall site columns are listed in the DataFrame in the order in which they are located with the catchment so there is a loose spatial coupling moving across the columns.
I was thinking of using something a little like a 3x3 or 3x4 convolution matrix, but rather than calculating new cell values it would find outliers by comparing the values from the central cells with the values in the outer cells. Any significant difference would indicate abnormal data.
The Pandas DataFrame API is quite large and I'm still getting familiar with it. Any suggestions on specific functions or methods I should be looking at would be much appreciated.
In the following example the 10:00:00 reading for Site 2 would be an obvious anomaly.
Timestamp
Site 1
Site 2
Site 3
09:00:00
0
0
0
10:00:00
0
20
0
11:00:00
0
0
0
20mm of rainfall at one site with zero rainfall at the adjacent sites, or at the same site for the hour before and hour after is a very clear and obvious case.
This is what a normal rainfall pattern might look like:
Timestamp
Site 1
Site 2
Site 3
09:00:00
6
4
0
10:00:00
0
20
2
11:00:00
0
0
11
This is a less obvious example:
Timestamp
Site 1
Site 2
Site 3
09:00:00
1
0
0
10:00:00
0
20
2
11:00:00
0
3
1
One possibility might be to compare the central cell value to the maximum of the surrounding cell values and if the difference is greater than 15 (or some other arbitrary threshold value).
The exact criteria will probably change as I discover more about the data. The mechanism of how to apply that criteria to the dataframe is what I'm looking for. For example, if the criteria were implemented as a lambda function that could reference adjacent cells, is there a way to apply that lambda function across DataFrame?'
An extra complication is how to deal with checking values for Site 1 when there is preceding site to the left, and Site 3 where there is no following site to the right.

Remove zeros in pandas dataframe without effecting the imputation result

I have a timeseries dataset with 5M rows.
The column has 19.5% missing values, 80% zeroes (don't go by the percentage values - although it means only 0.5% of data is useful but then 0.5% of 5M is enough). Now, I need to impute this column.
Given the number of rows, it's taking around 2.5 hours for KNN to impute the whole thing.
To make it faster, I thought of deleting all the zero values rows and then carry out the imputation process. But I feel that using KNN naively after this would lead to overestimation (since all the zero values are gone and keeping the number of neighbours fixed, the mean is expected to increase).
So, is there a way:
To modify the data input to the KNN model
Carry out the imputation process after removing the rows with zeros so that the values obtained after imputation are the same or at least near
To understand the problem more clearly, consider the following dummy dataframe:
DATE VALUE
0 2018-01-01 0.0
1 2018-01-02 8.0
2 2018-01-03 0.0
3 2018-01-04 0.0
4 2018-01-05 0.0
5 2018-01-06 10.0
6 2018-01-07 NaN
7 2018-01-08 9.0
8 2018-01-09 0.0
9 2018-01-10 0.0
Now, if I use KNN (k=3), then with zeros, the value would be the weighted mean of 0, 10 and 9. But if I remove the zeros naively, the value will be imputed with the weighted mean of 8, 10 and 9.
A few rough ideas which I thought of but could not proceed through were as follows:
Modifying the weights (used in the weighted mean computation) of the KNN imputation process so that the removed 0s are taken into account during the imputation.
Adding a column which says how many neighbouring zeros a particular column has and then somehow use it to modify the imputation process.
Points 1. and 2. are just rough ideas which came across my mind while thinking about how to solve the problem and might help one while answering the answer.
PS -
Obviously, I am not feeding the time series data directly into KNN. What I am doing is extracting month, day, etc. from the date column, and then using this for imputation.
I do not need parallel processing as an answer to make the code run faster. The data is so large that high RAM usage hangs my laptop.

Let's think logically, leave the machine learning part aside for the moment.
Since we are dealing with time series, it would be good if you impute the data with the average of values for the same date in different years, say 2-3 years ( if we consider 2 years, then 1 year before and 1 year after the missing value year), would recommend not to go beyond 3 years. We have computed x now.
Further to make this computed value x close to the current data, use an average of x and y, y is linear interpolation value.
In the above example, y = (10 + 9)/2, i.e. average of one value before and one value after the data to be imputed.

How to get statistics of once column of dataframe using data from a second column?

I'm trying to write a program to give a deeper analysis of stock trading data but am coming up against a wall. I'm pulling all trades for a given timeframe and creating a new CSV file in order to use that file as the input for a predictive neural network.
The dataframe I currently have has three values: (1) the price of the stock; (2) the number of shares sold at that price; and (3) the unix timestamp of that particular trade. I'm having trouble getting any accurate statistical analysis of the data. For example, if I use .median(), the program only looks at the number of values listed rather than the fact that each value may have been traded hundreds of times based on the volume column.
As an example, this is the partial trading history for one of the stocks that I'm trying to analyze.
0 227.60 40 1570699811183
1 227.40 27 1570699821641
2 227.59 50 1570699919891
3 227.60 10 1570699919891
4 227.36 100 1570699967691
5 227.35 150 1570699967691 . . .
To better understand the issue, I've also grouped it by price and summed the other columns with groupby('p').sum(). I realize this means the timestamp is useless, but it makes visualization easier.
227.22 2 1570700275307
227.23 100 1570699972526
227.25 100 4712101657427
227.30 105 4712101371199
227.33 50 1570700574172
227.35 4008 40838209836171 . . .
Is there any way to use the number from the trade volume column to perform a statistical analysis of the price column? I've considered creating a new dataframe where each price is listed the number of times that it is traded, but am not sure how to do this.
Thanks in advance for any help!

Pandas series function that shows the probability of the up and down moves of the stock price

Days Adjusted stock price
price
0 100
1 50
2 200
3 210
4 220
5 34
6 35
7 36
8 89
Assuming this table is a pandas dataframe. Can someone help me out with writing function that show the probability of the up and down moves of the stock price. For example, what is the probability of the stock price having two up days in a row.
Thanks I am new to python and I have been trying to figure this out for a while!

Actual stock price movement prediction is both a broad and a deep subject usually associated with time series analysis which I would consider out of the scope of this question.
However, the naive approach would be to assume the Bernoulli model where each price move is considered independent both of any previous moves and of time.
In this case, the probability of the price moving up can be inferred by measuring all the up moves against all moves recorded.
# df is a single-column pandas DataFrame storing the price
((df['price'] - df['price'].shift(1)) > 0).sum()/(len(df) - 1)
which for the data you posted gives 0.75.
Given the above, the probability of the price going up for two consecutive days would be 0.75*0.75 approximately equating to 0.56.